“Distinctively Logical Explanations”: Can thought explain being?

acknowledging the various debates of Hume and Kant.

Yes, and thanks for the summary. Is it clear to you that either Hume or Kant has the better explanation here? Are Jha et al. Kantians? (Note, too, that Kant did not think math was analytic, like logic. He thought it gave us synthetic knowledge about the intuitive concept of "magnitude" -- that is, number per se. This makes me wonder if he would allow math an explanatory role, as in the above discussion.)

The current volume of Philosophy of Science has a paper on mathematical explanations in the sciences that I realize is talking about something very similar. The paper is “Are Mathematical Explanations Causal Explanations in Disguise?” by Aditya Jha et al. The question raised is whether a distinctively mathematical explanation (DME) for physical facts truly exists – whether “the facts under question arise from a degree of mathematical necessity considered stronger than that of contingent causal laws.”

Does it matter, for this parallel, whether math is a branch of logic, as many philosophers (and scientists) believe?

Yeah, but remember Kant thought math was synthetic a priori. In other words, our minds are still structuring time and space and experience. The math wasn't "in the world", that would be violating his phenomenal/noumenal distinction

evolution does provide a certain flavor of answer whereby our brains could not but do otherwise.

Pancomputationalism . . . would make cause (i.e. how past states determine future states) a sort of stepwise logical entailment.

Math, like language, is a tool of logic with rules. If we use it with the idea that our abstraction is trying to match reality, and we are correct in matching our abstractions to reality, it works because that's how we perceive identities, and our identities are not being contradicted by reality

This seems to make the LNC, e.g., contingent on the way the world is. But don't we want something much stricter than that, some way we can talk about necessity and impossibility? Can we arrive at what you're calling "a necessary understanding of the world"?

I'll bring in Nagel any post now! :smile:

I see what you mean, but we can construct an infinite number of worlds with different abstract entities highlighted (see "grue and bleen", Sider, p. 16) and most of them won't "work" at all, if by "work" you mean "give us a useful conceptual basis for navigating the world." Yet there is nothing wrong, logically, with the way these abstractions are being matched to reality. So can you expand on what it is to "perceive an identity"? -- that seems crucial.

Does the "pan" part of pancomputationalism provide a response to Jha et al.'s objection? That is, are the background assumptions which Jha et al. call "the very facts that make a purely mathematical result applicable" also generated computationally? I'm out of my depth here, but is there meant to be a beginning to this process of entailment -- some first premises?

[Husserl] tries to show how the formal, logical structures of thinking arise from perception; the subtitle of Experience and Judgment is Investigations in a Genealogy of Logic. The “genealogy” of logic is to be located not in something we are born with but in the way experience becomes transformed. Husserl describes the origin of syntactic form as follows.

When we perceive an object, we run through a manifold of aspects and profiles: we see the thing first from this side and then from that; we concentrate on the color; we pay attention to the hardness or softness; we turn the thing around and see other sides and aspects, and so on. In this manifold of appearances, however, we continuously experience all the aspects and profiles, all the views, as being “of” one and the same object. The multiple appearances are not single separate beads following one another; they are “threaded” by the identity continuing within them all. As Husserl puts it, “Each single percept in this series is already a percept of the thing. Whether I look at this book from above or below, from inside or outside, I always see this book. It is always one and the same thing.” The identity of the thing is implicitly presented in and through the manifold. We do not focus on this identity; rather, we focus on some aspects or profiles, but all of them are experienced, not as isolated flashes or pressures, but as belonging to a single entity. As Husserl puts it, “An identification is performed, but no identity is meant.” The identity itself never shows up as one of these aspects or profiles; its way of being present is more implicit, but it does truly present itself. We do not have just color patches succeeding one another, but the blue and the gray of the object as we perceive it continuously. In fact, if we run into dissonances in the course of our experience – I saw the thing as green, and now the same area is showing up as blue – we recognize them as dissonant precisely because we assume that all the appearances belong to one and the same thing and that it cannot show up in such divergent ways if it is to remain identifiable as itself. [It's worth noting the experiments on animals show they are sensitive to these same sorts of dissonances].

[Such experience is pre-syntactical, nevertheless] such continuous perception can, however, become a platform for the constitution of syntax and logic. What happens, according to Husserl, is that the continuous perception can come to an arrest as one particular feature of the thing attracts our attention and holds it. We focus, say, on the color of the thing. When we do this, the identity of the object, as well as the totality of the other aspects and profiles, still remain in the background. At this point of arrest, we have not yet moved into categoriality and logic, but we are on the verge of doing so; we are balanced between perception and thinking. This is a philosophically interesting state. We feel the form about to come into play, but it is not there yet. Thinking is about to be born, and an assertion is about to be made…

We, therefore, in our experience and thoughtful activity, have moved from a perception to an articulated opinion or position; we have reached something that enters into logic and the space of reasons. We achieve a proposition or a meaning, something that can be communicated and shared as the very same with other people (in contrast with a perception, which cannot be conveyed to others). We achieve something that can be confirmed, disconfirmed, adjusted, brought to greater distinctness, shown to be vague and contradictory, and the like. All the issues that logic deals with now come into play. According to Husserl, therefore, the proposition or the state of affairs, as a categorial object, does not come about when we impose an a priori form on experience; rather, it emerges from and within experience as a formal structure of parts and wholes...

This is how Husserl describes the genealogy of logic and logical form. He shows how logical and syntactic structures arise when things are presented to us. We are relatively passive when we perceive – but even in perception there is an active dimension, since we have to be alert, direct our attention this way and that, and perceive carefully. Just “being awake (Wachsein)” is a cognitive accomplishment of the ego. We are much more active, however, and active in a new way, when we rise to the level of categoriality, where we articulate a subject and predicate and state them publicly in a sentence. We are more engaged. We constitute something more energetically, and we take a position in the human conversation, a position for which we are responsible. At this point, a higher-level objectivity is established, which can remain an “abiding possession (ein bleibender Besitz).” It can be detached from this situation and made present again in others. It becomes something like a piece of property or real estate, which can be transferred from one owner to another. Correlatively, I become more actualized in my cognitive life and hence more real. I become something like a property owner (I was not elevated to that status by mere perception); I now have my own opinions and have been able to document the way things are, and these opinions can be communicated to others. This higher status is reached through “the active position-takings of the ego [die aktiven Stellungnahmen des Ich] in the act of predicative judgment.”

Logical form or syntactic structure does not have to issue from inborn powers in our brains, nor does it have to come from a priori structures of the mind. It arises through an enhancement of perception, a lifting of perception into thought, by a new way of making things present to us. Of course, neurological structures are necessary as a condition for this to happen, but these neural structures do not simply provide a template that we impose on the thing we are experiencing...

-Robert Sokolowski - The Phenomenology of the Human Person

We’ve talked a lot on TPF recently about thinking and being – not just Irad Kimhi’s book of that title, but the larger issue of how thought mirrors reality. Does the Law of Non-Contradiction state a logical truth? a truth about how things must be in the world? or, somehow, both? neither?

Q2. Why are 23 objects not evenly divisible into three collections of whole and unbroken objects?

Q2 is a linguistic problem and results from a particular definition of "object".

23 things can be evenly divided into three collections of 723
7
2
3
things.

But Q2 defines an object as something that is whole and unbroken, meaning that if a thing can be divided into parts, then by definition that thing cannot be an object.

Therefore, although 23 things can be evenly divided into three collections, by the given definition of "object", 23 objects cannot be evenly divided into three collections.

