Simplest - The minimum possible building blocks of a universe
Electrons
In Quantum Mechanics (QM), an electron is a fundamental particle. (the name 'particle' is a bit of a misnomer, particles in QM are wave functions).
An electron is not composed of other particles. Protons and Neutrons are composed of Quarks. Quarks are also fundamental particles.
Electrons have position, momentum, spin, charge and mass.
If an electron is 'composed' of position, momentum, spin, charge and mass; aren't these properties more fundamental than the electron?
Simplest
If we were to create a universe, what are the simplest possible building blocks that we could use?
Graph Theory: This is a fully connected directed graph with 225 nodes and two edges per node. If you look closely you can see a little arrow on the ends of the edges indicating that they are directed edges.
The fundamental element here is "node and edge". A node has no innate properties. A node is just the point at which edges meet. A node without edges is just a mathematical point (see below).
An edge is just a connection. In this unlabelled graph the edge doesn't have a length (or - arguably - all unlabelled edges have unit length).
Change
A universe that doesn't change is hardly worthy of the name.
For a graph, the only mechanism of change is to shuffle edges. That is, we have some function that examines the current state of the graph and changes which nodes edges connect to.
This is the same fully connected 225 node directed graph as above after many iterations of the simplest possible change to such a graph.
What about a mathematical point
The node/edge in a directed graph is certainly reasonably simple, but is it the simplest?
A mathematical point and a Set Theory set are both candidates for extremely simple building blocks.
We can dispense with a mathematical point fairly quickly.
A mathematical point is a definition of nothing. We can't use 'nothing' as a building block.
Place an infinite number of mathematical points immediately adjacent to each other and you have... a mathematical point.
A mathematical point has no length, breadth of height. If we are generous we could grant a point a position within, say, a Euclidean plane. This is fine and reasonable except that to do anything with our point we have had to invent the entirety of Euclidean geometry. This negates the original simplicity of a single point.
Set Theory
Set Theory is another attempt at specifying an extremely simple element that can be built into arbitrarily large and complex structures.
Any sort of in depth analysis of Set Theory and its contention as a candidate for simplest possible building block is way too much for a single post.
We shall skip over Set Theory noting only that mathematicians have made multiple attempts to find a simplest possible building blocks.
Reading a Graph
It is possible to label nodes and edges in a Graph but labels are an extra (unneeded) complication.
Without labels, the only distinguishing feature of a node or edge is its position within the Graph.
In preparing these graphs I used a program that jiggled the position of nodes in the graph such that edges appear to have the same length. Nodes that are closely connected to each other tend to be positioned physically closer on the page. However, this positioning is not inherent to the graph itself.
Nodes do not have x,y coordinates. The graph is just the nodes and edges.
If you examine the 2nd graph above you can see that there are long chains of nodes with one little loop indicating one of the edges loops back to the same node. If we count the minimum number of edges to get from one node to another node; the first graph is much more closely connected than the second graph.
Expansion
If we take a large sample of graphs with the same characteristics (fully connected, directed, two edges per node) and iteratively apply Change A and count the average number of edges between every node in the system at each step...
We find that such a graph exhibits a fast initial inflation followed by a slower but accelerating expansion up to a final maximum entropy where the graph cycles through a series of equal entropy states without expanding (or contracting) further.
This behaviour seems common with graphs up to a few million nodes but does depend somewhat on the initial generation of the graph. Randomly generating edges between nodes tends to generate a relatively tightly packed graph (the mean edges between nodes is low).
This vague correspondence between early inflation and currently observed accelerating expansion of the universe is of note.
Complexity/Chaos
As a newly minted god creating our own little universes, we want to create interesting universes.
Conway's Game of Life illustrates that simple rules can lead to complex behaviours. Stephen Wolfram has built a career and reputation on the emergence of complex behaviours in simple systems.
Yet another simple system that exhibits complex behaviours is barely worth remarking.
However, a directed graph with two edges per node and Change A is a candidate for the simplest conceivable system that exhibits complex behaviour.
CPT Symmetry
Charge, Space, Time Symmetry is an observed physical Symmetry with interesting characteristics.
Charge Symmetry, Space Symmetry and Time Symmetry are each partial symmetries under which some particle interactions are perfectly symmetrical - but not all.
If you have positrons (the anti-particle of the electron) instead of electrons, almost all interactions are the same as for an electron - but some aren't.
If you reverse time, some interactions are invariant. But not all.
If you switch the handedness of space (switch left and right), some interactions remain the same. but not all.
If you switch Charge, Space and Time all at the same time - all interactions are symmetric with their unflipped comparisons.
There is exactly one way to achieve something that looks like CPT Symmetry.
The observation of CPT Symmetry, by itself, specifies the physics of the universe.
Our universe has to be the simplest possible universe that can exhibit complex behaviour.
Simplest
One way to understand the physics of the universe is to start with observation and develop theories to explain those observations.
An alternative that has the potential to bear fruit is to try and create a universe from first principles.
What is the simplest possible building block? What is the simplest possible component of change we could apply to that building block?
I'm not particularly trying to persuade you that this particular expression is our universe (that will come in time - "because CPT" is far more obvious as a compelling argument after you've invested significant effort trying to create a physics that exhibits CPT Symmetry)(Emergency Breath. Insert as required in previous sentence).
It is, as much, an exploration of the idea of 'simplest' and how it has been and can be applied in mathematics and physics.
In particular, even apparently foundational qualities like time and space can be emergent qualities and shouldn't necessarily be assumed to be fundamental in and of themselves.
In Quantum Mechanics (QM), an electron is a fundamental particle. (the name 'particle' is a bit of a misnomer, particles in QM are wave functions).
An electron is not composed of other particles. Protons and Neutrons are composed of Quarks. Quarks are also fundamental particles.
Electrons have position, momentum, spin, charge and mass.
If an electron is 'composed' of position, momentum, spin, charge and mass; aren't these properties more fundamental than the electron?
Simplest
If we were to create a universe, what are the simplest possible building blocks that we could use?
Graph Theory: This is a fully connected directed graph with 225 nodes and two edges per node. If you look closely you can see a little arrow on the ends of the edges indicating that they are directed edges.
The fundamental element here is "node and edge". A node has no innate properties. A node is just the point at which edges meet. A node without edges is just a mathematical point (see below).
An edge is just a connection. In this unlabelled graph the edge doesn't have a length (or - arguably - all unlabelled edges have unit length).
Change
A universe that doesn't change is hardly worthy of the name.
For a graph, the only mechanism of change is to shuffle edges. That is, we have some function that examines the current state of the graph and changes which nodes edges connect to.
This is the same fully connected 225 node directed graph as above after many iterations of the simplest possible change to such a graph.
What about a mathematical point
The node/edge in a directed graph is certainly reasonably simple, but is it the simplest?
A mathematical point and a Set Theory set are both candidates for extremely simple building blocks.
We can dispense with a mathematical point fairly quickly.
A mathematical point is a definition of nothing. We can't use 'nothing' as a building block.
Place an infinite number of mathematical points immediately adjacent to each other and you have... a mathematical point.
A mathematical point has no length, breadth of height. If we are generous we could grant a point a position within, say, a Euclidean plane. This is fine and reasonable except that to do anything with our point we have had to invent the entirety of Euclidean geometry. This negates the original simplicity of a single point.
Set Theory
Set Theory is another attempt at specifying an extremely simple element that can be built into arbitrarily large and complex structures.
Any sort of in depth analysis of Set Theory and its contention as a candidate for simplest possible building block is way too much for a single post.
We shall skip over Set Theory noting only that mathematicians have made multiple attempts to find a simplest possible building blocks.
Reading a Graph
It is possible to label nodes and edges in a Graph but labels are an extra (unneeded) complication.
Without labels, the only distinguishing feature of a node or edge is its position within the Graph.
In preparing these graphs I used a program that jiggled the position of nodes in the graph such that edges appear to have the same length. Nodes that are closely connected to each other tend to be positioned physically closer on the page. However, this positioning is not inherent to the graph itself.
Nodes do not have x,y coordinates. The graph is just the nodes and edges.
If you examine the 2nd graph above you can see that there are long chains of nodes with one little loop indicating one of the edges loops back to the same node. If we count the minimum number of edges to get from one node to another node; the first graph is much more closely connected than the second graph.
Expansion
If we take a large sample of graphs with the same characteristics (fully connected, directed, two edges per node) and iteratively apply Change A and count the average number of edges between every node in the system at each step...
We find that such a graph exhibits a fast initial inflation followed by a slower but accelerating expansion up to a final maximum entropy where the graph cycles through a series of equal entropy states without expanding (or contracting) further.
This behaviour seems common with graphs up to a few million nodes but does depend somewhat on the initial generation of the graph. Randomly generating edges between nodes tends to generate a relatively tightly packed graph (the mean edges between nodes is low).
This vague correspondence between early inflation and currently observed accelerating expansion of the universe is of note.
Complexity/Chaos
As a newly minted god creating our own little universes, we want to create interesting universes.
Conway's Game of Life illustrates that simple rules can lead to complex behaviours. Stephen Wolfram has built a career and reputation on the emergence of complex behaviours in simple systems.
Yet another simple system that exhibits complex behaviours is barely worth remarking.
However, a directed graph with two edges per node and Change A is a candidate for the simplest conceivable system that exhibits complex behaviour.
CPT Symmetry
Charge, Space, Time Symmetry is an observed physical Symmetry with interesting characteristics.
Charge Symmetry, Space Symmetry and Time Symmetry are each partial symmetries under which some particle interactions are perfectly symmetrical - but not all.
If you have positrons (the anti-particle of the electron) instead of electrons, almost all interactions are the same as for an electron - but some aren't.
If you reverse time, some interactions are invariant. But not all.
If you switch the handedness of space (switch left and right), some interactions remain the same. but not all.
If you switch Charge, Space and Time all at the same time - all interactions are symmetric with their unflipped comparisons.
There is exactly one way to achieve something that looks like CPT Symmetry.
The observation of CPT Symmetry, by itself, specifies the physics of the universe.
Our universe has to be the simplest possible universe that can exhibit complex behaviour.
Simplest
One way to understand the physics of the universe is to start with observation and develop theories to explain those observations.
An alternative that has the potential to bear fruit is to try and create a universe from first principles.
What is the simplest possible building block? What is the simplest possible component of change we could apply to that building block?
I'm not particularly trying to persuade you that this particular expression is our universe (that will come in time - "because CPT" is far more obvious as a compelling argument after you've invested significant effort trying to create a physics that exhibits CPT Symmetry)(Emergency Breath. Insert as required in previous sentence).
It is, as much, an exploration of the idea of 'simplest' and how it has been and can be applied in mathematics and physics.
In particular, even apparently foundational qualities like time and space can be emergent qualities and shouldn't necessarily be assumed to be fundamental in and of themselves.
Comments (71)
Ideas.
An electron is directly a quantum of the quantum electron field, which field appears to be fundamental.
The simplest fundamental would have no parts, which is fine, for elementary 'particles' would be rather stable arrangements of it, such as in QFT (Quantum Field Theory).
Guess #1: A vacuum fluctuation.
Guess #2: To make measurements with interacting via (massless) quanta.
The second sentence is granted, but the first sentence is not immediately intelligible. Suggest review Robinson's "h" and reconsider.
It is possible to consider the entire history of philosophy as an examination of ideas.
I struggle to imagine any scenario in which that history can be boiled down to "the simplest conceivable building block".
I can see ideas being a building block - just not a simplest building block.
Furthermore, there appears to be a wide variety of different ideas. Are you stating all ideas are trivial? or do you have a specific idea in mind as being a foundational starting point?
What do you think makes ideas simple? The lack of a physical component?
Quoting PoeticUniverse
There is some ambiguity in your statement. Are you saying an electron is fundamental, or the quantum electron field?
