Mathematical Truths Causal Relation to What Happens Inside a Computer
I was reading philosophy stack exchange, and I came across this absolutely gorgeous question today:
https://philosophy.stackexchange.com/questions/96799/how-can-mathematical-results-impact-the-physical-world
The "Domino" example is interesting, not because it's necessary to talk about it in terms of dominos - after all, whether it's a domino or a traditional computer, the question is still technically the same - but because it brings the question of causality to the forefront more obviously than if you asked the question about a normal computer. How can a physical system, in which each piece is truly only following local physical rules, be said to produce a certain output "because the number 7 is prime"?
https://philosophy.stackexchange.com/questions/96799/how-can-mathematical-results-impact-the-physical-world
In his 2007 book I Am a Strange Loop, Douglas Hofstadter uses an analogy based on a domino computer.
Indeed, it is possible to build logical doors made of dominoes (see e.g. here) and realize simple programs such as an adder (see here).
For definiteness, lets imagine a domino computer able of determining whether an integer (entered in binary) is prime or not. The result is read on the last domino. If the latter falls, the number is prime. If it remains standing, the number is not prime.
Now, assume we enter the number 7 as input in the algorithm. The last domino falls.
How can we answer the following:
Why did the last domino fall?
Answer 1: Because the penultimate domino made it fall.
Answer 2: Because the number 7 is prime.
The "Domino" example is interesting, not because it's necessary to talk about it in terms of dominos - after all, whether it's a domino or a traditional computer, the question is still technically the same - but because it brings the question of causality to the forefront more obviously than if you asked the question about a normal computer. How can a physical system, in which each piece is truly only following local physical rules, be said to produce a certain output "because the number 7 is prime"?
Comments (37)
Dominos can make logic gates, which means the domino system is turing complete. We already have algorithms to calculate if a particular position is check mate, so it's possible, in principle, to set up a series of dominos such that the last domino will only fall over if, say, Queen to D4 is checkmate given a particular arrangement of pieces.
So, you set up your dominos, you knock down the ones you're supposed to to represent "queen to D4" or whatever, and you watch them go, and eventually the dominos stop falling, and either the final Domino has fallen or it's still standing.
You've seen it fall, so you say "that domino fell because queen to D4 is checkmate".
Seems kinda crazy to me. And yet... how computers work already is not too far removed from that, don't you think?
As for the question in the stackexchange post:
Both correct answers of course, which simply illustrates that there is never just one correct answer to 'what caused X to happen?"
But 2 is debatable. It requires the assignment of meaning to the input, and that meaning can in theory only come from whatever set up the dominoes for this particular purpose. In the absence of the meaning that the purpose gives, the last domino falls only because of it being a causal outcome of some prior state.
Why was my house destroyed?
1) because a hurricane swept through
2) because the strain capacity of pine is below a certain threshold
3) because a butterfly in the Amazon wiggled its wings 6 months ago
Quoting flannel jesus
Well, because the physical system produces that output for certain input values, which in this case happens to correspond to only inputs that, when represented by some standard, happen to encode prime numbers.
Then there is a bigger question: Given the domino computer that lets the last domino fall only if the input is prime, suppose no input is ever made to it. The thing sits in its unfallen state awaiting the initial push. It is already determined that the last domino will fall if the encoding of 7 is entered. It being deterministic, the actual falling of the dominoes need not happen for the result to be determined, which means instantiation of the computation is not necessary for 7 to be prime.
Quoting flannel jesusI agree that it can be Turing complete, but it's hard to implement a normal gate since the domino one can only be used once, and gates need to be used multiple times. So it gets complicated, but I think it can be done anyway. The train track thing was easier since the same track and switch could be traversed multiple times.
Yes, that's just like the prime detector. There's no need even to describe the move. It matters not from whence the queen came, only that the board position includes it being at D4 as part of the state to be evaluated. Apparently you envision the prior state as the fixed setup, and the move in question as the input to be tested.