However, other definitions of "object" are possible.

For example, as the object "house" is the set of other objects, such as "roof", "chimney", "windows", etc, an "object" could have been defined as a set of three other objects, in which event 23 objects is evenly divisible into three collections of whole and unbroken objects.

I look at a notepad, and I think "notepad". A notepad is a conventional object. It is a socially created object, for all intents and purposes. But then there is various laws of mechanics that were used in the making of the machines that made the notepad. These are "laws of physics". Whilst the technological use is in a way conventional, the physical laws behind it, which we also derived, as humans reasoning, are supposedly the ones we are discussing, the "objective" ones "in nature". The "true mathematical laws" that we are not conventionalizing, but teasing out with our mathematical models, and cashing out in accurate predictions and technological usefulness. So it is those we are getting at. Yet, imposed on top of that, is the same brain that makes a conventional item like "notepad", into "something" real, something that I presuppose every time I look at a notepad. I don't just see a bunch of atoms grouped together- I see a type of object. Now this is the tricky part where Kant does come in. What is the part that is conventional, and what is the "objective"? How are we to really know? These are two very different types of capacities coming together and converging:

1) The ability to parse the world into discrete objects and arrange them and describe them.
2) The ability to parse out various empirical understandings of the world THROUGH THE PRISM of a kind of brain that does the capacity described in 1.

So Nagel might say something like, The 2 [objective laws/logic] has created the 1 [cognitive laws/logic]. There is something that connects the two.

A true agnostic or nihilist of this scheme would say 1 and 2 are not connected in any meaningful way. Kant, for example, will make the move that 2 is really a sub-species of 1 (or how I interpret Kant).

Q1. Why is the number 23 not divisible (evenly) by 3?
Q2. Why are 23 objects not evenly divisible into three collections of whole and unbroken objects?

What we really want is an explanatory structure that preserves both of the seemingly ineluctable realities – of logic and of being. Kimhi has his views about how we might get there. A theistic argument might posit a “perfect match” because creation is deliberately thus. Or – using a metaphor from Banno – we find ourselves with a Phillips-head screw and a screwdriver that matches, so let’s leave a designed creation out of it and try to work on the problem in evolutionary terms. (I don’t think such an approach will take us far enough, but it’s certainly respectable.)

My take is that the tremendous success of our efforts to understand the world, which has translated into the causal mastery embodied in techne, represents strong evidence that we do come equipped to know the world and that the world is intelligible.

I buy Gadamer's argument that it's quite impossible to make any inferences without begining with some biases. We can always question these biases later.

To say that the alignment between screwdriver and screw is an opaque and brute fact is to have abandoned the search for an overarching explanatory structure. If there is an explanatory structure that preserves both, then that explanation must encompass both the mind that knows reality and reality itself. I don't see how one could arrive at an explanatory structure such as you desire without this overarching aitia.

There is a major debate as to whether there are non-causal mathematical explanations of physical facts that show how the facts under question arise from a degree of mathematical necessity considered stronger than that of contingent causal laws

“The facts allegedly explained by a DME do not obtain because of a mathematical necessity but by appeal to the world’s network of causal relations. . . . [Mathematics] is not a constraint on what the physical world must be.”

Q1. Why is the number 23 not divisible (evenly) by 3?
Q2. Why are 23 objects not evenly divisible into three collections of whole and unbroken objects?

I don't just see a bunch of atoms grouped together- I see a type of object.

But that doesn't make Q2 a linguistic problem, since we've stipulated what an "object" will be in this question.

But what about the problem posed by the question itself, now disambiguated? -- presumably you'd say "No, it can't be divided evenly" and so we want to know whether this is due to a mathematical fact or a fact about the world.

Q4: Why can’t my cat be on my lap and in Paris at the same time? (constraint: I live in Maryland)

So mathematics models the world because the world exhibits regularities that can be mathematically described, not because the world is constrained by the mathematical framework.

are our abstractions mysteriously agreeing with the world?

origin of abstract
Middle English: from Latin abstractus, literally ‘drawn away’, past participle of abstrahere, from ab- ‘from’ + trahere ‘draw off’

So where are abstractions taken from? I suggest "the world" is a sensible answer, and one that explains the "mystery" rather well

I can see that you wouldn't like this approach on the grounds that it shoots your fox and spoils the fun of the chase.

It is the "I" that sees a relation between many different objects in the world. It is not the world that is relating a particular set of objects together.

It is indeed a sensible answer, but doesn't explain what appears to be the modally necessary character of the abstractions, and their role in explanation, if any. Have you read the target paper I cited? It might explain the problem better than I have.

I see what you mean, but we can construct an infinite number of worlds with different abstract entities highlighted (see "grue and bleen", Sider, p. 16) and most of them won't "work" at all, if by "work" you mean "give us a useful conceptual basis for navigating the world."

Yet there is nothing wrong, logically, with the way these abstractions are being matched to reality.

The larger puzzle is this: How is it the case that, no matter what definition we use, we discover these regularities between math/logic and the world?

The DLE problem assumes a linguistic stipulation that is uncontroversial or at least agreed-upon, or at the very least accepted for the purposes of discussion. With this stipulation in place, we then go on to ask about the relation between logic-or-math-as-necessity and the alleged necessity of events in the world, such as the 23 objects that can’t be evenly divided, or the cat that can’t be here and in Paris too.

A different world, if there could be such, would reveal different regularities, but the role of math would be unchanged.

So where are abstractions taken from? I suggest "the world" is a sensible answer, and one that explains the "mystery" rather well.

If you have 23 objects you have already mathematicised them by counting

Gravity, electromagnetism, chemical interactions, biological interactions, etc. work ways that impose on us their workings, not the other way around........................Kant, for example, seemed to conflate the two as part of the same "transcendental" constraints that our minds impose on "the thing-itself".

I just think this needs further explanation; logic and noncontradiction alone won't get us to why some matches seem more natural or reality-mirroring than others ("privileged structure").

?Philosophim I did read the summary. Is this the passage you're referring to (concerning "privileged structure" or the like)?:

Sider uses the "grue and bleen world" example (which you can read about here, p. 16) to refer to a situation that he believes needs explaining: If we encountered a people who used grue and bleen as their concepts, we'd be unable to fault them on any logical grounds.

Kant and a Transcendental Deduction that mathematical truths are necessary truths

In B276 of the CPR, Kant uses a Transcendental Deduction to prove the existence of objects in the world.

As the equation "d=0.5?g?t2

=
0.5
?

?

2
" does successfully and consistently predict what is observed in the world, we could use a similar Transcendental Deduction to prove that in the world is the underlying reality that d=0.5?g?t2

=
0.5
?

?

2
.

Using such a Transcendental Deduction, we could unify a world that imposes itself on the mind and a mind that imposes itself on the world.

As for the analytic/synthetic distinction, I'm not sure we really have to go there. Perhaps it won't do as a description of the difference between logic and facts-about-the-world, but wouldn't you agree that Jha et al. are pointing to something that can be talked about, and represents a genuine question?

Q. You claim that a person’s information, if we trust mathematics, is still there after death, dispersed throughout the universe, forever. Are we immortal?

A. If you trust the mathematics, yes. But it is not an immortality in the sense that after death you will wake up sitting in hell or heaven, both of which – let’s be honest – are very earthly ideas. It is more that, since the information about you cannot be destroyed, it is in principle possible that a higher being someday, somehow re-assembles you and brings you back to life. And since you would have no memory of the time passing in between – which could be 10¹?? billion years! – you would just find yourself in the very far future.