In either case... Okay. And?
I don't know how to engage with your comment. I don't know if you are just expanding on the idea of fundamental properties in Quantum Mechanics or you are correcting a misapprehension you think I have.
Perhaps you are just adding your own snippet to the conversation.
My expectation from philosophy forums is a discussion of ideas. A dialogue.
Your expectation doesn't have to match mine. It just means I'm likely to bug you to expand on your point until I can see something I can engage with.
Quoting PoeticUniverse
'Nothing' is certainly simple... but it isn't really a building block.
A field is hardly simple. You have an n-dimensional continuous field which can be infinitely sub-divided.
It took Russell hundreds of pages of dense mathematics just to get to 1+1=2. I'd have to look to see if there is any construction for real numbers.
It is true that Euclidean Geometry (and many non-Euclidean counterparts) take a field of some kind as a given.
In this sense, fields are certainly foundational/fundamental to large parts of mathematics and physics.
However, it isn't clear to me that Fundamental == Simple.
I'm not saying you are wrong - I'm saying you will have to do much more than mentioning the idea of fields to persuade me that fields constitute simple, let alone simplest.
Quoting 180 Proof
This is a good answer. I see where you are coming from. A vacuum fluctuation is among the smallest discrete measurements we can make in physics.
Furthermore, going to direct observations in physics potentially bypasses hidden assumptions in the way we think about things that may lead us to regarding complex concepts as simple.
On the downside, it isn't clear how to use a single interaction as a building block.
To get as far as a single observable interaction, Quantum Mechanics tells us we need a space/field within which that interaction can occur and the interacting components need a mechanism of interaction.
I'm not disagreeing with you. I'm wide open to the idea that an interaction is, itself, a fundamental building block. And that an interaction is potentially very simple.
Under what circumstances could an interaction (Quantum Fluctuation) be simple and constructible?
Quoting alan1000
Sorry, sticking "Robinson's "h"" into google isn't showing results I immediately recognise as relevant.
Can you give more context or a direct link, please?
Yes. Why assert there is any mind independent physical stuff? You can't prove it, it's unnecessary to explain reality, and you run into the mind-body problem, which seems insolvable at this point.
Guess #3: "The Big Bang" (i.e. planck-radius universe).
So you think every entity, including mind, is mind-dependent? (Btw, Spinoza dissolved the MBP with property dualism in the 17th century (Hume did so again with bundle theory a century or so later) and yet Kantian denial (Cartesian dogma) persists in philosophy despite cogent physicalist paradigms and developments in cognitive neurosciences).
An electron is temporary, as is all else but the permanent quantum fields. An electron can be annihilated by a positron, but electrons can persist awhile in the right emvironment.
Having no parts is not 'Nothing'. The Fundamental can't have parts because those parts world be more fundamental; thus, the fundamental consists of only itself; it does not get made and it cannot break, so there is no sub-dividing it. For example, a wave would be continuous and have no parts. Waves are also ubiquitous in physical nature. The Fundamental has to be the simplest, by the necessity shown above. We can also see this trend as we look more and more 'downward'
It's a pseudo-problem ...
https://thephilosophyforum.com/discussion/comment/611954
Yes, and a 'particle' could pop out, along with virtuals coming and going that didn't make it to a stable quantum energy rung.
A wild guess for why fluctuations happens is that is if 'they try' to be zero/nothing they cannot do it. The so-called zero-point energy is not zero, although it is not a useable energy.
Just for funsies. Are you thinking of a human building a physical universe from raw materials, or a god creating a dynamic world from scratch? For the human, no single element would ever be sufficient to produce something that is more complex than the original element. A pile of sand is just grains of rock particles, with nothing to hold them together, into a structural system. But concrete is loose sand bound together by a mineral matrix, the binder.
Regarding simplicity, hypothetical Quarks were once postulated as the fundamental particle. But years later, Quarks*1 are now differentiated by a multitude of imaginary "flavors" & "colors". Which would require some even more fundamental element to distinguish them. Technically though, the quark itself, like all other basic particles, is supposed to be an "excitation" (mathematical wave peak) in an energy field. Can you build anything from massless math or a matterless field?
suggested using an "idea". Which in this case could be construed as a Platonic Ideal or an Aristotelian Potential*2. Neither of which has any matter or mass until Actualized into something Real. So, if I was going to "create" a universe, I'd begin with the origin of all creations : the Idea or Design or Concept of the thing. After that, you could search for appropriate materials. :joke:
*1. Quarks: What are they?
Quarks are elementary particles. Like the electron, they are not made up of any other particles. You could say that they are on the ground floor of the Standard Model of particle physics.
https://www.space.com/quarks-explained
The colours red, green, and blue are ascribed to quarks, and their opposites, antired, antigreen, and antiblue, are ascribed to antiquarks. According to QCD, all combinations of quarks must contain mixtures of these imaginary colours that cancel out one another, with the resulting particle having no net colour.
https://www.britannica.com/science/quark
*2. What is pure potentiality Aristotle?
So everything we encounter is composite. In Aristotle's hierarchy of being, pure potentiality (prime matter) is at the bottom, pure actuality (Aristotle's God) is at the top. Formed matter (everything else, including our world) is in between.
https://lafavephilosophy.x10host.com/Aristotle_de_anima.html
Note --- Aristotle's "Prime Matter" is more like our modern notion of an invisible Energy Field than tangible Matter.
Quoting 180 Proof
The only problem with that is you have the wrong theorists in mind. 4ea ( embodied, enactive, extended , embedded and affective cognition) is a melding of phenomenology, hermeneutics and cognitive science. Id hardly call Metzinger and Dennett embodied cognitivists. Try Shaun Gallagher , Francisco Varela , Evan Thompson, Matthew Ratcliffe, Thomas Fuchs, Dan Zahavi , Hanne De Jaegher and Jan Slaby instead.
The only logical smallest object I could imagine could have have attraction or repulsion. Its just an existent mess. No rhyme, no reason, just a mess of whatever it is. Reality is full of them, and they constantly bounce around. But every so often, they bounce in such a way that the 'hook' into each other. Because it has to be a very specific angle, its also incredibly difficult to bounce out. If you get a few things going this way, you generate more appreciable mass.
What was interesting about this was that this would mimic heat. You see, everything vibrates. The higher the vibration, the higher the heat. Higher vibrations would accelerate the loosening of those very small particles, which would fly off. Higher vibrations also mean more chances per second for these small things to hook into other small things next to them, allowing chemical bonds, etc.
Just a fun thought experiment of course.
Okay. Are all ideas equally simple? Is the idea of an elephant the same as the idea of a line from the perspective of complexity?
The graph presented in the OP consists of nodes and edges. These are mathematical ideas. Do you agree that a network of nodes and edges is a simple idea?
Quoting 180 Proof
Your are proposing a self propagating construction in the Big Bang? Some process that caused reality to come into existence from a formless void?
I had in mind something like an existing pile of bricks that is constructed into a shape. You appear to be taking one step further back and proposing the construction of the bricks themselves from nothingness.
That is, I have taken the universe as a given and considered the simplest possible mechanism for the continuation of an already existing system.
You have prompted me to reconsider whether the question of genesis is amenable to some equivalent approach.
Infinite regression
A naive approach to first cause leads to infinite regression with each cause needing some prior cause.
Taking the universe as a given sidesteps the problem of genesis but doesn't really solve it. An eternal (has always existed, will always exist) universe has its own conceptual problems, not least of which is the emergence of entropy.
Anthropic Principles
I am tempted by the Strong Anthropic Principle in which the universe exists in order for us to observe it.
What is the point of a universe that isn't aware of its own existence?
However, I can't immediately see a way to make a testable hypothesis out of this.
Testable
With Simplest possible universes I can build teeny tiny complex systems (universes) and compare their characteristics with our observed universe.
The proposition that our universe can be described by iteration of a direct graph is testable.
The limitation is that I have to exist in order to make those teeny tiny universes and compare them to our observed universe.
I have to take my existence (and the existence of the universe) as a given.
I'm pretty sure this is a hard limitation. But your comments have prompted me to have another consider - and there is a little tickle in my mind that is suggesting such consideration is worth some effort.
Quoting Igitur
I'm glad I could tickle your brain bone a little. I'm not disagreeing with you - more refining a point I think is relevant:
As noted in the OP, I think that this is the mechanism of our observed universe.
Relevance
We have a direct graph with nodes and edges and Change A.
The closest thing to a dimension in this directed graph is an edge.
Space, time, mass, charge and consciousness are all emergent features of changing nodes and edges (according to me).
Edge as the fundamental unit of the universe
Instead of particles being the fundamental unit, we have the space between as the fundamental unit.
If an interaction is "one rearrangement of edges between nodes" we suddenly find that we don't have to think about what happens between interactions.
There is no space in which particles move. Like frames of a film, a series of interactions can give the impression of continuous movement in space.
Note: In real, genuine, actual physics we observe interactions. We never observe anything between interactions. The notion of particles travelling through space between interactions is entirely theoretical.
Our conception of space is based on trying to understand the sequence of interactions that we observe.
There are explanations of sequences of interactions that exhibit complex behaviour without the need for dimensions, mass, charge, spin or momentum as a priori assumptions.
We don't need to assume space time in order to observe the sequence of interactions that we see.
Quoting PoeticUniverse
It looks like we are in agreement here. Yes - a distinctive property of the very simplest thing is that it is indivisible. If it were divisible into component parts it would clearly not be 'simplest'.
I'm a little nervous about conflating 'fundamental' with 'simplest' insofar as an electron is described as a fundamental particle in Quantum Mechanics but is not simplest in regards to being composed of multiple, distinct properties.
It looks like your point regarding the persistence of fields vs electrons is making the same point?
Further discussion of simplest/fundamental
An ocean wave is emergent behaviour of large numbers of 'particles'.
If we cut a human up into smaller and smaller pieces looking for the fundamental unit of humanness we find ourselves with a mess of giblets and rather less essential humanity. Likewise for the fundamental waveness of a wave.
As such I can sort of, vaguely, see an argument that a wave is indivisible.
But, as a matter of practicality, we can divide a wave into component parts. A wave is divisible and hence not fundamental/simplest.
A mathematical point is, I would argue, indivisible. It is not composed of subunits. However, I think that a mathematical point is a complicated way of saying 'nothing'. Having a pile of mathematical points is functionally equivalent to having a pile of nothing.
A set is a container. The only inherent property of a set is that it contains. In principle, a set is independent of physics and not subject to reduction to physical fundamentals. A set is a candidate for simplest/indivisible.
An edge within a directed graph is a link. As with sets, the edges within a graph are supposed to be independent of specific physics.
Agree/Disagree
Quoting PoeticUniverse
I agree wholeheartedly.
Quoting PoeticUniverse
The Real Number line is a typical representation of the mathematical concept of field. This field can be divided into the individual real numbers. This does not seem to fit our definition of simplest.
Quoting Gnomon
As noted earlier, somewhere, I find myself constrained such that I require my own existence as a pre-requisite for... pretty much everything. At the moment I have no conception of how I would create myself and a universe out of sheer void. I have to take the existence of a universe as a given and work from there.
Quoting Gnomon
Well... funnily enough. Given the binder, it is sufficient by itself.
The little revolution I'm trying to foster is regarding the necessity of the bits between structure.
A network of relationships doesn't require us to define what the relationships are binding. The structure of the relationships is enough by itself.
Pursuit of knowledge: scenario 1
We wish to understand, say, consciousness. We want to drill down to the very core of what consciousness is to arrive at the heart of the conception.
As with when I was chopping up people earlier in this thread, we find that chopping up concepts into their component pieces tends to leave us with a messy pile and no sign of the original concept.
The definition of madness is doing the same thing over and over again and expecting different results.
Going all Sweeney Todd on concepts to find their essence is just murder. Philosophy finds itself chasing its own tail because a reductive approach to knowledge just lead to corpses.