Yes, just like 'because 7 is prime'. You don't need to see it fall. You need only to realize that it would fall if Q-D4 is entered to know that the move would be checkmate. And if you take epistemology away, Q-D4 is still checkmate even though no move is ever entered and nobody knows about the dominoes. It is still checkmate because the last domino would fall if that input were entered.
Turing machines are deliciously inefficient. Computers are simply far more optimized than these deliberately inefficient devices that accomplish the same thing.
You never asked if the domino setup can be conscious. Answer: Depends who you ask.
https://www.mathnasium.com/ca/blog/20160422-math-in-nature-a-prime-life-cycle-for-periodical-cicadas
"What caused the last domino to fall?"
This prevents at least some of the "resolution by ambiguity" responses we'd be tempted to make (different levels of "why" questions, etc.). The reason the question is interesting -- and hard to answer -- is because it's asking if some kind of mental or "rational" causality is even possible. You can't get to a putative "dual explanation" until you first take a position on this kind of causality, and whether chains of physical causality can ever be grounded in the mental.
I would want to say that the rational/mental meaning supervenes on the purely physical system, in much the same way that the meaning of a word supervenes on the written symbols or spoken phonemes. The difference is that a word-sign represents a non-discursive thought, whereas the domino-sign represents a discursive thought, and provides a validation method. The basis for the discursive domino-sign is the fact that logical reasoning or inference utilizes identifiable, deterministic patterns, and we are able to order the dominoes in such a way that they mimic those patterns. For Aquinas, reasoning is always a kind of ordering, and in this case there is parity between the order inherent in logical reasoning and the order imposed on the dominoes. Ergo, a decision procedure for determining whether a number is prime can be externalized in the relations between material objects in this case binary gates.
Interesting. I think the problem here is that a written symbol or a spoken phoneme already has meaning built into it, in your sense. Consider the written symbol, strictly as a physical object. If I remove a serif from one of the letters, this ought to change something in the meaning of the word, on strict supervenience. It doesnt, of course, because we dont really begin from the physical objects when we consider the word/meaning relation; weve already been taught how a letter of the alphabet works, and why there can be infinitely many permutations of calligraphy that dont affect meaning.
Not to say that supervenience is dead wrong here. Could you work up an example that preserves the basic if A changes, then B changes idea of supervenience as applied to symbols and meanings?
But I do think you are right that there is a difference, and I tried to get at the difference with the ideas of discursivity and a validation method. Yet the similarity is also worth noting, for in both cases a mind is infusing material reality with meaning. In the case of the domino-sign the meaning is somewhat active, and able to yield new information.
Right, thats what we want to say. But is this really a supervenience on strictly physical reality? Lets back up: What makes a letter the key unit of significance, and thus one of the physical items upon which the meaning of a word may supervene? What happens between the serif and the letter, as it were? This is all presumably a matter of convention, but we still must ask, At what point does the meaning get injected? I can say ArchG [that is, the archetypal letter G upon which various calligraphical variations may be built] is, in English, the 7th letter of the alphabet and say similar things about Hs position, and Is, etc. Thats what the physical item means, or symbolizes, along with, perhaps, some pronunciation rules.
But whats the difference, what happened, between, say, an upside-down G, which means nothing, and good old G? How does the correct physical organization produce meaning? Dont we want to say that the meaning comes from somewhere else entirely, namely whatever group of humans have contrived this alphabet? (Or, as you put it, a mind is infusing material reality with meaning.) So by the time we arrive at the level of the meaning of a word supervening on letter-changes, were already working with a dual description, i.e., G as physical item, and G as symbol. Therefore (finally!): Can this really be supervenience between the physical and the mental, if G is already being used as a meaning vehicle? What is the (allegedly) strictly physical description of the subvenient set?
These are real questions on my part. Im not sure about any of it.