Quine himself had very mixed feelings about whether the laws of logic were subject to revision. I think his final answer was yes, but it's a last resort, and they are very insulated, resistant to revision.

Why is math so faithful? It may be that we can't know that.

(Empiricists) view Platonism with skepticism. Scientists tend to be empiricists; they imagine the universe to be made up of things we can touch and taste and so on; things we can learn about through observation and experiment. The idea of something existing “outside of space and time” makes empiricists nervous: It sounds embarrassingly like the way religious believers talk about God, and God was banished from respectable scientific discourse a long time ago.

Platonism, as mathematician Brian Davies has put it, “has more in common with mystical religions than it does with modern science.” The fear is that if mathematicians give Plato an inch, he’ll take a mile. If the truth of mathematical statements can be confirmed just by thinking about them, then why not ethical problems, or even religious questions? Why bother with empiricism at all?

Let me try to work up an example that is less controversially stipulative.

OK. So no one of your factors would be something like "This set of concepts more accurately reflects the ontological structure of the world"?

In your other thread we touched on the Scholastic transcendentals or convertibles. Another transcendental besides being and truth is oneness (unum).

There was consensus among the scholastics on both the convertibility of being and unity, and on the meaning of this ‘unity’—in all cases, it was taken to mean an entity’s intrinsic indivision or undividedness. [19] In this, the tradition was continuing and affirming a definition first proposed by Aristotle in the Metaphysics. [20] This undividedness, in the words of Aquinas in his Commentary on the Sentences, is said to lie “closest to being.”[21] For the most part, ens and unum were distinguished by these thinkers only logically or conceptually—unum adding nothing real to being, or more properly, adding only negation, only a privation of actual division.[22] It was common practice in medieval philosophy to distinguish the transcendental sense of unum, running through all of the categories, from the mathematical sense of unum, restricted to the category of quantity. These two ‘ones’ are each in their own way opposed to ‘multiplicity.’[23] Aquinas offers a succinct account of this in his Summa Theologiae (Ia. q. 11, art. 2).[24] The ‘one’ of quantity is the principle of number; it is that which, by being repeated, comprises the sum (the multiple).[25] Aquinas says that there is a direct opposition between ‘one’ and ‘many’ arithmetically, because they stand as measure to thing measured, as just-one to many-ones. Likewise, transcendental unity is opposed to multiplicity, but in this case not directly. Its opposition is not to the many-ones per se, but rather to the division essentially presupposed in and formal with respect to the multiplication of actual multiplicity. This tracks with a consistent distinction in Aquinas between division and plurality in which division is seen as ontologically and logically prior.[26] Transcendental unity then, has a certain priority to its predicamental counterpart.

We will return below to the consequences for contemporary ontology that follow upon this fact that, in its developed form, it was division, not plurality, that was taken by the classical tradition to be the precise contrary to transcendental unity. . .

Are you sure we should call something like d=0.5?g?t2 a mathematical truth? I thought it was only true on some interpretation; as it stands, it has no meaning.

@RussellA: Eventually, after many attempts, we invent the equation [math]{d = 0.5 * g * t^{2}}[/math], discover that it works, and keep it.................We know it works, but we don't know if it is a necessary truth.

"Are the equations being imposed or simply reflected in the mathematics?"

Some neo-Logos philosophies might say the mind cannot but help seeing the very patterns that shape itself.

I can imagine a type of pattern whereby the mind works (X), and a pattern whereby the world works Y, and X may be caused by Y, but X is not the same as Y.

Is our language contingently relating with the world or necessarily relating to the world.

I can see a sort of holistic beauty in the aesthetic of the language reflecting the world because it is derived from (the patterns) of the world.

I can see a sort of nihilistic "contingency" in the aesthetic of language never really derived from, but only loosely reflecting the world.

Are mathematical truths necessary truths
Following the schema "snow is white" is true IFF snow is white as a definition of "truth", then "d=0.5?g?t2" is true IFF d=0.5?g?

What do you mean that the equation d=0.5?g?t2 has no meaning?

So I assumed you regarded d=0.5?g?t2 as a mathematical truth.

Both. For 100 days we observe the sun rise in the east, and invent the rule "the sun rises in the east". The rule reflects past observations, but is no guarantee that the rule will still apply in the future. We impose the rule on the world, in the expectation that the rule will still apply in the future.

Some neo-Logos philosophies might say the mind cannot but help seeing the very patterns that shape itself.
— schopenhauer1

I'm with Kant on that.

I can imagine a type of pattern whereby the mind works (X), and a pattern whereby the world works Y, and X may be caused by Y, but X is not the same as Y.
— schopenhauer1

Exactly. A postbox emits a wavelength of 700nm ( Y) which travels to the eye which we perceive as the colour red (X), where our perceiving the colour red in the mind was caused by the wavelength of 700nm in the world.

There is the general principle that an effect may be different in kind to its cause. For example, the effect of a pane of glass breaking is different in kind to its cause of being hit by a stone.

Aesthetics is perceiving a unity in the whole from a set of disparate parts. For example, the magic of a Monet derives from the artist's deliberate attempt to create a unity out of a set of spatially separate blobs of paint on a canvas. Such a unity exists only in the mind of the observer, not in the world, in that one blob of paint of the canvas has no "knowledge" as to the existence of any other blob of paint on the canvas. Patterns only exist in the mind, not the world.

As patterns don't ontology exist in the world, but do exist in the mind, to say that patterns in the mind have derived from patterns in the world is a figure of speech rather than the literal truth.

Perhaps it is more the case that the aesthetic brings meaning out of the meaninglessness of nihilism. It is the aesthetic that discovers the unity of a whole within disparate parts, finds patterns in randomness and seeks sense out of senselessness. For example, the aesthetic of Picasso's Guernica shows us the possibility of a greater good born out of the nihilism of war, and the aesthetic of the mathematical equation shows us a greater understanding born out of a nihilistic Universe that is fundamentally isolated in time and space.

I understand. Do you think there are mathematical truths that are independent of what is the case in the world? Plain old theorems, in other words?

My understanding of truth is that it is defined by the schema "snow is white" is true IFF snow is white, where "truth" is the correspondence between propositions in language and equations in mathematics and what is the case in the world.

If I am correct, then if a proposition in language or an equation in mathematics is independent of what is the case in the world, then by the definition of truth, such a proposition or equation can neither be true nor false.

Unum in the same sense as in non-dualism, advaita, non divided.

My understanding of truth is that it is defined by the schema "snow is white" is true IFF snow is white, where "truth" is the correspondence between propositions in language and equations in mathematics and what is the case in the world.

Or perhaps indivisible, and that seems to be a bit different. A chicken is indivisible. To divide it is to lose your chicken.

There was consensus among the scholastics on both the convertibility of being and unity, and on the meaning of this ‘unity’ —in all cases, it was taken to mean an entity’s intrinsic indivision or undividedness.

For example, the magic of a Monet derives from the artist's deliberate attempt to create a unity out of a set of spatially separate blobs of paint on a canvas. Such a unity exists only in the mind of the observer, not in the world, in that one blob of paint of the canvas has no "knowledge" as to the existence of any other blob of paint on the canvas. Patterns only exist in the mind, not the world.

As patterns don't ontology (sic) exist in the world, but do exist in the mind, to say that patterns in the mind have derived from patterns in the world is a figure of speech rather than the literal truth.

the neo-logos philosophies might say something like, "If nature has patterns, and our language has patterns, and we are derived from nature, it may be the case that our language is a necessary outcome of a more foundational logic".