Scenario 2
Concepts are defined by what they are not.
The significance of the Integer 1 is its distinction from the Integer 2 (and 3, 4, apple, infinity,...)
To fully understand consciousness, we need to fully understand everything that is not consciousness.
Everything is a single connected whole and each piece is an aspect of the whole.
Yes - hippy dippy "everything is one" except seriously.
Your experiences are part of your existence. If you try to consider your existence in isolation from your experiences you are liable to find you don't exist anymore.
In order to argue, you first need to exist. Every argument you engage in requires your existence. If you try to divorce the process of argument from your existence your argument ceases to exist.
That is circular
"If each idea is defined by every other idea, then reasoning is circular; there is no starting point."
Yes.
We are living inside a closed system. When you point to something it is one piece of universe pointing at another piece of universe.
When you describe something you are using one piece of universe to relay information about another piece of universe. Your concepts of the universe all derive from the universe.
Physics is literally describing the behaviour of the universe in terms of the behaviour of the universe.
Not Nihilism
Understanding the relationships between things is knowledge.
The relationship between the integers 1 and 2 is our understanding of those integers.
Context matters
Everyone knows that context matters.
Dial that up to 11 and keep going.
Context is everything. Without context there is nothing.
This isn't new territory.
Quoting Count Timothy von Icarus
Reasonable answer - but I'm going to disagree.
In order to build a computer, the bits have to have specific relationships. There has to be structure between individual bits.
So while bits are notionally simple, by the time you can build anything with them you have stealth included some assumed structure. The bits+structure is less than trivial (simplest).
There is still the potential for a very simple system - but without an explicit statement of the structure, I'm inclined to think you are hiding more complexity than you realise within your implicit assumptions.
If I may impart my own spin to your thoughts...
I think your scepticism is/was well placed.
Physics faces the same problem as philosophers:
What caused the first cause.
Physics as a statement of observations is fine: "If we do x we observe y".
Physics as an explanation is less founded than Lord of The Rings by J.R.R. Tolkien. At least Tolkien understood what an allegory was.
Saying the Higgs boson did it isn't an explanation when you don't understand why the Higgs boson does it. As explanations go it is no different to saying God did it. It doesn't explain. It is a null statement.
It isn't clear to me that individual physicists understand that physics cannot explain observation - only describe it. I fear the myth of physics as explanation is near universal.
"This is what we observe" is in no way equivalent to "this is why we observe...."
Can properties (e.g. position, momentum, spin, charge, mass...) exist independently of objects that have them (i.e. is a property a particular, or is a property necessarily an attribute of a particular?)
Regarding a simple universe: a single particular. Depending on one's preferred ontology, could be:
- a property (existing independently)
- an object with zero properties
- an object with exactly one property (if particulars necessarily have at least one property).
I Googled the phrase "network of relationships" and found it most often applied to social relations between humans. But, on a universal or sub-atomic scale, the term might also refer to Positive & Negative interactions, or Attractive & Repellent behaviors, or Back & Forth exchanges of Energy. In every instance I could think of, relationships are not physical things, but as-if mental images, where the invisible bonds are imagined, not seen. Causal Energy/Force is invisible & intangible, so only its after-effects are detectable by human senses.
Since relationships are attributed to systems, not observed, they seem to be meta-physical (mental) instead of physical (material). Attributes are imaginary qualities, not physical objects. Attributes are attempts to explain Causal relationships between things. So, the answer to "what the relationships are binding" could be just about anything. And "the bits between structure" are Ideal, not Real. For example, a structural engineer analyzes the "structure" of a building by omitting all the steel & concrete, in order to "see" the invisible lines of force that bind the building together, or tear it apart. The binding "bits" are causes, such as Energy & Force, that offset (neutralize) each other to make the system stable. The forces are "given" but the binding beams & columns must be artificially assembled to produce a "sufficient" structure.
The building blocks of the natural universe are Matter & Energy. But we understand that structure by imagining and attributing a mathematical/logical Matrix of interrelationships that is invisible to the naked eye. For humans, Mind & Matter are an interrelated indivisible system such that we humans can't have one without the other. :smile:
STRUCTURAL DIAGRAM :
Blue arrows represent invisible lines of natural force, such as gravity. The red arrows represent artificial beams & columns to resist the forces that would otherwise destroy the building. And the black lines represent the man-made parts that are constructed to resist those forces. Together, the forces & frames bind into an interrelated system that we call a Structure.
https://cdn-ikpnogb.nitrocdn.com/cdPGWyOaMJgCoqiEOEpUSTgMoqloHDjJ/assets/images/optimized/rev-061a090/1qwi8ndt698on.cdn.shift8web.com/wp-content/uploads/2020/10/Building-Information-Modeling-BIM-structural-analysis.png
Quoting Treatid
The why is bound up with the qualitative structure of the theory which explains and organizes the observation. As one theoretical explanation is overthrown for another, the why changes along with it.
I'm sympathetic to your objection. Information is inherently relational, and so of course, for bits to be the building block of even the simplest "toy universe," they must exist in some sort of relationship to one another. A 1 can only be distinguished from a 0 against some background that lies outside that individual bit itself. I think that, properly understood, information theoretic understandings of physics and metaphysics are anti-reductive, since context defines what a thing is, rather than vice versa.
So I guess it comes down to what you mean by "building block." If you take a substance metaphysics-based approach where the properties of building blocks must inhere in their constituent makeup, then the bit isn't going to work. But in a process/relational view, where a thing "is what it does," the bit seems to work fine as a "building block" in that there does seem to be some fundemental level of ontological difference (reducible to 1 or 0 if it is quantifiable at all) underlying any and all more complex structures. Perhaps "building block" is the wrong way to look at it here though. In a certain sense, I think the "entire context" matters for fully defining constituent "parts" role in any universe, and this might preclude things' being "building blocks" at all in the normal sense.
If I were writing a computer program to create my universe; each property would be assigned to an independent variable.
This suggests to me that a particle with multiple properties is not indivisibly simple.
As to individual properties - I think we can create a further hierarchy of simplicity among properties corresponding to information content.
A property that can only have two states seems simpler to me than one which has an infinite number of continuous states (binary is simpler than the set of real numbers).
As to your table of possibilities you are implying that a property is distinguishable from an object.
I'm inclined to re-write your table as:
- a property (existing independently)
- a property with zero properties
- a property with exactly one property (if particulars necessarily have at least one property).
which in turn seems to simplify to:
- a property (existing independently)
Which then just leaves the question of whether a property, by itself, is sufficient to construct complexity.
My solution to this is an edge within a directed graph.
Quoting Gnomon
This is interesting. In contrast, I think the only things we ever experience are relationships (or possibly interactions which are the same thing with a different label).
From a physics perspective, the only things we ever measure are interactions. We don't see particles moving through space. We don't see particles at all.
An electron is a hypothetical particle intended to explain the specific sequence of interactions that we observe. No-one has ever seen an electron. No-one has ever seen a particle move.
What we measure are sequences of individual interactions.
Mass, momentum, charge, spin, colour are all hypothetical constructs used to describe the sequences of interactions we observe.
The idea that particles travel through space is just an idea.
A theory that had no space-time, no particles; but explained the sequence of interactions as well as Quantum Mechanics does would be exactly as real as QM.
From a mathematics perspective, there are infinitely many formulations that are equivalent to Quantum Mechanics.
A physics theory needs to explain our observations. We don't observe anything between interactions.
I'd like to get into what we can and can't describe. In the meantime I'm hoping the above diatribe gives you some insight into why I don't immediately accept your distinction between ideal, real, structure and substance.
Quoting Joshs
Except that can't be correct.
"Because I said so." "Because God decreed it." "Because it does."
Physics runs into the same infinite recursion as asking what caused the universe. At each stage there is still the question "what caused that cause?".
If we propose that God caused the universe, we haven't moved the territory. What caused God/universe? Is God/universe eternal?
"The Higgs boson does it." What causes the Higgs boson to do it? "The quantum Field." What causes the Quantum Field?
Physics (and any other discipline) is incapable of addressing the fundamental why. Any suggestion to the contrary is smoke and mirrors.
Your perception that a physics theory addresses the why is a mistake. A very common, widely believed mistake, but a mistake nevertheless.
Quantum Mechanics (QM) works because it works. There is no reason behind QM. Given enough observations you will arrive at a statistically accurate summation of those observations.
The entire field of Quantum Mechanics is nothing more than a Large Language Model fed with a data set of observations.
Don't get me (entirely) wrong. It has taken heroic efforts to make better and better observations. We have some phenomenally precise and accurate statements of observation (albeit massively overcomplicated by needless assumptions).
Quoting Count Timothy von Icarus
Music to my ears.
We seem to be on the same page here.
Quoting Count Timothy von Icarus
I could kiss you on the lips (or some other hyperbolic expression of affection for your ideas).
Your comment indicates to me that you have a significant understanding of what it means for the universe to be a single, connected (indivisible) entity with each part being an aspect of the whole.
I find myself mildly discombobulated. Like the dog who caught the car - I'm not sure what to do with such significant agreement. (not entirely true - but I do want to put some thought into it and I'd like to get this post out).
I'll be back.
The model of mechanical causation may not be the best way to understand the historical development of scientific theories. Efficient cause is itself a theoretical perspective, one which only emerged at a particular point in the history of science and has undergone numerous modifications. It was developed for , and is most useful for dealing with the behavior of non-living phenomena, but runs into trouble when we try to explain living systems this way. Over the course of your life you have likely formed and changed overarching perspectives or worldviews a number of times. Do you want to understand each new perspective as caused by the previous in the way the behavior of billiards balls are caused by each other, or is there a more useful way of understanding the development of ideas in persons and cultures? Complex dynamical systems theory is one alternative to linear causation that can be applied to why questions without the risk of infinite regress. Since they function via the principles of non-linearity, they dont run into the problems of linear causation models. Put simply, in a dynamical system, the effect is not the mere product of a pre-assigned cause, but modifies the cause. Cause and effect are reciprocally affected by each other.
As chatgpt says
They're properties of the electron. Position, momentum, etc. are how we talk about the electron. A property isn't a constituent part or component of an electron or anything else.
What is more fundamental than electrons are quantum fields. I am very far from being knowledgeable in physics, but I do watch YouTube videos. That counts for some kind of knowledge these days.
A particle: be it an electron, a quark, a gluon, whatever; is nothing more than an excitation in a quantum field. Imagine space filled with the fluctuations of the quantum field. If there's a region where the fluctuations are highly concentrated, that's where we see a particle. And out of all that, all the rest of the stuff that the particles make.
So we're all just fluctuating vibrations in the quantum field.
This is my understanding of fundamental physics these days. Particles are excitations in the quantum field.
From Wiki:
[quote=Wiki]
QFT treats particles as excited states (also called quantum levels) of their underlying quantum fields, which are more fundamental than the particles.[/quote]
https://en.wikipedia.org/wiki/Quantum_field_theory
Quoting Treatid
Well an electron is an emergent composite and not fundamentally simple in some reductionist/atomistic sense. It exists as the result of a chain of symmetry-breaking events that leave it as a particle that has indeed hit its lowest possible mass state, so exists"fundamentally" as it can't decay further, while also representing the specific world-building property of "a negative charge". It has a property that is cosmically meaningful because it can stand in relation with its partner-in-crime, the proton.
So to think about it in a holistic, structural, emergent, evolutionary, thermodynamic and systems sense, the Big Bang is a cosmic dissipative structure that organises itself to dispose of its entropy by expanding and cooling. It undergoes a whole series of phase changes like steam to water to ice as it globally restructures in ways that minimise its entropy. Like a cooling iron bar, it can suddenly lock in a global field that creates an emergent state which then has its own second-order excitations or "particles" doing their own second-order entropic thing.