I'm inclined to believe that the same principle applies in the case of rational inference and neural biology, contra 'neural reductionism'.
Quoting Leontiskos
Consider this analogy. There is a sentry in a watchtower, looking through a telescope. The watchtower stands on top of a headland which forms the northern entrance to a harbour. The sentrys job is to keep a lookout. When he sees a ship on the horizon, he sends a signal about the impending arrival. The signal is sent via a code - a semaphore, comprising a set of flags. One flag is for the number of masts the ship has, which provides an indication of the class, and size, of the vessel; another indicates its nationality; and the third indicates its expected time of arrival - before or after noon. When he has made this identification he hoists his flags, and then tugs on a rope which sounds a steam-horn. The horn alerts the shipping clerk who resides in an office on the dockside about a mile away. He comes out of his office and looks at the flags through his telescope. Then he writes down what they tell him - three-masted ship is on the horizon; Greek; arriving this afternoon. He goes back inside and transmits this piece of information to the harbourmasters cottage via Morse code, where it is written in a log-book by another shipping clerk, under Arrivals.
In this transaction, a piece of information has been relayed by various means. Firstly, by semaphore; secondly, by Morse code; and finally, in writing. The physical forms and the nature of the symbolic code is completely different in each step: the flags are visual, the morse code auditory, the log book entry written text. But the same information is represented in each step of the sequence.
In such a case, what stays the same, and what changes?
Answer 1: efficient cause
Answer 2: formal cause
Yes. But only because the person who set the dominoes up did so so that they would end that way if they began falling in certain ways, then choose the way the dominoes would begin falling.
Which is the same reason a computer comes up with the answer it comes up with.
It's all because of what those numbers mean to humans.
Those who cannot read English cannot tell the difference between a letter-change and a serif-change, but I used the example precisely because you can read English. English speakers are in a position to understand that, "the meaning of a word supervenes on the written symbols," because they understand that when words change, meaning changes, as is said in the quote by Pascal in my bio. In English serif-changes cannot effect word-changes.
Quoting J
By convention. Word-signs are based on convention.
Quoting J
That's what a sign is: a perceptible reality with an attached meaning. The strictly physical description is simply the perceptible realities, without taking into account any meaning they might possibly have.
Do copyists need to understand the language they are copying? No, although it can be helpful to have such understanding. Similarly, when a copy machine makes a copy, it is copying the physical reality without in any way interacting with the meaning.
I recall a story about Bobby Fisher where he delivered an audible message in a language he did not know. He simply memorized and repeated the sounds he had heard, and the person to whom he delivered the sounds was able to understand their meaning. Similarly, it is possible to find an ancient text which we cannot interpret, and nevertheless know that it has meaning within a linguistic context that we are ignorant of. These are all ways in which the material sign and the formal sign differ; or in which the material aspect of the sign and the formal aspect of the sign differ.
One of the interesting things about the OP is that the dominoes are "copying" a form of human reasoning (about prime numbers), and this domino setup is to the decision procedure for prime numbers what the manuscript of Huck Finn is to Huck Finn, or what Fisher's vocal sounds are to the meaning of those sounds. In all such cases non-mental artifacts are imbued with meaning.
I think that's probably right. From above, "logical reasoning or inference utilizes identifiable, deterministic patterns, and we are able to order the dominoes in such a way that they mimic those patterns."
Quoting Wayfarer
Right, and it is an interesting example.
Quoting Wayfarer
If Morse code can handle all of the nuance of semaphore, and the written language can handle all of the nuance of Morse code, then the fidelity of the original message could be preserved throughout. I would want to say that if everyone involved is from the same culture and equipped with the same linguistic abilities, then the communication will be effective.
Of course the simpler answer is that the meaning stays the same while the physical media change. What are your thoughts?
The letter G, on my understanding, is not a (merely) physical item. To be seen as the letter G, to be recognized as such, is also to apprehend its meaning. One reason we know this is true is that infinitely many versions of the letter may be written physical alterations, in other words without altering our ability to recognize it as the letter G.