This is the principle that animates all living beings, from the most simple up to and including humans. it is why, for instance, all of the cells in a living body develop so as to serve the overall purpose of the organism. So the 'one-ness' of individual beings is like a microcosmic instantiation of 'the One'.

By referring to "accurate representation," you've introduced an epistemologically normative factor that is nowhere implied in the first three factors.

Maybe "it just is"? But isn't that super-convenient for us?

To put it in simple terms (borrowed from Sider), are we really not in a position to say that the Bleen people have gotten something wrong?

Well, perhaps, but how can "accuracy" be a factor at all? What would make something an "accurate representation," to use your phrase, and of what is it a representation? None of the three factors talk about how such an idea could arise.

To put it in simple terms (borrowed from Sider), are we really not in a position to say that the Bleen people have gotten something wrong?

chickens

I think what's strange about this problem is that the setup makes human beings helpless before the implacable necessity of mathematics, and that's the wrong story to tell.

In real life, a case like this is more likely to play out this way: you've got these 23 thingamabobs, and there's talk of splitting them three ways. You say, "Won't work," and someone less numerate than you says, "Well, let's just try." As they fail, with a puzzled look, they say, "Wait, I messed up somewhere. Let me start over." You will want to explain to them that it's impossible, because 23 is not only not a multiple of 3, it's a frickin' prime.

What's of primary interest here is that you, because of your relative expertise in mathematics, understand the situation better than the person who, even after trying and failing several times, still believes it might be possible.

what is your alternative?

Either way the math/reality constrains our options.

there is very little difference between the less numerate and the more numerate. The less numerate just takes a few more minutes

Well, I know it's all off-topic for this thread, but that passage you quoted resonated with me.

In an artificially bounded task like this

Life is not like that.

Either we find a creative way to complete this subtask (making do with rough equality ? 7 or 8 each, cutting the strawberries, if that's an option, or switching measures, say from units to weight, and so on) or we mark this path off in the search and backtrack until we find a path.

Reality, sure, but mathematics is how we conceptualize our situation and can inform both our choice of action and our method. Mathematics is adverbial.

Anywhere you want to look, it is plain as can be that thinking and acting mathematically is empowering for humans, not some implacable constraint.

But for the general distinction in approaches, which this little problem illustrates, the entire business world disagrees with you, the natural sciences disagree with you, the various branches of engineering disagree with you.

I think J's OP is interesting. It is something like: if mathematical necessity is not self-supporting, then whence is the necessity derived?

But, all organic life displays just the kind of functional unity that a painting does, spontaneously. Those patterns most definitely inhere in the organic world. DNA, for instance.

Because if within a world absent of observers, spatial and temporal relationships had no ontologically existence, then there would be no way of spatially and temporally relating disparate things together, meaning that in the world there would be no patterns, as a pattern can only exist if its parts are somehow related together.

do the patterns that we see exist in the world or only in our mind

A pattern has a unity because of the particular way things are spatially and temporally related to each other, where the whole is more than the sum of its parts.

One might push back on Aristotle's categories sure, but science certainly uses categories. The exact categories are less important than the derived insights about the organization of the sciences. And the organization of the sciences follows Artistotle's prescription that delineations should be based on per se predication (intrinsic) as opposed to per accidens down to this day.

This is why we have chemistry as the study of all chemicals, regardless of time, place, etc. and biology as the study of all living things as opposed to, say: "the study of life on the island of Jamaica on Tuesdays," and "the study of chemical reactions inside the bodies of cats or inside quartz crystals, occuring between the hours of 6:00am and 11:00pm," as distinct fields of inquiry. Certain sorts of predication (certain categories) are not useful for dividing the sciences or organizing investigations of phenomena (but note that all are equally empirical).

Of course, there have been challenges to this. The Nazis had "Jewish physics" versus "Aryan physics." The Soviets had "capitalist genetics" and "socialist genetics," for a time. There are occasionally appeals to feminist forms of various sciences. But I think the concept that the ethnicity, race, sex, etc. of the scientist, or the place and time of the investigation, is (generally) accidental to the thing studied and thus not a good way to organize the sciences remains an extremely strong one.

That said, if all categories are entirely arbitrary, the result of infinitely malleable social conventions, without relation to being, then what is the case against organizing a "socialist feminist biology," "astronomy for leap years," and a "biology for winter months," etc ?

They certainly wouldn't be as useful, but that simply leads to the question "why aren't they useful?" I can't think of a simpler answer than that some predicates are accidental and thus poor ways to organize inquiry. We could ground this in the structure of things but it seems it might be simpler to ground it in phenomenology and the quiddity (whatness) of things as experienced. We can think here if how Husserl imagines changes to the noema (object of thought) and considers which changes force it to become an entirely different sort of thing.

Is this meant to be Tarski's view? Surely he didn't talk about what was the case in the world -- only about the correct relations between language and metalanguage. If one language has to be "about the world," then we wouldn't have any logical or mathematical truths at all, or at least that seems to be the necessary consequence. I don't think Tarski intended this. Unless I'm mistaken, he included these kinds of truths in his schema.

Within the modern correspondence theory, "snow is white" is also within the object language whilst snow is white is a fact in the world.

So, without observers, nothing is related to anything whatever. That is the thrust of the OP

As per above, this question can be asked not only of patterns, but of phenomena generally..........................There are patterns that appear in inorganic nature, in crystals, snowflakes, larva formations etc.

The book’s argument begins with the British empiricists who raised our awareness of the fact that we have no direct contact with physical reality, but it is the mind that constructs the form and features of objects. It is shown that modern cognitive science brings this insight a step further by suggesting that shape and structure are not internal to objects, but arise in the observer.

?Philosophim What a cromulent response! :smile:

This just pushes the question back a level -- why is it effective?

Wouldn't it make more sense for you (if I've understood your thinking here) to abandon any talk of accuracy or truth?

Suppose bleen is "green and "first observed" during or before 2004," or "blue and 'first observed' after 2004." Could you go walk around where you live and determine what was grue or bleen?

Suppose there is a famous green landmark in your town and it got flattened by a tornado in 2006. It was rebuilt with largely with materials salvaged from the original, but has a substantial amount of new material. Is it bleen or grue?

What if only small parts of it were replaced each year since 2004?

A theorem (as opposed to an equation that's given a real-world interpretation) isn't described as effective, it's described as true, or at least provable in L.

Do you want to abandon that way of talking? If a correspondence theory of truth demands that we do so, I'd argue that it represents a reductio ad absurdum and should be rejected on that ground.

If a correspondence theory of truth demands that we do so, I'd argue that it represents a reductio ad absurdum and should be rejected on that ground.

What would be the point of limiting ourselves in this way?

If you understood the essential properties and context of what grue and bleen is, then yes

the case of grue and blue, we're not asking what the definitions should be, we already know what they mean. Our decision is then, "should we use grue or blue"? And I mentioned earlier, as long as both are accurate to the point they are not contradicted by reality, its really a personal choice. It may be as simple as, "I like one word more than another" or as complicated as, "Those dirty grueians are a stupid people that I find inferior. Blue is obviously superior and the 'right' way to identify a color."

If you understood the essential properties and context of what grue and bleen is, then yes

You can tell when things were created down to the year just by looking at them? When you drive through a neighborhood you know the year each house was built just as readily as the the color it is painted?

This seems like "because difference is not a logical contradiction it is arbitrary."