An electron is what you get left with at this stage of the Universe when it has cooled and expanded to almost zero in energy density and almost unbound in effective distance scale. A baked-in defect like you find topologically trapped in a crystal.
To exist as the distinct and fundamental thing it is, an electron had to be produced by the Higgs symmetry breaking. Before the temperature of the Universe fell to the 160 GeV range, electrons were chirally broken, left and right, Weyl particles. Gaining mass from the Higgs field glued the two halves together to make a whole electron turn it into a Dirac particle, along with creating electromagnetism with its photons as part of the whole reorganisation of the cosmic topological order.
This only got us as far as a hot soup of electrons and positrons though. A stew of matter and antimatter creation and annihilation which lacked any great particularity of the kind we would associate with "a particle". Location and momentum were just an averaged blur within the general thermal confusion of a charged plasma, not really anything individual.
But more symmetry breaking saw a slight excess of electrons (as the negatively charged matter particle) being left over and positrons (as the positively charged antimatter) being eliminated from the cosmic topological order (being wasted to hot photons that made up the fast-fading CMB radiation background).
So we have this fundamental kind of thing that we call "electron-ness" which only emerges as everything else gets more crisply and counterfactually suppressed. The Weyl left-right difference has to be welded together to create a Dirac particle which is now divided at the higher topological level of being a matter or antimatter particle. Then the electron must outlive the positron to create a general negative charge difference the one that the proton on its own symmetry breaking story is heading towards to become the positively charged fundamental particle that is its counterpart in turning the Universe into a realm dominated by electromagnetic radiation as its most visible thermalising characteristic.
Even when we get to electrons as the negative charge stamped out as material form, we still have to have it decay through its three mass generations taus, muons, then electrons to arrive at the thermal bottom rung simplicity of a particle that can decay no further ... at least not until black holes eventually sweep up all mass particles and themselves evaporate to leave an empty Heat Death void.
So the holistic or structural take on this is that we have the general thing of a heat sink cosmos winding its way down its entropic gradient. That is the fundamental relation, the fundamental thermal context. Then as it cools, it also goes through major phase changes that each throw up the local topological features the excitations that obey the symmetries which characterise that stage of organisation.
The reason the rather mixed and complex brew of radiation, electrons and protons seems such a "fundamental" state of order is that these indeed proved to be a suitable ground for the nuclear chemistry of atoms, the atomic chemistry of materials science, the material chemistry of biological life, etc.
By comparison to the lifetimes of stars, planets, mountain ranges and haircuts, photons, electrons and protons do fit the ontological bill of "atomistic materials existing in an acausal, large and frigid, cosmic void".
But photons, electrons and protons are all topologically composite particles that happened to land in a place where they formed an electromagnetic level of entropic organisation. They are only fundamental to the degree they are Platonically inevitable mathematical structure a place a cooling cosmos had to arrive at because thermodynamics can't avoid being self-organised by the maths of its own symmetry breaking.
A ton of other "particle stories" also condensed out of the Big Bang, but add so little further to the complexity and wonder of nature that even if they contribute much more actual entropification to the total dissipation budget, we don't think of them as being "fundamental" it the same way. They don't carve a history of individuated and counterfactual events. Stuff like the CMB, dark matter, dark energy, blackhole evaporation, are just background stuff to us, given our very human concerns when it comes to metaphysical story telling.
So in summary, our very notion of "fundamental" is rather screwed by our natural psychological prejudices. But physics does tell us about dissipative structure, topological order, gauge symmetry and all the stuff we need to be able to see through to what is really going on. The Universe is a heat sink rattling through a series of phase changes on the way to its eventual heat death. The present moment is an especially complexified mid-stage with its stars, planets and life.
But even that accounts for a few percent a round-up error in the matter budget of the Cosmos. And if we include all that exists, then black holes are already the dominant "particles of being" and themselves on the way to be shown the door as they are swept up and exported over the cosmic event horizon, leaving a pure void near absolute zero apart from the faintest rustle of dark energy blackbody radiation the least interesting fluctuations possible in the most empty spacetime possible.
Given your interest in nodes and edges, or information-centric, accounts of all this, this is a way of telling the thermodynamic story using a topological mathematics. There is a reason to think this way for the practical purpose of modelling.
But then you have to dig into the logical atomism being built into the models to be able to step back to the larger metaphysics you might want to frame. Atomism succeeds by simplifying by severing the immediate from its evolutionary history and self-organising tendencies.
Reality is a fabric of relations. But the simplicity of nodes and edges is the constructive simplicity that emerges from self-constraint. It is what you get like photons, electrons and protons clattering about in an electromagnetic void when a heck of a lot of other possibility has been cut away to leave only that as the material stuff you want explained.
The deeper question becomes how does causality and logical counterfactuality even arise as something so apparently simple and inevitable? That is the where systems thinking and other forms of holistic metaphysics comes in.
My personal worldview is ultimately Holistic and Monistic. But when we begin to "describe" the world, in language or math, it is necessary to make "distinctions". Reductive Science is all about naming & knowing particular things. But Holistic Philosophy is about wisdom & understanding of All things. Structure is interrelationships between things that bind them into a knowable Whole. Substance is the indivisible essence of a thing, which makes it a knowable concept. Real is what we interact with physically, Ideal is what we imagine metaphysically. :smile:
Tao Te Ching :
[i]The Tao that can be told is not the eternal Tao;
The name that can be named is not the eternal name.
The nameless is the beginning of heaven and earth.
The named is the mother of ten thousand things.
. . . . Naming is the origin of all particular things.[/i]
https://en.wikiquote.org/wiki/Laozi
"A network of relationships doesn't require us to define what the relationships are binding. The structure of the relationships is enough by itself."
___ Treatid
The world, without definitions, is a white-out fog. We understand the world scientifically by drawing distinctions between things. Philosophy attempts the put things back together --- to reassemble the analyzed relationships --- in order to grok the Whole system.
:roll: :snicker:
fyi Natural sciences are both "reductive" and "holistic" by fallibilistic abduction, each defeasibly explains various levels (e.g. hierarchies) of 'self-organizing wholes' mereologically. On the other hand, sir, "metaphysics" is a synoptic (not "holistic") interpretation categorical idealization of, among other things, the presuppositions necessary for natural sciences and their findings to rationally make sense.
I think you are each asserting that it is possible to do something that is impossible.
I'm not saying you, specifically, are making a mistake. I'm saying that (almost) everyone is incorporating a mistaken assumption into their sense of what knowledge is.
Possible/impossible
You can do possible things. You cannot do impossible things.
You cannot point to something that is outside the universe.
You are part of the universe. Your thoughts are part of the universe. Language is part of the universe.
You cannot reference not-universe in any way. It is flat out, unequivocally, impossible.
"Outside the universe"
The concept of "outside the universe" is null. It doesn't mean anything.
Your concept of "outside the universe" is part of the universe. It is inside the universe.
Your concept of "outside" has been formed from experiences that are wholly contained within the universe.
There is a baked in component of "outside" that can be almost universally omitted:
"Outside of x (inside the Universe)"
"outside the universe" should be read as "outside the universe (inside the universe)".
Post illustration
I would bet dollars to donuts that even now you feel that you are conceptualising something in response to the phrase "outside the universe".
Before the universe
What came before the universe? Philosophers have already explored the fact that our sense of time is a product of the universe we inhabit. "Before Time" is a non-sequitur.
Feel
Take note of how compelling the notion of "outside the universe" feels. You know what 'outside' means. You know (roughly) what 'universe' means. Of course you understand what "outside the universe" signifies...
Physics doesn't explain squat
We can compare the differences and similarities between one piece of universe and another piece of universe.
That is what is possible. This is what knowledge is. This is everything.
Explanations in physics are equivalent to "before time", "outside space"; they contain no information.
Why is this bit of universe similar to that bit of space? Because it is.
The universe is the way it is because we observe it to be that way.
We can measure the similarities and differences. We can make note of common patterns. Any attempt to justify stuff always boils down to "because".
Comparing the universe to itself
The only thing we have available is the universe. Our thoughts and actions are intrinsic parts of the universe. The universe is our starting point - our given.
Every statement fundamentally assumes the existence of the universe.
Anything and everything we say about the universe is the universe referencing itself.
This isn't a problem or a limitation. This is simply what is.
We can, in fact, describe what is. We can observe the universe and describe what we see. This is possible.
Doing possible things is easy.
We cannot explain the universe independently of the universe. Doing so would be impossible.
Doing impossible things is futile. A waste of time and effort.
Other end of the scale
I've read a few of your recent posts. You are clearly understanding concepts with the depth and clarity that I initially perceived.
I have deep respect for the arguments you have made and the insight that they represent.
The following smack down is only possible because you are most of the way there already.
As with the Count above, My deepest respects. Think of the following as an argument made with vigour. I am arguing against a position.
Smack Down
Quoting Gnomon
Well Whoop dee doo! Look at Mr. Holistic. He thinks the universe is a thing.
Of course it is a whole f&^%*$g thing. It isn't an option. It's the law.
Of course you can't step outside your existence. Of course you can't step outside the universe.
What is even the alternative? That bits of the universe are disconnected but connected at the same time?
But
Quoting Gnomon
No. Stop it. No Buts.
You have the truth right there in your hands and you are turning away from it.
The universe exists and everything (EVERYTHING) is part of that existence.
Everything you think, feel, imagine, do and communicate is indivisibly an aspect of the single whole.
"Ah, but - what if it wasn't?" It is. You and every mathematician, philosopher and physicist who ever lived cannot describe anything that is not inextricably a facet of the universe.
Your words are part of the universe. Your thoughts are part of the universe. Your existence is part of the universe.
Everything that we are capable of understanding, is expressed with reference to the universe.
Context
You know that context matters. Your personal, direct experience shows you that context matters. Of all the certain truths in the universe, you can see context mattering.
And then you turn around and suggest that if we remove enough context from essential mathematical concepts we'll arrive at truth!?
In a universe where the only comparison we have for one piece of universe is another piece of universe you want to remove our only reference point in the hopes of understanding concepts in isolation!?
Connected
The universe is a connected whole. This is the foundation of knowledge/understanding/meaning/significance/...
In order to understand the universe, a good place to start is with the universe. The pieces of the universe are not disconnected (distinct).
Trying to understand the universe by assuming not-universe is silly.
99.9%
Quoting Count Timothy von Icarus
Here Count Icarus looks the universe square in the face and then just stops.
Solispism, Godel's incompleteness theorems, General Relativity, every philosophical and mathematical argument that has tried to find an essence independent of bias...
We've already considered this from every angle and we are still banging our heads against the wall.
"Context matters" is right there. It isn't hidden. There's no secret.
The only possible mechanism of knowledge is with respect to the universe.
It boggles my mind how a person can be looking right at the evidence in front of their nose and then turn around and say "But when we begin to "describe" the world, in language or math, it is necessary to make "distinctions"" as if somehow, magically, the rules don't apply to language or mathematics.
We don't have the universe plus a backup universe.
Language and mathematics don't have a secret backdoor access to an objective viewpoint independent of the universe.
Possible/impossible
This is not a debate between competing theories.
It is impossible to reference something outside the universe.
An argument that references "outside the universe" isn't even wrong. The idea of an objective viewpoint free from observer bias is meaningless.
We can compare, contrast and interact with different aspects of the universe. And that is it. That is everything we can do.
There isn't anything else we can examine. There isn't anything else we can interact with.
All your thoughts, ideas, actions, experiences and dreams are aspects of a singular universe within which you exist.
Not Nihilism
Knowledge independent of your subjective experience has always been a null concept.
Objective truth has always been meaningless.
It is possible to describe one aspect of your experiences with respect to other aspects of your experience.
Possible is so, so much easier than impossible.
Everything humans have achieved is what is possible. Aligning our expectations with reality will be orders of magnitude more productive than the alternative.