So we cant use the letter G as the subvenient term in a supervenience relation between the strictly physical and the strictly mental. The letter G is already a hybrid, it already requires mental content, or meaning (or whatever term is least controversial) in order to be paired with what supervenes upon it.
Now theres no rule that says that the only kind of supervenience is between the strictly physical and the strictly mental. But that is the most common use of the term, and I think its the one we should be concerned about here. Again, remember that we want to wind up with a better understanding of the OP question about the two kinds of causation, re the dominoes. I agree with @Wayfarer that these correspond to efficient and formal cause, but this merely shows us that the problem is a very old one. Formal cause is a sort of blank check, and we need to cash it out in a way that doesnt turn it into just another physical cause in fancy dress.
So maybe the question about the letter G becomes: If there were a strictly physical subvenient item somewhere in the neighborhood, where would we look for it? On my view, it has to be beneath or prior to the letter G itself, which is already a physical/meaning hybrid.
Right. Your recognition of a G supervenes on a much more complex system involving your eyes, optic nerves, and processing in neural networks in your brain.
Yes, I think I have understood what you are asking, but I think my last post to you illustrates where the strictly physical item is located. In one sense you are asking an Aristotelian to show you matter without form, and this is impossible. Incidentally, @apokrisis has written well on these topics, but let me try to say more
This is where I think I most clearly addressed your question:
Quoting Leontiskos
For English speakers the shape, 'G', carries with it an intrinsic meaning. For someone who has no knowledge of the English language, the shape 'G' (presumably) does not carry with it an intrinsic meaning. The non-speaker encounters the physical shape in isolation from linguistic meaning; the speaker encounters the physical shape as already intrinsically bound up with the meaning. For the English speaker the mere shape can only be accessed by prescinding from the attached meaning as far as possible (this is in fact possible albeit difficult, and is called "deautomatization").
So if you are looking for the physical perception in G-conceived-as-a-letter you will not find it, because G-conceived-as-a-letter is already a matter-form compound (where "form" here indicates semantic/linguistic form). Instead, the matter of the G-letter sign is found in G-conceived-as-a-shape. It seems to me that you are looking in the wrong place, and thereby committing a kind of category error. The linguistic form of 'G' is a mental relation, existing in the mind and not in mind-independent reality. Its complement (G-conceived-as-a-shape) is also a mental relation, a conception, albeit an inverted mental relation which is difficult for the English-speaker to access given the speaker's intellectual habit of associating the shape with a linguistic meaning. For the non-English speaker 'G' does not have a linguistic form; it has only a shape form, and therefore the non-speaker is immediately able to access G-conceived-as-a-shape, and they are entirely unable to access G-conceived-as-a-letter (unless they learned English).*
You are a musician. You have an audience of two, one person who has never heard the Beatles and one who has. You play the melody of "Eight Days a Week" on your instrument. One person hears a linguistic form and one does not, although both are hearing a matter-form compound. That which the person who has heard the Beatles does not hear is precisely what is the matter relata in the linguistic matter-form compound; and it is only the person who has not heard the Beatles who is able to easily and fully access this "relata." But the subtlety lies in the fact that for the Beatles-person this relata is a relata or indecipherable aspect of the melody they hear, not a separately existing thing; and for the non-Beatles-person it is a separately existing thingit is the melody itself, devoid of any linguistic or lyrical aspect, and therefore not a relata. In one way these two things are the same thing, and in another way they are different things. Both listeners hear the "material" melody, yet for one it is complete in itself and for another it calls out to the lyrics. The non-Beatles-person's matter-form compound is the matter relata of the Beatles-person's linguistic matter-form compound.