Human languages distinguish between shape and color

If someone argued that chemistry should be split into chemistry done by people with blue eyes and chemistry done by people with other colored eyes, or argued that we should divide chemistry into pre and post 1990 chemistries, or a chemistry of federally recognized holidays, they would be rebuffed for non-arbitrary reasons.

This might be filtered through "personal preference," but personal preference doesn't spring from the aether uncaused and neither do our concepts and languages.

three kids who want to play with the same toys

I go to the car dealership and I am offered whole cars. They don't let me buy a half car for half the money.

I agree with the introduction to Pinter's book Mind and Cosmic Order

The book’s argument begins with the British empiricists who raised our awareness of the fact that we have no direct contact with physical reality, but it is the mind that constructs the form and features of objects. It is shown that modern cognitive science brings this insight a step further by suggesting that shape and structure are not internal to objects, but arise in the observer.

I read this as saying that patterns exist in the mind, not the world.

The question raised is whether a distinctively mathematical explanation (DME) for physical facts truly exists – whether “the facts under question arise from a degree of mathematical necessity considered stronger than that of contingent causal laws.”

If you substitute “logical” for “mathematical,” you can see that the question is very much about whether our analytical (for lack of a better term) knowledge imposes itself on the physical world in a way that is genuinely explanatory. Jha et al. think not, and present a strong argument that all purported DMEs are actually rephrased or disguised versions of the causal explanations that ordinarily obtain.

So what I think needs to be questioned is why we think a hard and fast separation can be made between mind and world in the first place.

I think the sentiment against this relationship goes back to the same basically nominalist and empiricist attitude that animates most analytical philosophy, which is unwilling to admit that ideas - mathematical ideas, logical principles - might possess any kind of intrinsic reality which can't be reduced to 'contingent causal laws'.

Jha et al. argue that various presuppositions such as the principle of mass conservation and the physical integrity of individual objects (this has to be assumed in order to get “whole and unbroken”)

Q3: Why must the LNC hold (under the usual constraints) as a principle of thought?
Q4: Why can’t my cat be on my lap and in Paris at the same time? (constraint: I live in Maryland)

The fact your cat can't be simultaneously be in Maryland and Paris is because you have chosen to define "Maryland" and "Paris" in ways that are mutually exclusive and so one is not the other.

This is Jha et al’s argument, more or less. Math only appears to be causal when we state the problem in terms that remove, or demote to “background conditions,” the physical constraints that actually provide the explanation.

We haven't chosen this arbitrarily though.

Well, I suppose ones attitude towards reductionism and smallism will probably guide the extent to which one thinks quantum foundations is particularly relevant here. On the one hand, there seems to be increasing consensus around the idea that there is no hard dividing line between "quantum and classical worlds." On the other, there is strong consensus in physics that the same living cat cannot be simultaneously in College Park and strolling the the Champs-Élysées.

If we are unsure that being in Rome, New York differs from Rome, Italy, I think we have left empiricism and the natural sciences behind a long time ago.
40m

But for there to be a pair of apples, this presupposes a prior relation between the individual apples.

Jha et al are asking the very question about whether logical principles can be more than contingently causal. They’re not at all “unwilling “ to entertain the idea; it’s the topic of their paper. They do end up arguing against it, true.

He is the author of the blockbuster bestseller Laws and Lawmakers: Science, Metaphysics, and the Laws of Nature (Oxford, 2009), which is soon to be a major motion picture. More recently, he has written the iridescently lyrical “Because Without Cause: Non-Causal Explanations in Science and Mathematics” (Oxford, 2016). Earlier he wrote the gripping page-turner An Introduction to the Philosophy of Physics: Locality, Fields, Energy, and Mass (Blackwell, 2002) and the steamy, heart-rending Natural Laws in Scientific Practice (Oxford, 2000).

1) So, the neo-logos philosophies might say something like, "If nature has patterns, and our language has patterns, and we are derived from nature, it may be the case that our language is a necessary outcome of a more foundational logic". Thus, the logic would not be transcendental, but (for lack of a better term) "immanent" in nature, not some outside observing entity that is detached from it.
2) Kant never explains why our minds would compose such a world, but evolution does.
3) Wouldn't evolution put a connection between the efficacy of the mind and the world?
4) But what is the world outside of an observer?
5) Otherwise it's just "I have believe" without an explanation, which though is valid in terms of asserting an idea, is not necessarily valid as an fully informed reason for why you think that way.

That is, how can being be in one sense "one," i.e. everything interacts with everything else, there are no truly isolated systems

If a correspondence theory of truth demands that we do so, I'd argue that it represents a reductio ad absurdum and should be rejected on that ground.
— J

Very harsh. The word "true" has different meanings in different contexts

So we shouldn't limit a robust correspondence theory to "facts about the world"

Therefore, we can use the Correspondence Theory and say that the proposition "there are infinitely many prime numbers" is true because there are infinitely many prime numbers.

Kant argues in the CPR that we have transcendental knowledge of a world the other side of our senses, but never explains how this could work.

how can we transcend our senses in order to know what has caused these experiences in our senses?

For me, the problem about objects existing in a world independent of any observer, is, what mechanism is there in such a world independent of any observer that relates atom A to atom B but doesn't relate atom A to atom C?

Well, a question here is what it means to be "independent from observers." In a certain sense, everything we think of is, in at least some sense, not independent of observers. We have thought of it, therefore it is not independent of our thought. It is in this very broad sense that Parmenides contends that "the same is for thinking as for being."

I would say the weight of virtually all empirical evidence is that an apple being an apple doesn't depend on us specifically for its existence. When we leave a room, the apples don't vanish. We can tell they continue to exist because they are subject to corruption. being eaten by mice, etc. while we are gone.

We can ‘see’ things through deductive inference that are not empirically knowable. There’s a sense in which even arithmetic is transcendental in that it reveals aspects of nature which sense could not otherwise discern.

Well, a question here is what it means to be "independent from observers.

I would say the weight of virtually all empirical evidence is that an apple being an apple doesn't depend on us specifically for its existence. When we leave a room, the apples don't vanish.

Arithmetic and mathematical reasoning exemplify this because they allow us to grasp necessary truths that, although not sensory, still inform our understanding of the world

I'm simply drawing an analogy to show how there are forms of knowledge, like mathematical deduction, that function beyond sensory input and can help us conceive of Kant’s transcendental structures. Modern mathematical physics is full of examples where mathematical reasoning anticipates empirical confirmation

They’re not real ‘from their own side’ is one of the ways it is expressed. That is quite different to the Platonist take on it but that’s enough for one post.

Justice . . . is concerned with what is truly himself and his own. . . . [The person who is just] binds together [his] parts . . . and from having been many things he becomes entirely one, moderate, and harmonious. Only then does he act. (Republic 443d-e)

Our interest here (I’ll discuss the “justice” issue later) is that by “binding together his parts” and “becoming entirely one,” this person is “truly himself.” That is, as I put it in earlier chapters, a person who is governed by his rational part is real not merely as a collection of various ingredients or “parts,” but as himself. A person who acts purely out of appetite, without any examination of whether that appetite is for something that will actually be “good,” is enacting his appetite, rather than anything that can appropriately be called “himself.” Likewise for a person who acts purely out of anger, without examining whether the anger is justified by what’s genuinely good. Whereas a person who thinks about these issues before acting “becomes entirely one” and acts, therefore, in a way that expresses something that can appropriately be called “himself.”

In this way, rational self-governance brings into being an additional kind of reality, which we might describe as more fully real than what was there before, because it integrates those parts in a way that the parts themselves are not integrated. A person who acts “as one,” is more real as himself than a person who merely enacts some part or parts of himself. He is present and functioning as himself, rather than just as a collection of ingredients or inputs.