Quoting Treatid
The universe is not a box with furniture in it (whether understood as individual bits or relationally and linguistically) which it is our job as scientists to describe. It is a continually changing development, and we change along with it. Thanks to the unidirectional arrow of time, the universe is continually outside itself, continually overcoming its former states. Freedom is built into the real, and the past doesnt determine the future, it only provides constraints and affordances.
Quoting Treatid
Reality is a moving target. Knowledge is praxis, a way of changing how we interact with our world in ways that are useful to us. The changes we make in our interactions with the world feed back into our understanding to further change our knowledge. There is no limit to the variety of ways we can scientifically construe our world. A multitude of competing accounts can all be true, that is, can work perfectly well for what we wish to do with them. Some ways will be found to be more useful others.
My position is formally an internalist epistemology. I'm a Peircean pragmatist. So problem dealt with. :smile:
Quoting Treatid
You seem to be arguing rather passionately employing what you consider to be "good logic". You talk as if this is giving you a secret backdoor access to truths others don't grasp. So a little contradictory right there.
Pragmatism deals with the essential subjectivity of reasoning. Structuralism is then the ontology which emerges from applying that reasoning to the world at large. As Peirce argued, the "best logic" is the one with which we would both think and the one that itself organises the world.
And it is that pragmatic logic the holistic logic of Peircean semiosis that would help you deal with the emergent and evolutionary nature of Being. In terms of mounting a physicalist inquiry into the nature of Nature, the structure of an expanding~cooling cosmos, it leads you to thermodynamics and dissipative structure theory.
Particle physics, for example, is all about how the Big Bang fell into inevitable gauge symmetry structures as it expanded and cooled.
Electrons don't exist. They are the irreducible residue of a process of "universal" constraint on possibility itself. In the beginning was everything. Then what survived were all the possibilities that didn't get cancelled away by their opposite possibilities. In quantum jargon, the wavefunction of the Universe is the sum over all its possibilities. It was so hot, everything was possible at the start. It will be so cold that almost nothing will become possible by the end.
Peircean holism as a fully internalist perspective gives you a very different way of thinking about the questions of existence.
Whether the universe is deterministic and the possibility of free will in a deterministic universe are interesting and relevant questions.
Unfortunately, your assertion doesn't appear to be falsifiable.
Quoting Joshs
This seems reasonable to me.
Quoting Joshs
No.
All definitions within a system are circular.
A description consists of one piece of universe describing another piece of universe.
A --> B --> A
We can describe what we observe (with respect to everything else we observe).
Anything else is a figment of your imagination.
Quoting Joshs
If you want to conceptualise each new moment as being a brand new universe that's fine.
This argument doesn't depend on a specific definition of 'inside', 'outside' or 'universe'. It depends on us being part of the process - lacking the omniscient god like view as an entity that can observe the universe without interacting with the universe.
Quoting apokrisis
Is that 'Pragmatist' in the same way that The Democratic Republic of North Korea is Democratic?
All definitions inside a system are circular
A defines B. B defines A.
Your quantum jargon == The universe is like the universe.
In what way is observing that the universe has similarities to itself pragmatic?
I mean - you're not wrong. But neither are you advancing knowledge.
Apology
I'm sorry (rubs nipples).
I know the intent behind theories. I know I'm denigrating the scientific method. I know I'm committing heresy of the highest order.
But all definitions within a system are circular.
There has never been a single, objective, universal, unambiguous definition of anything. Ever.
For all your ability to reference distance, you cannot define distance free of circularity.
A pragmatist would deal with reality.
Post Script
I am most gratified that I am, at least, able to communicate my enthusiasm.
Piercian Pragmatism seems nice. Personally I'm a fan of describing the universe as it is.
And a really, truly do not mean to offend anyone. I simply wish to convey that:
All definitions within a system are circular.
Incorrect. They are dichotomies. They are reciprocally connected by the constraint of being mutually exclusive yet jointly exhaustive.
So take a basic definition to any vague notion of "a system". It is hierarchically divided between its local and global scales of being. It is bounded in measurable fashion in that the local is defined as that which is the least global, and the global is that which is the least local. Or local = 1/global and global = 1/local.
What you call going around in a meaningless circle a rotational symmetry adding no information is always in serious metaphysics an effort to split possibility towards its mutually complementary aspects. And this is the basis of science as it is the basis of measurability. We place reality between limiting bounds that are then each the proper measure of the other ... even when the reciprocality is between the infinite and the infinitesimal.
So circularity can be a problem for some folk. But dichotomies have been going strong since ancient Greece and now stand as the metaphysical foundation for our scientific descriptions of nature.
OK if the mode of time is not Presentism but Eternalism; however, we don't yet know the mode of time. If Presentism, the 'particles' roll along their fields, like a kink in a rope moves.
What I read is "yes, and..."
All definitions are circular, AND your description of dichotomies.
I agree that dichotomies have been around forever. How could it be otherwise - they are the nature of the universe.
Quoting apokrisis
Yeah... I'm not sure that everyone received that memo. Specifically, Axiomatic Mathematics and Quantum Mechanics are predicated on the idea that it is possible to have non-circular definitions.
I'm delighted that there is any acknowledgement of the nature of knowledge with respect to dichotomies. I agree that it should be foundational to scientific descriptions. I'm just noting that as it stands, your assertion of standing is more aspirational than actual.
It is in this light that I question your consistency.
Empirical evidence
You are absolutely right that knowledge of the significance of context is ancient.
And yet throughout that history science has tried to deny that evidence in favour of impossible definitions and explanations.
From solipsism it is crystal clear that it is impossible to prove anything beyond personal existence; yet mathematics pretends that proofs are possible.
Understanding with respect to dichotomies is not the same as 'objective definitions'.
They are not compatible world views.
The relationship is much the same as that between Newtonian Mechanics and General Relativity. There is no iterative path from Newtonian Mechanics to General Relativity. General Relativity does not make sense given the assumptions of Newtonian Mechanics.
Incompatible World Views
You can't have logic and dichotomies at the same time.
A relational universe is incompatible with an objective universe.
It isn't possible to comprehend one in terms of the other.
Recognising the dichotomous nature of the universe is fine (its right there). Trying to bend that evidence to fit objectivist assumptions is madness.
Prejudices should yield to the evidence, not the other way around.
Logic
A specific example of why objectivist is incompatible with relativist:
One of the assumptions of logic is that the original premise is a constant.
This seems to be a reasonable constraint. Imagine how much more complicated arguments would be if the meaning of the premise changed during the course of the argument.
Except, of course, it isn't possible to specify an initial set of premises in a fixed and unambiguous fashion. Before we can wonder if the premise is static we have to deal with never knowing exactly what the premises are in the first place.
It gets worse. In a relativistic system, the act of observing is a process. Both the observed and the observer are changed during this process (The process of observation is a change of relationships). There is no omniscient observation that leaves the target unchanged.
As a kicker we can round off with General Relativity, wherein the notion of objective truth can get bent.
The alternative: If not Logic - then what?
A consistent, relativistic (context matters, dichotomous) universe doesn't contain objective contradictions. A consistent system cannot illustrate what a contradiction is.
The universe is exactly what it appears to be. You don't need a theory to describe what you see. You just look and write down your observations.
Every statement you make is a shape within the universe. You literally cannot shape the universe into an impossible shape.
Humans are lying, hypocritical, scum bags that will behave inconsistently and contradict themselves for fun. And the Liar's paradox is just a squiggle in the universe.
Your ability to look at some squiggles and perceive a paradox is a 'you' thing.
Everything that is possible within the universe (including languages) is possible. Language works with the same mechanism as the rest of the universe. Just like the universe, everything that is possible is possible.
You do, of course, make subjective evaluations of statements.
Dichotomies
I appreciate your description of dichotomies. As far as it goes, I'm in full agreement.
However, your comment regarding the foundation of science makes me think your pragmatism is superficial. That you are holding onto old assumptions despite the evidence.
Possible is easy
I might be maligning you and you are already ten steps ahead of me... but a consistently dichotomous view works really well. Describing the universe on its own terms is productive. Like "Oh my god - it is so simple!"
Existing mistaken assumptions have been blinding us to the truth: The universe is exactly what it appears to be.
The trick is to see what is there - not what we think is there.
TimeQuoting PoeticUniverse
You are right - whether intermittent or continuous, Time is that which we perceive as time.
My argument is that it is far more productive to describe what we see.
We do not see particles. We do not see movement through space. We do not see Hilbert spaces or integers.
We have entire industries devoted to describing our world in terms of perpetually invisible and undetectable qualities.
Such practices should be the domain of religions - not science.
Good science is empirical. Things we can see and measure.
Quantum Mechanics runs around all the houses describing particles and fields and produces nothing better than we would get through statistical analysis of our observations.
Indeed, a straightforward statistical analysis would avoid all that mucking around trying to define undefineable quantities.
God is defined as all powerful and all knowing but super, duper invisible - you can only know him through faith. "yeah, yeah - whatever you say. Sure."
Physicists do exactly the same and its "Wow - All hail the Quantum! Praise be to the waveform collapse! How sexy is that many worlds interpretation".
The universe is exactly as it appears
What you see is what you get "WYSIWYG".
The universe is what we directly experience.
Inventing new pantheons (of gods or particles) does nothing to elucidate.
Indeed, persisting in false assumptions despite the evidence clouds our vision and hampers our perception of the reality that is right there.
Trying to understand the universe in terms of invisible fields that can't be measured is the antithesis of science.
What? There is no path from mechanics with Galilean invariance to mechanics with Poincare and eventually de Sitter invariance? Tell me it ain't so. :cry:
Quoting Treatid
More piffle. As came up in another discussion, Aristotle codified both. The Organon was followed by his hylomorphism.
Of course folk can take them as incompatible or contradictory. But done properly, atomism can be shown as a subset of holism. They indeed form a dichotomy. A complementary pair. Both the same and yet also different as they are each the other's inverse operation.
Quoting Treatid
All this is true but built into the structure of Peircean logic. He accepted chance as real just as real as law or globalised constraints that then emerge as the "other" to the logical vagueness of an indeterminate (or yet to be contextually determined) potential.
This is all perfectly familiar ground. We can move on.
Quoting Treatid
Or another way of looking at it is the triadic systems approach to causal structure. GR defines the coherence of the metric, QFT defines its incoherent content. Decoherence within a de Sitter spacetime metric is how you arrive at the critical balance that is the Cosmos in terms of its VeV vacuum particle action at some given temperature and pressure.
So GR and QFT make the bounding dichotomy on what Peirce called synechism (global continuity) and and tychism (local chance). A flexi container and its flexing contents. Then these two opposites get mixed over all scales in a fractal or powerlaw statistical fashion. The thermal decoherence constraint that "collapses" the quantum wavefunction of the Universe itself.
This then turns your epistemic dichotomy of objective~subjective into the more useful one of an internalist vs an externalist metaphysics. Peircean logic and Systems Science speak to an internalist view of nature in which "objectivity" is what a community of inquirers hopes to arrive at in the limit.
The goal can't actually be achieved that is assumed. But it can be approached asymptotically. And that is demonstrable as agreement becomes increasingly universalised among those doing the inquiring.
So GR seems pretty robust on that score. QFT too. It is agreed by all who rely on GPS systems or semiconductors at least. And too bad if you hold some different metaphysics that would want to quarrel with that level of detailed reality modelling.
Quoting Treatid
Only consistency could be held up as the proper measure of what we might mean by inconsistency. Relativity is already built in by standing in opposition. The question then is only to what degree they are able to stand far apart.
How much inconsistency does it take to undermine a claim of consistency, and vice versa?
Quoting Treatid
I think your theory of possibility needs more work. It presumes modal realism and so would need to be supported against other possibilities, like Peircean propensity for instance.