(I think your question about specifying what counts as G-conceived-as-a-letter and what does not count as G-conceived-as-a-letter is a somewhat different topic, because for the English speaker some things count as G-conceived-as-a-letter and for the non-English speaker nothing at all counts as G-conceived-as-a-letter. That question is a question only for English speakers, and it speaks to a much more subtle question of the relation between matter and form in English writing. For Aristotle the matter-form compound is irreducible, and so this phenomenon is everywhere, and like "turtles all the way down." There simply is no getting outside of it.)
* And what is the difference between a linguistic-conception and a shape-conception, or between the speaker's shape-conception and the non-speaker's shape-conception? The former elements of both pairs are more abstract and "mental" than the latter. For example, we could say that, for 'G', the linguistic form builds upon the shape-form which builds upon the ink-form. Or if we wanted to speak in geometrical terms, the linguistic form builds upon two-dimensional shape which builds upon one-dimensional points. The linguistic form is always higher in the sense that it presupposes the lower forms, whereas the lower forms do not presuppose the higher forms. Language users are able to do more with shapes than non-language users.
I think computers - or even neurons - are basically fancy dominos without that limitation.
What I meant by a system of dominoes includes a machine that continually sets them up after they fall according to some program.
Though I'm partial to the idea that, rather than dominos being conscious, or a computer being conscious, or a brain made of neurons being conscious, what if it's the *process* that's conscious? The process is substrate independent, maybe THAT'S the thing that's conscious, and not the thing the process is implemented on.
I believe someone linked to process philosophy earlier in the thread.
If it's substrate independent, there could be "flashes" of consciousness happening all around us as processes occur in various things: meteor swarms, shifting sand dunes, clouds, etc.
There doesn't seem to me to be much difference between dominos falling over and sand grains moving around.
Well, if there are a lot of processes that result in consciousness, and a lot of sand dunes being blown around by the wind, then occasionally, through random shifting of sand particles, some process that results in consciousness should occur through random chance.
Like, we know how it could happen with dominoes, because we can concretely set up that process - not for consciousness, but for some computations - so if you said to me, "if there was a sand storm of dominoes, maybe after millions of years eventually some sequence of those dominoes would line up to implement that process, and then actually run that process", I would know exactly what you mean - because I've seen it, in a video. And I would be like, yeah, that specific arrangement of dominoes could line up, and the process could run.
But I don't know what you mean when it comes to sand. How can you set up a logic gate with sand?
I think these are two different perspectives. We can ask similar questions for any complex system. So in my opinion this goes all the way back to Aristotle. Answer #1 would be the efficient cause and answer #2 the final cause.
Quoting Leontiskos
This is an important clarification, and if I appeared to be asking for matter without form, I shouldnt have been. The question, whether matter can be known without form, is an interesting one, and I tend to agree with Aristotle that it cant, but its not germane to the question that I (and I think the OP) was raising, which is about meaning, not form.
I assume that Aristotle, while averring that its form all the way down, would still call any such combination of matter and form physical. So would I. Otherwise, wed have nothing to contrast with mental. Simply adding form to matter assuming they could even be cognized as separate doesnt make the resulting phenomenon mental. (Lets sidestep phenomenal vs. noumenal, which also doesnt seem germane here.) So what were left with is what most everyone agrees to call the physical world, matter plus form . . . but then theres the pesky issue of meanings, which is something else again. It may be form all the way down, but it isnt meaning all the way down, and thats the problem.
Lets try to rephrase it: We both agree that an upside-down G is matter-plus-form but no meaning (for English speakers). We also agree that the rightside-up G is matter-plus-form-plus-meaning. Here is where the strictly physical and strictly mental supervenience takes place. The meaning is now supervenient on the matter-plus-form, aka the physical object. But my point all along has been that the infusion or importation of meaning occurs at this level, not at the level of words. By the time we get to the meaning of a word supervenes on letter-changes, were already working with a subvenient term (the letter) which involves the physical coupled with a meaning. So the (not very dramatic) conclusion is that the supervenience relation between letter and word cant be called strictly physical / strictly mental. Weve agreed that the letter G already has meaning, and I think we agree that meaning is a mental phenomenon, albeit at times obscure.