We all from time to time experience periods of distraction, absence of mind, or depression, in which we aren’t fully present as ourselves. Considering these periods from a vantage point at which we are fully present and functioning as ourselves, we can see what Plato means by saying that some non-illusory things are more real than other non-illusory things. There are times when we ourselves are more real as ourselves than we are at other times.

Indeed, we can see nature as a whole as illustrating this issue of how fully integrated and “real as itself ” a being can be. Plants are more integrated than rocks, in that they’re able to process nutrients and reproduce themselves, and thus they’re less at the mercy of their environment. So we could say that plants are more effectively focused on being themselves than rocks are, and in that sense they’re more real as themselves. Rocks may be less vulnerable than plants are, but what’s the use of invulnerability if what’s invulnerable isn’t you?

[b]Animals, in turn, are more integrated than plants are, in that animals’ senses allow them to learn about their environment and navigate through it in ways that plants can’t. So animals are still more effectively focused on being themselves than plants are, and thus more real as themselves.

Humans, in turn, can be more effectively focused on being themselves than many animals are, insofar as humans can determine for themselves what’s good, rather than having this be determined for them by their genetic heritage and their environment. Nutrition and reproduction, motility and sensation, and a thinking pursuit of the Good each bring into being a more intensive reality as oneself than is present without them.[/b]


Philosophical Mysticism in Plato, Hegel, and the Present - Robert M. Wallace

My belief is in Enactivism, in that life has evolved for about 3 billion years through a dynamic interaction between an organism and its environment.

In other words, the "mind-independent word" is not the name of an unknown thing, but rather is the name for an unknown cause of known sensory experiences.

On page 233 Sokolowski writes about the "categorial, syntactic activity, along with the intellection that accompanies it," that comes with our "neural lens." It seems to me like this facet of "the internal structure of our sensibility" is useful for elucidating how we can have intelligibilities and essences "present to us."

One of the claims that is often made by the representationalist position that Sokolowski critiques is that many of the properties of objects that we are aware of do not exist "in-themselves," and are thus less than fully real. For example: "nothing looks blue 'of-itself, things only look blue to a subject who sees." If the property of "being blue," or of "being recognizably a door" does not exist mind-independently, they argue, such properties must in some way be "constructed by the mind," and thus are less real.

[b]What I'd like to point out is that this sort of relationality seems to be true for all properties. For example, we would tend to say that "being water soluble" is a property of table salt. However, table salt only ever dissolves in water when it is placed in water (in the same way that lemon peels only "taste bitter" when in someone's mouth). The property has to be described as a relation, a two-placed predicate, something like - dissolves(water, salt).

I think there is a good argument to be made that all properties are relational in this way, at least all the properties that we can ever know about. For how could we ever learn about a property that doesn't involve interaction?[/b]

So, "appearing blue" is a certain sort of relationship that involves an object, a person, and the environment. However, this in no way makes it a sort of "less real" relation. Salt's dissolving in water involves the same sort of relationality. The environment is always involved too. If it is cold enough, salt will not dissolve in water because water forms its own crystal at cold enough temperatures. Likewise, no physical process results in anything "looking blue" in a dark room, or in a room filled with an anesthetic that would render any observer unconscious.

Intelligibilities require syntax. They result from bringing many relations together in such a way that they can be "present" at once. They are a very special sort of relationship. This isn't just because they involve phenomenal awareness. "Looking blue" or "tasting bitter" is a relationship between some object and an observer, but these do not "actualize" an intelligibility. What an intelligibility does is it allows many of an object's relational properties to be present together, often in ways that are not possible otherwise.

For example, salt can dissolve in water. It can also do many other things as it interacts with other chemicals/environments. However, it cannot do all of these at once. Only within the lens of the rational agent are all these properties brought together. E.g., water can boil and it can freeze, but it can't do both simultaneously. Yet in the mind of the chemist, water's properties in myriad contexts can be brought together.

In a certain way then, things are most what they are when their intelligibility is grasped by a rational agent. For, over any given interval, a thing will only tend to manifest a small number of its properties — properties which make the thing "what it is." E.g., a given salt crystal over a given interval only interacts with one environment; all of its relational properties are not actualized. Yet in the mind of the rational agent who knows a thing well, a vast number of relational properties are brought together. If a thing "is what it does," then it is in the knowing mind that "what it does" is most fully actualized. And this is accomplished through syntax, which allows disparate relations to be combined, divided, and concatenated across time and space.

So, rather than the relationship between knower and known being a sort of "less real" relationship, I would argue it is the most real relationship because it is a relationship where all of a things disparate properties given different environments can be brough together.

Well, enactivism is generally presented as a counter to indirect realism and representationalism.

It seems to me that the way we get into trouble here is by positing knowledge of things "in-themselves" as the gold standard of knowledge

I suppose another related issue lies in correspondence theories of truth. One can never "step outside experience," in order to confirm that one's experiences "map" to reality. But this to me simply seems to suggest something defective in the correspondence theory of truth.

One of the claims that is often made by the representationalist position that Sokolowski critiques is that many of the properties of objects that we are aware of do not exist "in-themselves," and are thus less than fully real

Kant's synthetic a priori is the principle that we can discover a priori necessity from a posteriori contingency

Is 1 + 1 = 2 a necessary truth by definition or because in the world 1 + 1 = 2?

If I invent a mathematics and define 1 + 1 = 3, then within my mathematics 1 + 1 = 3 is a necessary truth.

If in the world 1 + 1 = 2, then in mathematics 1 + 1 = 2 would be a necessary truth. However, this depends on justifying that numbers exist in the world.

If numbers did exist in the world, then this would require a relation between 1 and 1. But what has not been shown is the ontological existence of relations in the world.

The ontological existence of relations in the world introduces a number of practical problems, suggesting that numbers don't exist in the world.

Well, the bolded might work in a (Neo)-Platonist, Aristotelian, Thomistic, etc. context, depending on how we define "real from their own side."

It's this relationship between mathematical logic (DME) and contingent causation that is central to the argument.

@Wayfarer: Mathematics doesn’t require numbers to exist as physical objects.
Numbers, therefore, need not exist in the world to guide explanations of physical forces, provided they symbolically represent the appropriate values.
I think the 'practical problem' you're referring to, is how numbers can be real if they don't exist in a physical sense.

@Wayfarer: The fact that mathematical reasoning often anticipates empirical phenomena (such as Dirac’s prediction of anti-matter) suggests a deep correspondence between mathematical structures and causal relations in the world.

@Wayfarer: Whatever mathematical system we invent must, by necessity, align with these constraints to be applicable.

@Wayfarer: You can't get around it by declaring that mathematics is purely arbitrary, because it ain't.

@J: whether “the facts under question arise from a degree of mathematical necessity considered stronger than that of contingent causal laws.”

Indirect Realism, aka Representationalism, holds the position that any world the other side of the senses is fully real. This is why it is called "Realism". However, what we perceive is only a representation of what exists in any world.

The properties we perceive are representations of the properties that exist in the world.

This doesn't mean that the properties in the world as less real, because if they were, we wouldn't have had any perceptions in the first place.

The mind perceives fully real properties, believed to have been caused by fully real properties in the world, which may or may not be the same as what we perceive.

I perceive the colour red even though I believe that the colour red doesn't exist in the world. I perceive pain even though I believe that pain doesn't exist in the world. I perceive numbers even though I believe that numbers don't exist in the world.