There is a whole history of metaphysical case-making that you just glibly dismiss in your scattergun mini-rants.
Quoting Treatid
Of course you must find ways not to engage with actual arguments. Discussing is losing. Thinking is hard. Researching takes up too much time.
For all A
{
A is NOT (Everything else)
}
Example:
This is just a re-statement dichotomies.
The following are equivalent statements:
A as an object independent of relationships is an irrelevant entity. Object A has no impact on our understanding of the relationships of A.
Even if it was possible to describe object A - Our definitions are dichotomous. The relationships of A are the entirety of A. Object A is superfluous, redundant, unneeded.
Relationships (whatever they are) are all that exists.
Flip side
Every description is a description of relationships. It is impossible to describe anything else.
Objects aren't a limit to approach; they are nothing, less than an illusion. Trying to reach understanding by stripping away extraneous relationships is exactly the wrong direction. Those stripped relationships are knowledge.
Relationships are existence.
Circular definitions
Circular definitions are an artefact of trying to define Object A.
Describing the Relationships of A is an actual description. A network of relationships has a shape. We can describe that shape. Networks of relationships are possible.
Object A (without relationships) is an impossible concept. As with non-circular definitions - they simply don't exist.
Simple
We observe context, therefore context.
The world is exactly what it looks like. And it looks like relationships. It does not look like objects.
But small is not not-large. So small is the least possible large. Thus largeness and smallness are defined in terms of the excluded middle. But the LEM as applied to defining the contrasting limits of a potential rather than a pair of actualisable states.
Quoting Treatid
The way out of circularity is hierarchy. A feedback growth spiral. This is what is missing from your notion of logic. It is what Peirce's logic of semiosis (or logic of vagueness) was intended to remedy after he had already sorted out regular logic before Frege got in on the act and won the credit.
So you can go round the circle the symmetry-breaking that is the dichotomy - and come out at a higher level. Ascend a hierarchy. You don't need to be bamboozled by circularity because going around in a circle as a point is what in fact creates a circle as now a new level of symmetry to be broken.
Quoting Treatid
Well yes. But there is then the hierarchical story where the dyadicy of relations (Peircean secondness) becomes such a thickness of interacting that it takes on the solidity of a statistical equilibrium. It becomes the regularity or continuity of a Peircean thirdness.
And that then becomes a state of form or matter which can now in turn have its symmetry broken.
A quantum vacuum fluctuates freely and so expresses its zero point average. This then allows the production of actual particles when higher level constraints are placed on the vacuum. Those particles in turn can thermalise and form their own collective average. Fundamental particles can become a condensate that then develop their own new topological order the phonons of the condensed matter view.
You need a Peircean strength logic to talk about "relations" in terms of what the world is actually like from a cosmological and particle physics point of view.
The world looks exactly like how you expect it to look that is normal psychology. But even at the level of the logic, we have an upgrade available that makes much sense of what ought to be seen.
What I am reading is: "All definitions are circular, but..." or "Knowledge is dichotomous, except..."
We have a solid observational foundation that you appear to feel the need to refute or minimise.
Quoting apokrisis
I hope I'm misunderstanding your intention, but "ought to be seen"!?
This reads as an outright rejection of reality in favour of mysticism. "only through special, super dooper peircean logic and a wholesale rejection of the evidence of our senses can we approach truth".
Quoting apokrisis
The world is exactly what it looks like. Your reading comprehension is lacking if you think these two statements are equivalent.
Absolute knowledge
I think you (and Peircean Logic) are clinging to the idea of absolute, objective knowledge.
While you concede that it can't be achieved in and of itself - you still think it is something that can be approached in the limit.
This is a mistaken belief.
In an objectivist paradise where non-circular definitions exist and every point is fixed and immutable; then objective knowledge is a rational and attainable goal.
Here, in reality, things are their relationships with everything else. Meaning, knowledge and significance change every time relationships change.
Knowledge is relationships. Stripping away relationships to reach the essence of a thing is discarding the very knowledge that you are seeking.
The objectivist perception of knowledge doesn't apply in a relational universe.
Logic
Dichotomies and Logic are incompatible.
For those raised with the presumption of logic there might be some inertia in correcting this presumption.
Peircean logic recognises that logic is constrained - but persists with the fallacy of fitting the round peg into the square hole.
Knowledge (along with the rest of the universe) is fundamentally relational.
Relativistic
There is no amount of hoop jumping that can turn a relationship into a fixed point.
Subjective experience cannot be converted into objective knowledge. The context of subjective experience is the knowledge you are seeking. To strip the context is to remove the very thing you are looking for.
Solipsism told us we couldn't prove anything objectively. General Relativity told us the universe is relativistic. Context tells us the world is relativistic.
It isn't like the evidence is hidden. The subjective nature of experience is front and centre of your existence.
The ideas of absolute knowledge, absolute definitions and a fixed point are actively harmful in our pursuit of knowledge.
Relationships aren't some second order consequence of an objective universe. Relationships are the universe.
Logic doesn't work. Logic never worked. Absolute truth isn't a limit you can approach.
Your conception of knowledge, understanding and meaning is the relationships you have built internally and externally.
Summary
You appear to be claiming that it is possible to approach (but not reach) absolute objective knowledge within a system that is relational.
This seems to me to be a claim without any justification AND a flat out contradiction of the observed evidence.
Information within a relational system exists entirely within relationships (observed, c.f. Dichotomies).
In light of this, there is no way that Peirce, Frege or yourself have sorted out logic.
You/they are making claims that are flatly refuted by the evidence.
In a system where all definitions are relative to everything else, it is impossible to have definitions that are not relative to everything else.
If somebody tries to sell me a perpetual motion machine - I know it is a scam without ever seeing the machine itself.
If someone is arguing for even the tiniest scrap of objective knowledge within a relational universe, we can be certain that they are mistaken.
Can you waste mine instead? I'm up for it.
The universe is a single connected entity within which differences can be discerned.
All definitions/descriptions are of the form: X is not (Everything else).
Changing X changes (Everything else). And vice versa: changing (Everything else) changes X.
There have been extensive efforts made to establish some fixed point. These efforts have not borne fruit.
Where X is defined by its relationships to (Everything else); removing those relationships to find intrinsic properties, essence and identity is counter productive.
Listening
feels that I am not properly listening to him. For my part, I am addressing the core of my disagreement with his position: any claim (direct or indirect) to objective (fixed) knowledge is counter factual.
As such - I rather think I am engaging directly with what apokrisis is saying.
Pompous ass
Yeah - I'm a smug git who thinks they knows what they are talking about.
I'm practically begging to be knocked on my ass. I mean, I've declared Formal Logic and Axiomatic Mathematics to be so wrong that they barely qualify as illusions...
Nothing new under the sun
The limitations of objective knowledge aren't a closely guarded secret.
All definitions are circular. The universe is a connected whole.
These are simple observations.
There are whole branches of philosophy dedicated to holism, and Axiomatic Mathematics really can't specify what axioms are without getting stuck in a closed loop of circular definitions.
And yet, it seems, everyone still wants to find objective (fixed) truth!?
Despite clearly(?) understanding the nature of dichotomies, Peircean Logic is still trying to approach objective truth. (picking on an illustration from this thread - the sentiment applies more widely).
So annoying
The observations of context mattering and the universe being a connected whole are just that: observations.
There is no (rational) gainsaying.
I become annoying when I insist that these observations apply. It is not possible to have or approach objective truth. Trying to apply the principles of objective truth cannot work in a holistic universe.
It is annoying because it is just a reiteration of the observations: Given the observation of a relativistic universe; the universe is relativistic.
Unless you can point to a single instance of a fixed point, independent of relationships, there is no counter-argument.
Note: Peircean Logic accepts that the limit can't be reached but proposes it can be approached. A point is fixed, or it isn't. In terms of definitions - a definition is circular - or it isn't. There is no path for a circular definition to cease being circular.
So...
I can sit here and proclaim that words do not have intrinsic meaning; There are no absolute, unambiguous definitions; Mathematical proofs don't exist; The particles and fields of Quantum Mechanics are phantasms...
And in the absence of any fixed point - all I'm doing is re-stating our observation that context matters. As such - there is no rebuttal. Words don't have intrinsic meaning, there are no non-circular definitions and mathematical proofs are sheerest fantasy.
The thing is...
The notion of objective (fixed) truth should be dead and buried millennia ago. Peircean Logic should not be trying to approach objective truth even as an unreachable limit. Quantum Mechanics shouldn't be trying to define particles when every definition is circular.
Axiomatic Mathematics should have folded the moment it failed to definitively and unambiguously specify a set of axioms. Axiomatic Mathematics had one job - specify some axioms...
At this point there is nothing rational behind the assumption of an objective (fixed) truth.
Back to roots
Simplest
We can only describe (networks of) relationships.
The simplest relationships is a directed edge.
A directed edge isn't defined in any absolute sense.
We can combine arbitrarily many directed edges into arbitrarily large and complex structures.
The universe is an iterated network of relationships.
We can't describe something that is not an iterated network of relationships.
There are no options here. No-one has ever described a single intrinsic property. The essence of an object is permanently outside our experience.
Quarks, leptons and fields are circular definitions. Our concept of a field is a direct consequence of the things we are trying to describe using fields. A describes B, B describes A.
Any feeling of comprehension regarding Quantum Mechanics is an illusion.
We can, however, describe networks of relationships. If we describe something it is (necessarily) a network of relationships.
X=not(Everything else)
This is the linchpin observation. If you can find an exception - my position collapses.
Quoting Treatid
i.e. a truth claim such as ...
[quote=Treatid]The universe is an iterated network of relationships ... This is the linchpin observation.[/quote]
therefore "should be dead and buried" as well, which is self-refuting and so there's no need for
[quote=Treatid]If you can find an exception - my position collapse(s).[/quote]
:confused:
You are most welcome.
Quoting 180 Proof
You exist. This is self-evident to you.
However, you cannot prove your existence to me beyond all possible doubt (as a definite and fixed truth). The reverse also holds, of course. I am aware of my existence but cannot objectively prove my existence to you.
This is the whole Descartes thing: our senses are potentially fallible and thus nothing about the objective world can be proven.
So - "your existence is self evident" is subjectively true. Your existence is evident to you. But your existence isn't an objective truth.
This applies to every concept you can imagine. It is impossible to objectively prove anything. Your concepts and meanings are entirely subjective.
Wider issue
When faced with solipsism, people have tended to disregard it as being little better than nihilism.
It isn't obvious how human society and communication can function based solely on subjective knowledge.
However, no one has ever demonstrated objective knowledge. There isn't a single objective definition.
Your understanding is irrevocably subjective. You can't understand for someone else.
The world still works.
objective interpretation
You interpreted my declaration of the nature of the universe as an objective statement.
In a world that doesn't contain a single objective fact - how can you perceive any statement to be objective?
This isn't a rhetorical question. Why is an objective interpretation of language the default?
Truth
"The only certainty is your own existence. All else is un-provable."
A naive reading of this might be that nothing is knowable beyond the self.
For seekers of understanding this is unpalatable and appears to deny our own experience of knowledge.
There is, however, a more nuanced interpretation.
Your existence consists of everything you ever experience. Your existence encompasses everything you will ever think, dream, experience and every action you perform.
You know that Sensory Data exists because you experience it.
You know that differences exist because you experience them. There is no doubt. Differences are part of your existence, and exactly as certain as your existence (to you).
The universe is a network of relationships because that is your (subjective) experience of the universe (when you stop trying to deny that experience in favour of a fictional objective reality).
Subjective experience isn't the second class citizen of knowledge. Subjective experience is the only game in town.
TL;DR
Your perception of any statement as being an objective statement is faulty.
"Cogito Ergo Sum et al" isn't a suggestion; it is the law.
I can assert your existence because your experience demonstrates your experience to you. But your existence is not an objective fact.