Quoting Leontiskos
Based on the above, we now need to make this more precise. We know that the G-shape would be a matter-form compound regardless, since turtles etc. By introducing the idea of semantic/linguistic form, weve moved into a different use of the word form -- indeed, its what Im calling meaning (or perhaps cf. Clive Bells significant form). And you rightly point out that the form in this sense cant be perceived physically. To look for it absent the mental would be a kind of category error. (I leave aside whether its really a good idea to use form in both these senses.) And then everything you say about how the mental and physical intermingle follows.
About the Beatles example: I had trouble following it because I wasnt sure how you were using linguistic form here. Do you mean that the Beatles-person hears the lyrics in their head as the tune plays, while the other doesnt? Why would this mean that the Beatles-person cant hear the matter-relata at all? Im not clear about the indecipherable aspect of the melody. Im sure theres more to it, if you wouldnt mind breaking it down for me. (Or do you simply mean that the non-Beatles person is having a better time of it because unbothered by those silly lyrics? :wink: )
Quoting J
Either matter/form applies everywhere or else it doesn't. If matter/form does not apply to words (and meaning), then matter/form does not apply everywhere. For Aristotle the matter/form duality does not merely apply to "physical" realities, although such realities are the clearest example, and are therefore the starting point. Perhaps we could say that there is a literal sense and an analogous sense of matter/form, but for Aristotle it seems to be more complicated than that.
But this position need not be merely Aristotelian. In this post I gave all sorts of examples of the subvenient term. If you think the subvenient term does not exist, then what do you make of those examples? To take one, when a copy machine makes a copy of a book page do you deny that it is merely copying the subvenient term (the Aristotelian matter-correlate)? And if it is copying the subvenient term, then obviously the subvenient term exists and is specifiable, no?
Quoting J
No, it sort of is meaning all the way down, and we are coming up against the problem of universals. I said:
Quoting Leontiskos
In this argument I was saying that there are things that are more mental and less mental, but there is nothing which is non-mental. All truths are mental, whether they be meaning-truths or shape-truths or ink-truths.
Quoting J
I think you may be conflating meaning with the mental. I would either want to say that an upside-down G has shape meaning but not linguistic meaning, or else I would want to say that it has no (semiotic/linguistic) meaning, but it is nevertheless "mental."
Quoting J
To say that words supervene on the physical is not to say that words supervene on letters, although words do also supervene on letters. To talk about letters qua letters is to talk about entities that already have linguistic meaning, as you have pointed out. My original statement which began this was, "the rational/mental meaning supervenes on the purely physical system." A letter is not a purely physical system. The thing that the copy machine copies is a purely physical system, and mental meaning does supervene on that purely physical system.
Now the deep issue is that meaning never supervenes on what is non-mental simpliciter. If it did then we might think sand dunes are conscious, as some users in this thread apparently do think. In the case of Bobby Fisher, the copy machine, or the archeologists who turn up a dead language, a dormant or implicit meaning is being resuscitated. At the end of the day it would seem that either mind arises from matter or matter arises from mind, and as a theist I hold to the latter. Meaning and intelligibility are part of creation because creation comes from a Mind.
Quoting J
Yes, even when I wrote that post I thought that to be the weakest sentence, but I decided to keep it given the contextual discussion. First, by "linguistic form" I mean that the musical melody has taken on a lyrical form that has become inseparable for the Beatles-person. In their mind the melody is welded to the lyrics. Now it is arguable whether they are able to hear the melody absent the linguistic form (sans deautomatization). For them, the melody is always in-formed by the lyrics and their linguistic meaning. They can't directly access the isolated subvenient term, and the subvenient term only exists in its fullness for the non-Beatles-person.