If all the contents of experience cannot be said to "exist in the world" in virtue of "only existing in the mind," I don't see how that isn't denigrating the relationships that exist between things and thinking beings as in a way "less than fully real."

If we're allowing the world to be unintelligible and unknowable why not simply allow that Y (the mind) generates itself as a brute fact?

J: whether “the facts under question arise from a degree of mathematical necessity considered stronger than that of contingent causal laws.”

Isn't "contingent causal law" a contradiction in terms?

Enactivism, by contrast, is focused on dissolving the strong subject-object dualism that is presupposed by the division of thought from being.

The term does invite confusion as it stands.

Where in the pertinent text might I find support for such an assertion?

even though I believe that the colour red, pain and numbers don't exist in the world, I believe there is something real in the world that has caused my perception of the colour red, pain and numbers, even though I will probably never know what it is....As I know that my perceptions are real, I believe that the cause of my perceptions are also real, even if I will never know what these causes are.

Kant is not an Innatist, in that a priori necessity is not something we are born with. He uses a transcendental argument that although cognition of inner necessity is prior to a posteriori empirical cognition, such a prior cognition has in fact been determined by a posteriori cognition.

Enactivism, by contrast, is focused on dissolving the strong subject-object dualism that is presupposed by the division of thought from being.

Cartesian anxiety refers to the notion that, since René Descartes posited his influential form of body-mind dualism, Western civilization has suffered from a longing for ontological certainty, or feeling that scientific methods, and especially the study of the world as a thing separate from ourselves, should be able to lead us to a firm and unchanging knowledge of ourselves and the world around us. The term is named after Descartes because of his well-known emphasis on "mind" as different from "body", "self" as different from "other".

They're (physical laws are) called contingent to distinguish them from mathematical necessity, which the authors believe is modally stronger. They're also contingent in the sense that we can easily imagine a physical world with different constants, different explanatory equations, etc. In this world, to be sure, they are nomic.

Ah, but can you?

phenomena like mathematically necessary statements, which we can't even imagine to be otherwise.

I question whether mathematical axioms count as 'phenomena', which is 'what appears'.

I question whether mathematical axioms count as 'phenomena', which is 'what appears'

Quine’s critique where he argued that even mathematical axioms aren’t purely necessary but depend on the broader network of empirical and theoretical commitments.

I think you're wrestling with a real conundrum inherent in modern culture and philosophy.

Kant maintains that the structures of cognition, like time and space, are necessary preconditions that shape any experience we might have; and that they are not derived from or contingent upon empirical experiences.

Common solutions: we introduce other toys so that everyone gets something (not an option in our example); no one gets it (not allowed in our example); they each get the whole thing because they will play with it together (not helpful for consumables, as in our example, which is why we split them); we divvy up not the toy but the time playing with it, take turns, and we can even measure the duration of those and make them equal-ish.

….how does Kant explain the origin of these a priori pure intuitions and a priori pure concepts?

it seems to me that the CPR only makes sense if a priori necessity has transcendentally derived from a posteriori contingency.

I know that I perceive the colour red and feel pain.

I believe that neither the colour red nor pain exist in the world.

I believe that sometimes my perceptions of red and pain have been caused by something this side of my senses, such as dreams and headaches, and sometimes have been caused by something the other side of my senses, such as the wavelength of 700nm or a thistle. [/Quote]

There is that hard dividing line again. Yet causation, information, energy, etc. seem to flow across the boundaries of animal bodies as if there was no boundary at all, so I see no reason to presuppose such a dividing line.

[Quote]
As I don't believe that pain exists in the thistle, I don't believe that the colour red exists in the wavelength of 700nm.

Do you believe that the colour red and pain exist in a world outside a mind?

The question is, how is it logically possible to overcome the dualism between thought and being when life only knows about being through thought?

I question whether mathematical axioms count as 'phenomena', which is 'what appears'
— Wayfarer

I tried to pick the most neutral word possible. Is there a better term for the denizens (another neutral word!) of the "formal realm"? Happy to use it instead.

Quine’s critique where he argued that even mathematical axioms aren’t purely necessary but depend on the broader network of empirical and theoretical commitments.
— Wayfarer

Is there a particular reference you have in mind?

Quine himself had very mixed feelings about whether the laws of logic were subject to revision. I think his final answer was yes, but it's a last resort, and they are very insulated, resistant to revision.
— Srap Tasmaner

Just as an aside, I think Quine believed the laws of logic were true because we could supply clear definitions for all the operators and connectives. This is in Word and Object. In a subsequent work which I haven’t read, The Philosophy of Logic, he extends this to non-classical logics, according to [Susan] Haack. She says that he accepts “a meaning-variance argument to the effect that the theorems of deviant and classical logics are, alike, true in virtue of the meaning of the (deviant or classical) connectives; which, in turn, seems to lead him to compromise his earlier insistence that fallibilism extends even to logic.”

I'd rather say the relationship between some red object and someone seeing that object as red is essentially of the same sort that exists between two meteors colliding in interstellar space

Yet causation, information, energy, etc. seem to flow across the boundaries of animal bodies as if there was no boundary at all, so I see no reason to presuppose such a dividing line.

Well, presumably the number 700 doesn't exist outside minds either, right?

How do we reconcile this seeming multiplicity (the Many) with the equally apparent unity of being (the One)?

But thought is obviously something with being.

I don't think solipsism is good philosophy.....................My take would be that we experience the things we do for reasons, due to causes, etc. and such reasons do not bottom out in the inaccessible and unintelligible as soon as we leave the confines of our own discrete phenomenological horizon.

That appearances are the necessary antecedent occasions for their employment, it does not follow they are derived from them, and in accordance with the theory, they are indeed, not, nor can they be.

I perceive as a phenomenal experience a red object, and believe that there is some unknown thing the other side of my senses that has caused this phenomenal experience. For convenience, I call this unknown thing a red object.

I agree that information flows across these boundaries, but would add that the carrier of the information changes across such boundaries, meaning that there is a dividing line.

Yes, we cannot think about "being" without thoughts, but we can also think about "being" existing outside the mind. Otherwise we come to the conclusion that the Universe didn't begin 13 billion years ago, but only began 200,000 years ago when humans developed language.

Modern science paints a strange picture of the world. Our world is one of tremendous diversity. It includes many types of star and galaxy, a vast number of species, each with their own complex biology, a “zoo” of fundamental particles, etc. At the same time, it paints a picture of a word that is unified. There are no truly isolated systems. Causation, energy, and information flow across the boundaries of all seemingly discrete “things,” such that the universe appears to be not so much a “collection of things,” but rather a single continuous process. How do we reconcile this seeming multiplicity (the Many) with the equally apparent unity of being (the One)? How can we make true statements about the world given this problem?

Yes, we cannot think about "being" without thoughts, but we can also think about "being" existing outside the mind. Otherwise we come to the conclusion that the Universe didn't begin 13 billion years ago, but only began 200,000 years ago when humans developed language.

“I am conscious of my existence as determined in time" is an a priori pure intuition.

“The existence of actual things that I perceive outside myself" is a posteriori empirical experience.

….my a priori pure intuition is possible only by means of a posteriori empirical experience.

What things do we not know through their effects/acts? How could we know anything immanent if not through its effects/acts?

The dividing line is at the eye because the mind/brain is assumed to be the dividing line between the world and the observer. Yet one could make the same sort of case for any dividing line one wants to defend.

How unknown is it if you know what it causes and that it is red?