Communication relies upon common subjective experiences. Experiences are always subjective. There are no objective experiences; That would be a non sequitur.
Quoting NotAristotle
I think this is wrong.
Euclidean Geometry assumes/proposes infinitely divisible space - but we know it is not an accurate theory of physics.
Quantum Mechanics assumes continuous space and time - but that is an assumption going into the theory - not a demonstrated conclusion.
Fundamental particles are, currently, believed to be indivisible and I'd wager that most physicists believe that there is a bottom to physics even if we may not have reached it yet.
The idea of quantised space-time isn't strictly part of Quantum Mechanics - but the relationships between planck length, planck time and the speed-of-light-in-vacuum appears to be a significant hint towards quantisation.
So from a status quo perspective - I can see no compelling evidence to think that there are any infinitely divisible qualities to the universe. It is a possibility - but I see nothing that persuades me we should take that possibility as a given.
Change or not-change
I think that the universe must be quantised.
Mathematics has run into issues with infinitesimals within real numbers.
Along the lines of 0.999 recurring equalling 1; there is an issue deciding when a real number stops being itself and becomes the next real number.
In a continuous, infinitely divisible space; there are always infinite points between two points. Two particles travelling through such a space each traverse an infinite number of points each time period.
The trouble is, an infinite number of infinitesimal distances is... complicated...
With regard to change, the question is at what point is change measurable?
If a change is sufficiently infinitesimal, we cannot measure it. If we cannot measure a change - has a change actually occurred?
As such - the question becomes: "What is the smallest measurable change?"
Given there is a smallest measurable change - then for practical purposes, that is the quantum of change.
Mathematicians have played with this - and the answer is basically: infinitesimals don't really make sense. It is somewhat like the singularity in a black hole - all the rules break down. Mathematicians have created (several) new rulesets to apply in these circumstances but generally the idea of infinitesimals is close neighbours with dividing by zero - best avoided if possible.
Quoting NotAristotle
I do think there is a "thing" that is "the universe".
Holism
Holism isn't just an interesting approach to knowledge. It is the only possible approach.
You exist
As above, your existence is the only thing you know for certain. And everything you think, feel and do is part of that existence.
Your existence is a single, connected whole. You, I think, recognise this.
Everything you experience is an aspect of your existence.
Your experience of stars and planets and the connecting space around them are aspects of your existence.
This, right here, is the nature of the universe.
Your ability to think and experience is an aspect of the universe.
You cannot separate yourself from the universe. You cannot separate yourself from your experiences.
You can communicate because you are an aspect of a universe that facilitates communication.
The distinctions you perceive are measured in terms of your other experiences.
Show that two points are not connected
It is impossible to show that two points are not connected.
Everything you are capable of experiencing is connected to everything else. Whether conceptual or physical your ability to reference two things demonstrates their connectedness.
Every part of the universe is connected to every other part of the universe.
You cannot shave off chunks of the universe.
Each part of the universe is defined by every other part of the universe: X = not(Everything else).
All this to say: You cannot show an absolute distinction between any two things. All things are connected.
How do you know this if it is only "subjective"?
Firstly, "proof" only pertains to logic and mathematics, not matters of fact.
Secondly, "beyond all possible doubt" is neither a necessary condition nor sufficient condition for any claim to have a(n objective) truth-value.
Thirdly, whether or not you/we believe "beyond all possible doubt" any X exists is neither a necessary condition nor sufficient condition that that X exists.
Lastly, given that you/we/I lack compelling, reasonable grounds to doubt any X exists, believing that that X exists is reasonable until such grounds for doubt are evident. Thus, Descartes' "Cogito" fails due to the unwarranted premise of "doubting everything that can be doubted" since, though merely "possible", there are no grounds ever to do so. (Read Wittgenstein's On Certainty.)
Again, how do you know my so-called "self-evident ... subjective truth"?
e.g. Such as this merely "subjective" statement. :roll:
Like the logician Lewis Caroll's "Alice", Treatid, you've fallen down the ancient sophist Gorgias' self-refuting rabbit hole to "Jabberwocky"-land.
You are trying to criticise me for your interpretations.
Quoting 180 Proof
This is sheerest nonsense.
I feel as though you are trying to gaslight me.
Do you really mean to say that proofs are not intended to demonstrate facts?
Were you in such a hurry to gainsay that you forgot to pay attention to what you were writing?
Can you elaborate your point, please?
Quoting 180 Proof
Is this "objective truth" in the room with us now?
People have been looking for objective truths for a long time.
As it stands - all definitions are circular: for all X: X = not(Everything Else).
Our best definition of "true" is: true is not(not true).
I don't know what you think is objectively true - but if you ever manage to describe it you will have achieved something that no philosopher, mathematician or physicist has managed. I await with bated breath.
Quoting 180 Proof
Sort of.
You are free to speculate about the existence of things we cannot measure or describe.
However, if we cannot describe something - it is moot whether we believe that thing exists or not.... We can't even describe what it is that doesn't exist.
So, you are free to declare that things we cannot comprehend exist. You can never be proven wrong. But nor does it lead to a further line of enquiry.
Quoting 180 Proof
If you can describe it, it is possible.
If you cannot describe it, then it is of no relevance.
When you sit down at a table; you can describe the relationships of the table. You cannot describe the table sans relationships.
Solipsism isn't (just) about what we can prove - it is about what we can describe.
The reason we can't prove anything objectively is because we can't describe anything objectively.
We can, and do, describe relationships (aka Sensory Data).
Summary
You have a belief in objective truth. This belief leads you to try to interpret the world in an impossible fashion. You are trying to apply impossible standards and perceive confusion when those standards are not met.
Your belief is widespread. However, it has no basis.
Every description is a description of relationships. We can describe the relationships of X; we cannot describe X.
Hello.
In my opinion any idea of minimal blocks of the universe to be valid or true must specify what those blocks are and carry out an effective reconstruction of the world (as we know it). And that is something that cannot be done. What the title of this topic asks for can also be interpreted as: Is it possible to reduce the universe to a few small objects that would explain everything we know about the world? Every reduction has a starting point, the universe as we know it; but to be valid the reduction must have a way back and forth.
For example, we can say that a geometrical object like the triangle is composed of atoms since the triangle is an idea, ideas are physical-chemical processes of the brain. But at the moment of saying this we must immediately ask ourselves if we can reconstruct the triangle with which we started with those atoms, their relations, compositions, etc. In the same way we reconstruct the triangle through the relations of three lines (which is a correct reduction, because you can reconstruct the triangle from three lines in an euclidian space).
"Hurr durr - "absolutely no absolutes" sounds silly so you are wrong".
Language does not work according to the principles of logic.
Heck, Logic doesn't work by the principles of logic.
The Liar's paradox exists as a valid sentence. Your brain doesn't (I assume) implode just because you read: "This sentence is a lie."
Language describes networks of relationships. That is all language does.
A network of relationships isn't wrong or inconsistent. One network of relationships does not rule out any other network of relationships.
A network of relationships is just.... a network of relationships.
We can compare and contrast different networks; but one network never precludes another. Just as one painting doesn't prevent certain other painting existing; or one melody preclude the existence of other melodies; so one sentence does not preclude another.
sense
You are struggling to make sense of the idea that there are "absolutely no absolutes". This seems like a paradoxical statement to you.
However, the sentence is just squiggles on the screen. The universe isn't offended by particular squiggles. Squiggles don't break the laws of the universe and summon supernatural being. Squiggles are just squiggles.
The idea of paradox and inconsistency exists in your head - not in the written squiggles.
You interpret the squiggles. You apply meaning to the squiggles.
Paradoxes are a you problem - not a squiggle problem.
The very fact that you perceive certain squiggles to be paradoxical indicates that you have misunderstood something.
There are no inherently wrong squiggles. Your perception that some squiggles are paradoxical doesn't come from the squiggles.
Paradox
So - in light of this - can you explain why you think certain squiggles are paradoxical? Can you define 'contradiction'? Can you point to an instance of a contradiction and say how one squiggle precludes another?
Everything is made out of universe stuff.
Thoughts are made of universe stuff. We are made of universe stuff. The universe is composed of 100% Grade A universe stuff.
The only thing left to do is describe "universe stuff".
Euclidean Geometry
The problem with triangles and Euclidean Geometry is that all definitions are circular. A defines B and B defines A for all A and B. (X=not(Everything Else))
Lines, planes, angles and geometry each define all the others in a perpetual ouroboros snake of definitions.
This applies to every possible definition. We cannot define "universe stuff" in a non-circular fashion.
Trying to describe the universe in terms of Euclidean Geometry (or non-Euclidean Geometry) necessarily leaves us in a closed loop of saying the universe is like Euclidean Geometry and Euclidean Geometry is like the universe.
However
What we can do is describe relationships by relation to other relationships.
That is it
That is everything we can do. There isn't anything else.
We can contrast, compare and describe relationships with respect to other relationships.
This makes things simple.
We cannot describe triangles or spatial geometries or electrons as intrinsic entities.
When we stop trying to do impossible things - the possible things are easy.
It is possible to describe one set of relationships by relation to other sets of relationships. All the mucking around with objective definitions is a waste of effort.
We just describe the relationships we see and we have described the universe. Done and dusted.
Simplest
The simplest (smallest) relationships we describe (by relation to other relationships) are the "building blocks" of everything else.
:lol: STFD
First Order Logic is a subset of Axiomatic Mathematics.
Axiomatic Mathematics is predicated upon deterministic progression from a set of axioms.
In order to specify exactly one, unique, progression from a set of axioms we need to know exactly how to interpret a given set of axioms.
As such, for any given set of axioms we need a set of axioms that uniquely defines how to interpret that set of axioms.
In order to uniquely understand axioms we need axiom^2. In order to understand axioms^2 we need axioms^3. In order to understand axioms^3 we need axioms^4. ....
This leads to infinite regression or a closed loop of circular definitions (A defines B and B defines A).
Axiomatic Mathematics has one job: define axioms. It is impossible to uniquely define a set of axioms.
Without axioms, axiomatic mathematics isn't a thing.
First order Logic, a subset of axiomatic mathematics, doesn't exist.
[i]Technically: it is impossible to define axiomatic mathematics and first order logic. We haven't actually proved they don't exist - just that we cannot say anything meaningful about them.
For all practical purposes, we can treat them as if they don't exist. The distinction between "can't be described" and "don't exist" is moot.[/i]
:lol: Principle of explosion > STFU, kid.
Now you're getting it!
You are absolutely right. The Principle of Explosion is a prime demonstration of the ridiculousness of Logic.
The Principle of Explosion tells us that given an inconsistency, every conceivable statement is inconsistent.
Some people mistakenly believe that The Principle of Explosion is constrained to a single system.
However, as you so perspicaciously draw attention to; The mechanism of The Principle of Explosion is entirely unconstrained:
Given any inconsistency - we can show that any statement is simultaneously true and false.
And since The Principle of Explosion is an observation, not a deduction, there is no cop out clause.
The Principle of Explosion applies everywhere it can apply.
It is so refreshing to meet someone who can actually read what the Principle of Explosion actually says. Thank you for bringing it to our attention.
This makes zero sense.
Quoting Treatid
Those "sets of axioms" are the logical language chosen.
Quoting Treatid
Also makes zero sense.
This makes zero sense to you.
Okay. Fine.
You're not giving me anything to work with.
You provide no clue as to why you perceive my statement regarding meaninglessness to be meaningless.
You've made a statement with no associated context or argument.
Do you agree with everything else I say, but this specific statement is causing you problems?
Quoting Lionino
And that Logical language has a set of axioms that need a set of axioms that need a set of axioms.
Formal languages are, very specifically, axiomatic systems. They don't just magically exist as handy off-the-shelf starting points.
This is the fundamental problem with the axiomatic approach to knowledge: there is no fixed, known starting point. You have a choice between infinite regression of definitions or Circular definitions.