(We could also think about this in terms of degrees, and say that the subvenient term is more accessible to the non-Beatles-Person than the Beatles-person, but I prefer thinking in terms of polarities for pedagogical purposes. If you wish to press the point that the non-linguistic 'G' is nowhere to be found, then I would submit that the Beatles-person also cannot find the subvenient melody. If you wish to press the point that the subvenient melody is accessible, then I would submit that G-conceived-as-a-shape is also accessible.)
Quoting J
:lol:
Interesting, I didnt know that. So a proposition, say, has something resembling a matter/form division?
Quoting Leontiskos
Yes, I do, if the subvenient term youre referring to is the one that is subsequently going to be part of a supervenience relation with words and sentences. What the copier copies is a physical object, without any meaning level. No surprise, the copier cant enter into any sort of relation with anything, so its copy isnt a subvenient term. Now, if a person reads the copied page, something different happens. The meaning-level of the letters is revealed, first, and then a supervenience relation is created between this subvenient term (a hybrid that comprises both physical objects and meanings) and what supervenes upon it (the meaning of the words, the sentences, the entire page).
For this to make sense, you also have to accept a kind of principle of indiscernibles which states that a copied page can be two things at once, depending on whos looking. Before you reject that out of hand, consider that this principle can explain, among other things, how art happens how a physical object can be simply that, and also, under the right circumstances, a work of art. (cf. Arthur Danto) For that matter, consider transubstantiation . . .
Quoting Leontiskos
Yes, but what they are true about can range on a spectrum from strictly physical to strictly mental. I admit I dont understand why there cant be anything non-mental.
Quoting Leontiskos
Similar perplexity here. I suppose a hardcore idealism would insist that everything is mental, in the sense that everything we know about is a product of our minds . . . but thats a hard sell, and I wouldnt have thought you endorsed it. (Unless you mean that, since according to theism a creator Mind creates matter, then in that sense its all mental? But surely that doesnt alter our human distinctions of mental and physical?) Maybe you could say more about the upside-down G shape understood as (semiotic/linguistic) meaningless but nevertheless mental. Get rid of those scare-quotes! :wink:
I understand the Beatles example now, thanks. The phenomenon youre describing is a common one for musicians, and often vexing. For instance, I would dearly love to be able to hear song X with an innocent ear, unencumbered by theoretical baggage, but since Ive been a working musician all my life and my brain now performs certain kinds of analysis automatically, this is extremely difficult for me. So the Beatles lyrics are like the theoretical baggage, in that both obscure something more basic and, arguably, more purely musical.
I actually don't follow this argument at all. Why is it that the copy machine does not copy and produce the subvenient term? For reference here are some quotes from our conversation. I began:
Quoting Leontiskos
You introduced the notion of a "subvenient set":
Quoting J
...and then I pressed the idea of a copy machine: the physical item is the thing that the copy machine copies. I actually don't see how it can be denied that meaning supervenes on the physical thing that the copy machine produces. If I fax you a letter what you receive is a physical copy, and that physical copy is where the meaning comes from. If the copy is faulty then the meaning will be faulty, and if the copy is accurate then the meaning will be accurate. The meaning is clearly supervening on the physical copy.
It seems to me that on your view copy machines can't exist, because you think a strictly physical meaning-carrier cannot exist. Yet copy machines seem to simply prove, contrary to your presuppositions, that physical objects can have a "meaning level."
Quoting J
Okay, but are you saying that the copy is simultaneously a subvenient term and not a subvenient term? Above I said, "In one way these two things are the same thing, and in another way they are different things" ().
Perhaps you are saying that the dominoes are strictly physical in one sense, and yet in another sense meaning goes before their physicality given their logical ordering? We could utilize a variant of Paley's Watchmaker and say, therefore, that someone who stumbled upon the dominoes would be able to infer a source of meaning (usually called a mind).