This seems to be equivocating between different sorts of mind-independence.

The quoted section is only a synthetic judgement based on a pure a priori intuition.

CPR B276
Theorem = The mere, but empirically determined, consciousness of my own existence proves the existence of objects in space outside me.
Proof = I am conscious of my existence as determined in time.
All time-determination presupposes something persistent in perception.
This persistent thing, however, cannot be something in me, since my own existence in time can first be determined only through this persistent thing.
Thus the perception of this persistent thing is possible only through a thing outside me and not through the mere representation of a thing outside me.
Consequently, the determination of my existence in time is possible only by means of the existenceb of actual things that I perceive outside myself.
Now consciousness in time is necessarily combined with the consciousness of the possibility of this time-determination:
Therefore it is also necessarily combined with the existence of the things outside me, as the condition of time-determination;
i.e., the consciousness of my own existence is at the same time an immediate consciousness of the existence of other things outside me.

The quoted part is a pretty good definition of sensation. The assertion as a whole is false, insofar as experience is not of things perceived, but representations of them.

Maybe YOUR a priori pure intuitions according to your transcendental argument, but if Kant with his means for humanity in general the only two are space and time, and they are the necessary conditions for possible experience, it is the other way around from yours.

Certainly we can imagine the early universe, devoid of organic life, but that imagined universe still contains a perspective and a sense of scale provided by the observing mind.

Nothing will ever lead me to understand what a nebula, which could not be seen by anyone, might be. Maurice Merleau-Ponty

We cannot step outside the life-world, because we carry it with us wherever we go.

Whereas, I think you're taking what you understand as the scientific picture of the world as being real independently of any observer, attributing with a kind of absolute or taken-for-granted reality. But then you can't see where 'mind' fits in, because that picture is purportedly 'mind-independent'!

Also see How Time Began with the First Eye Opening

Those who like mythological interpretations may take the birth of Kronos, the youngest of the Titans, as a symbol of the moment here referred to at which time appears, though, indeed it has no beginning; for with him, since he ate his father, the crude productions of heaven and earth cease, and the races of gods and men appear upon the scene - Schopenhauer

This is the purpose of Kant's Refutation of Idealism, an attempt to prove the existence of objects in space outside a representation of them.

This seems to be a transcendental argument.

I cannot literally know the early universe, but I can metaphorically know it.

But naturalism then presumes that the mind which knows it, is the product of that process it only knows metaphorically.

Kant isn’t proving the existence of things as much as he’s proving the material idealist’s denial or doubt of things, is improperly justified.

In B276, Kant starts with the theorem: "The mere, but empirically determined, consciousness of my own existence proves the existence of objects in space outside me."

While that is the case, it is merely beside the point. It needs be shown why external objects as considered by the established idealisms of the day were conceived without proper regard for what came to be posited as transcendental conditions, the foremost being, of course, time.

One must not overlook the significance embedded in propositions such as, consciousness of determinations of existence in time.

Over the course of seven days, you’ve included B276 in every single one of seven consecutive responses to my posts to you, but never say any more than the text itself.

“Kant's synthetic a priori is the principle that we can discover a priori necessity from a posteriori contingency".

Such realistic assumptions so pervade our normal use of concepts that the claims of transcendental idealism disclose their own non-absurdity only after difficult consideration, whereas criticisms of them at first appear cogent which on examination are seen to rest on confusion. We have to raise almost impossibly deep levels of presupposition in our own thinking and imagination to the level of self-consciousness before we are able to achieve a critical awareness of all our realistic assumptions, and thus achieve an understanding of transcendental idealism which is untainted by them. This, of course, is one of the explanations for the almost unfathomably deep counterintuitiveness of transcendental idealism, and also for the general notion of 'depth' with which people associate Kantian and post-Kantian philosophy. Something akin to it is the reason for much of the prolonged, self-disciplined meditation involved in a number of Eastern religious practices.

Don't you think the issue here is the difficulty of questioning the instinctive sense of the reality of the sense-able world?

my understanding is wrong, and that is the issue

synthetic a priori isn’t a principle, it’s a relation of the content of certain kinds of conceptions to each other;

"Synthetic a priori judgments are contained as principles in all theoretical sciences of reason."

.synthetic a priori isn’t a principle, it’s a relation of the content of certain kinds of conceptions to each other

You said synthetic a priori is a principle; Kant says synthetic a priori judgements are principles.

The "Transcendental Analytic" has prepared the way for this critique of traditional metaphysics and its foundations by its argument that synthetic a priori principles can be established only within the limited domain of sensible experience.

At this point in the Critique Kant has completed the largest part of his constructive project, showing how synthetic a priori principles of theoretical cognition are the necessary conditions of the application of the categories to sensible data structured by the pure forms of intuition.

Kant writes about synthetic a priori unity (B264), synthetic a priori concepts (A220), synthetic a priori about appearances (B217), synthetic a priori cognitions (B19) and synthetic a priori judgements (B19).

Of course the synthetic a priori is a principle.

’m inclined to suggest Bergson was Kantian, but the article doesn’t support me, so I better not.

In Time and Free Will, Bergson argued that this procedure would not work for duration. For duration to be measured by a clock, the clock itself must have duration. It must exemplify the property it is supposed to measure. To examine the measurements involved in clock time, Bergson considers an oscillating pendulum, moving back and forth. At each moment, the pendulum occupies a different position in space, like the points on a line or the moving hands on a clockface. In the case of a clock, the current state – the current time – is what we call ‘now’. Each successive ‘now’ of the clock contains nothing of the past because each moment, each unit, is separate and distinct. But this is not how we experience time. Instead, we hold these separate moments together in our memory. We unify them. A physical clock measures a succession of moments, but only experiencing duration allows us to recognise these seemingly separate moments as a succession. Clocks don’t measure time; we do. This is why Bergson believed that clock time presupposes lived time.

Bergson's critique aligns with Kant in suggesting that time is not merely a succession of isolated moments that can be objectively measured, but a continuous and subjective flow that we actively synthesize through consciousness.

Synthetic a priori is not itself a principle; it is the condition of principles, unities, conceptions and anything else to which it applies, in which representations relate to each other in a certain manner, re: synthetically, and, representations are of a certain origin, re: a priori................If you want to say certain forms of representations adhere to the synthetic a priori principle, you haven’t in the least said anything about those forms, other than give them a name, without anything about what it means to be so.

The "Transcendental Analytic" has prepared the way for this critique of traditional metaphysics and its foundations by its argument that synthetic a priori principles can be established only within the limited domain of sensible experience.

Yes, "synthetic a priori" is the name of a principle, not a description…..

It does not follow from the fact all sciences of reason contain synthetic a priori judgements as principles, that instances of particular relations of particular conceptions, are all principles in themselves................................If you wish to stipulate that Kant’s synthetic a priori is the principle that….that’s fine, but I doubt it’s what Kant intended for it.

B356 The term "a principle" is ambiguous, and commonly signifies only a cognition that can be used as a principle even if in itself and as to its own origin it is not a principle.

B358 Thus the understanding cannot yield synthetic cognitions from concepts at all, and it is properly these that I call principles absolutely; nevertheless, all universal propositions in general can be called principles comparatively.

page 13 - At this point in the Critique Kant has completed the largest part of his constructive project, showing how synthetic a priori principles of theoretical cognition are the necessary conditions of the application of the categories to sensible data structured by the pure forms of intuition.

page 85 - Synthetic a priori judgments are contained as principles' in all theoretical sciences of reason.

I could change the wording of my belief….