You are right, that whenever possible, mathematicians prefer a formal language over a natural language to describe new axioms. However, formal languages have axioms that need to be described (just like every other axiomatic system).
In practical terms, the first axiomatic systems were described by natural languages - So this rock solid foundation of formal languages turns out to be built on a foundation that can't be defined.
The only difference between a natural language and a formal language is the degree of obfuscation between the two.
Formal languages cannot and do not define anything with any more precision than natural language (c.f. circular definitions and infinite regression).
You've got a post on metaphysics and mathematics on the front page right now that directly refers to the foundational crisis in mathematics. This is that crisis: axioms cannot be defined.
Quoting Lionino
Again: why make this statement?
Meaning of words
You declare: "This makes no sense" as if a given sentence has a fixed, objective meaning independent of context.
Even axiomatic mathematics recognises that the meaning of a given sentence is relative to the axioms.
A sentence in one axiomatic system can be true while it is false in another axiomatic system.
You appear to be implying that meaning is independent of context. That a sentence always has a fixed meaning (or lack thereof).
This presumption is not unique to you. It is, however, impossible to justify.
Mathematicians have been trying to pin a single fixed meaning to a set of axioms since the first axiom. It can't be done.
Meaning always depends on context. Truth depend on context. Not sometimes. Not when we feel like it. Always.
Axiomatic mathematics wants axioms to have a fixed meaning but knows that meaning of statements within an axiomatic system depend on the axioms of the system.
Pick a lane. Are axiomatic statements context dependent or not?
You can't define statements in a formal language according to their axioms - and then turn around and claim that the statements of the formal language are fixed and independent of context when used to describe the next axiomatic system.
The confusion in your thread on Grundlagenkrise and metaphysics of mathematics is entirely down to an inconsistent approach to language in which sometimes meaning is contextual and sometimes it is inherent.
Recognising that all meaning is context dependent and being consistent with respect to this observation causes everything to neatly slip into place.
The idea that because something doesn't make sense to you - it therefore cannot make sense to anyone else is utterly unsustainable.
Many people cannot make sense of General Relativity. Are we to suppose that their perception is necessarily universal and that General Relativity is nonsense?
Is that really how you think knowledge works?
Is my perception of your statements the only possible way to interpret them?
Roundup
At some level you know that meaning is context dependent. You know that different people interpret the same words differently.
All I'm pointing out is that there are no exceptions.
Axiomatic mathematics is trying to find fixed axioms while defining axiomatic systems contextually. One or the other has some potential to succeed. Mixing the two just leads to confusion.
No, I am informing you that your string of words makes zero sense. It perhaps "makes sense" to you in the same way that 12+12=22 made to me in my early childhood.
Quoting Treatid
That is not how it works. A language is not a theory. The axioms of language, in this case n-order logic, are not the same as the axioms of a mathematical theory. And the axiom tree/chain does not keep going forever.
If I wanted to release the kraken, I would tag Tones and he would inundate this thread with corrections on your posts. I am using my posts to inform you that you don't really understand what it is that you are saying. It is up to you to insist in mistakes or not.
Quoting RogueAI
Quoting Count Timothy von Icarus
Quoting Wayfarer
I may be hearing Heraclitus playing the lyre here, but it seems to me that oppositeness is the simplest possible building block of the universe. In fact, our entire universe and existence are built upon oppositeness.
With oppositeness, there are electrons and protons; negative integers and positive integers; matter and energy; photons and waves; infinity and infinitesimal; vacuum and pressure; apoptosis and paligenosis; black and white; life and death; poetry and prose; work and play; sleep and wakefulness; mountains and beaches; art and commerce; music and cacophony; notes and rests; sterility and fertility; heat and cold; real and imaginary; laughter and tears; fact and fiction; good and evil. (And even agreement and disagreement, which is the hallmark of this forum!)
Oppositeness is patently a simple building block. It is easy-to-understand and readily applicable. Objects, processes, states of affairs, feelings whatever can all be paired with other objects, processes, states of affairs and feelings of opposing qualities. (See the above list for examples.)
And yet, as simple as oppositeness is, an entire, rich, diverse and wondrous universe can be constructed from it. Life itself is an expression of opposites and even develops from it e.g., the sperm fertilizes the egg.
So I stake my claim with Heraclitus, who argued that the world could not exist without opposing qualities like the tension that is created from the opposite ends of the strings on a lyre. Its as simple as that.
Argumentation from authority is a fallacy.
I get that you think you are right.
For my part, I'm pretty sure I know what I'm talking about.
You reiterating your assumptions, claiming you are right by fiat - isn't an argument.
Saying your dad can beat up my dad isn't an argument.
The very fact that you think someone else can put me in my place tells me you don't actually understand the position you are trying to defend. If you understood it - you'd be able to present the evidence to me yourself.
As it stands - you are telling me I'm wrong but providing no justification for that position.
It is almost as if you aren't trying to persuade me you are right. It looks somewhat as if you are trying to defend your own beliefs without understanding where those beliefs are coming from.
Quoting Lionino
I would be delighted to engage with someone who knows the difference between a dialogue and a sermon.
Your claim that a given sentence has a fixed (nonsensical) meaning in all possible languages across the entirety of time and space is simply absurd.
Your claim that formal languages are not axiomatic systems is straightforwardly counterfactual. ZFC set Theory is the axiomatic system for which the axiom of choice was invented. This is an easy lookup. No-one who has the slightest knowledge of axiomatic mathematics thinks otherwise. This suggests to me that you a regurgitating something you heard - not talking about things you understand.
If you can find a single instance of a non-circular definition - you can rub that in my face.
I thought your post on the metaphysics of mathematics was interesting - but when you claim that a sentence has a fixed meaning (albeit nonsensical) you demonstrate beyond reasonable doubt that you don't understand the questions you are asking.
"Context matters" is basic English comprehension.
TL;DR
I don't mind that you think I'm wrong. The feeling is mutual.
I'm bothered that you aren't trying to show me exactly how I'm wrong.
You appear to be going out of your way to avoid presenting an actual argument. On a Philosophy Forum.
It looks to me like you aren't trying to persuade me. It looks to me like you are trying to preserve your own unfounded beliefs.
Care to demonstrate that you know what you are talking about rather than merely declaring it?
And please do sick any tame lapdogs on me. (no typo - bring it).
I think General Relativity is physics done right.
The significant difference between Quantum Mechanics (QM) and General Relativity (GR) is that QM tries to describe an objective universe that can't be directly experienced, while GR describes what an individual observer sees.
In my estimation, most people struggle with GR because they are trying to interpret it from a Newtonian/Eucildean framework.
So the twin paradox is paradoxical given the assumptions of a fixed, objective universe in which The Law of Identity holds - but is just a description of what we would see in GR.
cannot imagine a framework without his implicit assumptions about the world. In his perception, a paradox is always a paradox. But the "twin paradox" is only a paradox within Newtonian/Euclidean space. In GR - the "twin paradox" isn't a paradox of any kind. It is simply what is observed.
GR is such a fundamentally different approach to knowledge that there is no path from Newtonian Mechanics (NM) to GR. GR cannot be constructed using NM. There is no iterative set of steps from one to the other.
Albert Einstein had to go back to first principles. The theories of relativity are built from the single observation that the speed-of-light-in-vacuum is constant for all observers. His theories then take this observation to its ultimate conclusion.
Trying to comprehend GR while holding onto the assumptions of "objective reality" is impossible. Each observer experiences a different reality. Changing the relationships (relative velocity) in GR changes the perception of what reality is. Talking about a singular objective reality isn't meaningful within GR. No observer is "the correct observer" and every observer perceives a different universe - similar, connected, but unique for each observer.
Relational universe
Context Matters.
Meaning is defined by context. Einstein was referring to physics - but the universe is relational in every aspect.
The world you experience is genuinely different from the world everyone else (individually) experiences.
Not chaotically different. There are many similarities - but no two people's experiences are identical.
Everyone knows that experience is subjective. But most are still trying to understand a relational universe in objective terms.
The fixed, objective knowledge that craves doesn't exist. A relational (subjective) universe cannot be understood from the perspective of an objective worldview within which objects are static (The Law of Identity).
Quoting Thales
Yes, yes, yes, yes, yes.
So much yes.
You win all the prizes. This is the right answer.
Some more agreement
I call them relationships or connections or differences - Opposites/oppositeness is just as good a name.
A rose by any other name...
So - yes - there is some fundamental quality of oppositeness and this quality is the building block of the universe.
Way back in the OP - I stated that the minimum possible oppositeness (relationship, connection, difference) is a directed edge in a graph.
Does this make sense to you as a minimum oppositeness. How do you picture/imagine a universe made out of pure oppositeness.
To be clear: I'm impressed with your description of oppositeness and I want to listen to you develop the idea more. Stepping away from the conventional "particle" centric models seems to me to be a huge step.
I think that recognising this oppositeness nature of the universe is the lynch pin. That it is impossible to describe a particle based universe - and (relatively) trivial to describe an oppositeness universe.
You don't have to ... anything. I'm not expecting immediate agreement. I am already sincerely impressed by your insight. I would be honoured to agree, or disagree, with any further thoughts on the matter you have.
That is not what I said and that is not what counterfactual means.
Quoting Treatid
There is no twin paradox in Newtonian physics. The twin paradox is a paradox in Einstenian physics, paradox is not synonym with "contradiction".
You have no clue what you are talking about. I will not bother with the rest of the uninformed ramble.
So do flat earthers. But alas you are both clueless.
In point-set topology, a point of space can be any set. The simplest set is the empty set, which is not nothing but something that has no parts.
Im humbled and honored to be named discussion winner. But what is my prize? (I hope its the poker Ludwig Wittgenstein brandished at Karl Popper!) :cool:
Yet again you respond with assertions but no justification for your position.
Why?
You aren't even trying to show me that I'm wrong.
If you want to win trolling points; reddit has upvotes and downvotes to keep score.
Quoting Lionino
I assure you, the feeling remains mutual.
Quoting litewave
That seems a lot like a definition of nothing to me.
One of the sub-threads here is that all definitions are circular.
An empty set is defined by set theory. Set theory is defined by the axioms of set theory. The axioms of set theory are defined by something else which is defined by something else which is defined by something else...
This results in infinite regression or circular definitions.
As a result axiomatic mathematics cannot define the meaning of anything. Hence "The Foundational Crisis in Mathematics" among other things.
The good news is that I can't definitively prove that a mathematical point and an empty set are equivalent to "nothing".
The bad news is no-one can demonstrate they are not equivalent, either.
And this brings us to the age old questions: What can we know with certainty? What can we describe?
For example, all definitions related to Quantum Mechanics are circular (this isn't just a mathematics problem). Our perception of what fields and waves are - derives from the universe we are trying to describe.
Quantum Mechanics says that electrons look like (other) bits of universe. This bit of the universe looks similar to that bit of the universe.
It isn't wrong. But it doesn't explain anything.
The reason 's answer is so good is because we can describe the relationships (oppositeness) of things. Indeed - we can only describe relationships.
I believe the standard prize is "a sense of pride and accomplishment". I'm told it nourishes the soul.
I'll certainly consider your suggestion of a physical prize. But I have been assured that "Exposure" is superior to mere material possessions.
Empty set? Emptiness is a property, which is something. And so is that which has it.
Quoting Treatid
Is that a problem? As long as all things are consistently defined, in all relations to each other, it seems fine to me. Of course, we can never prove the consistency of all things, due to Godel's second incompleteness theorem. But that's an epistemical problem, not ontological. Consistency doesn't care whether it can be proven.
Quoting Treatid
What do you mean by "meaning"?
Quoting Treatid
We know our own consciousness with certainty. From that we form, in our consciousness, a representation of an external reality -- not with certainty but with various degrees of certainty.