Quoting J
On this forum I have found that a lot of people conceive of propositions like objectively floating clouds that can be "tapped into," much like Plato's Forms. For Aquinas (and I believe also for Aristotle) a proposition is always dependent upon a mind, and therefore the material element in the mind that corresponds to the proposition will always accompany the proposition, yes. In the case of an immaterial mind I believe Aquinas would say that there is not knowledge that exists in a propositional or discursive form. Or else, if we don't want to quickly get off track, I would probably need to know how you conceive of a proposition.
Quoting J
Because truth is inextricably tied up with the mental, for we do not know anything apart from our mind. My mind conceives the shapes, the letters, the words, the sentences, the meaning, etc. In one way this represents an increasing sequence of mental-ness, for the latter terms presuppose the mental conceptions of the former terms in addition to other mental conceptions. Still, there is no first term that is a non-mental truth or is known non-mentally.
What's interesting here is that the copy machine does enter into a relation with the thing it is supposed to copy, namely at the level of shape. It is able to recognize and reproduce shapes.
Quoting J
It's not that everything is reducible to mental powers, but rather that there is no object of cognition that is known in a non-mind way; and it seems like your search for a "physical subvenient term" is the search for an object of cognition that is known in a non-mind way.
Quoting J
"...an upside-down G has shape meaning but not linguistic meaning..." The ability to recognize shapes requires a sufficiently sophisticated mind and visual apparatus. You could think about this developmentally. Children can recognize shapes. Older children can recognize letters. Older children can recognize words, etc. Even the recognition of shape in that first step is mental.
Quoting J
Okay, great. But I think it is also worth noting how valuable and incarnational this phenomenon can be. It allows music to take on other dimensions. John Williams' Imperial March was surely better after Star Wars than before. In fact the more closely sound engineers and composers work with other members of a creative endeavor (directors, writers, poets, actors, etc.), the better the result and the less extricable the material music.
I agree that this is a difficult argument to make, because it challenges our basic intuitions about what makes an X an X. I could reply, Right, I think a strictly physical meaning-carrier cant exist, and go on, Yes, the copy is, in a sense, simultaneously a subvenient term and not a subvenient term. But instead, lets look at an analogous situation.
Suppose I showed you an arrangement of objects on the floor of a museum a shoe, a T-square, and a rope, perhaps. We could say several things about what this is. We could identify each object accurately. We could put our mereological hat on and declare it a composite object, and name it Trio. We could also and this is the important part call it an art object. Now what makes it an art object is debatable; it may be as simple as its presence in a museum, or it may be more complicated than that. (Never mind, of course, whether its good art.) But we have to agree that there is indeed this third level of is-ness, of being, without which wed be at a loss to explain almost all of the important facts about the "three objects on the museum floor" situation.
The two factors I would point to as most significant in making Trio an art object are, first, the meaning that is given to it by human consciousnesses, and second, the fact that this meaning is essentially relational, that is, at least one other person has to agree to see Trio as art.
Now for the photocopy. Im arguing that it isnt yet a subvenient term because no human consciousness has entered into that relation with it. Nothing is naturally a subvenient, or supervenient, term, just as nothing is naturally an art object. If someone comes along and reads meaning into the copied page, we can now identify a supervenience relation, with the page + letter-meanings as the subvenient term, and the meaning of the page as a whole as the supervenient term. You wrote, In one way these two things are the same thing, and in another way they are different things," and thats it exactly.
A ways earlier, Id suggested that this is largely a terminological matter, and this is part of what I meant by that. Not much rests on how we choose to designate all this. For most discourse about supervenience, its probably easier to use the familiar shortcut and think of mental meanings supervening on physical objects, as if this were the only way it could happen. I was just wanting to hold out for the more complex formulation, as being (perhaps pedantically) more accurate.
Quoting Leontiskos
Im sure this is true, but arent you begging the question if you talk about a shape meaning? Im questioning whether what we recognize in a shape is any sort of meaning at all. I think I have ordinary usage on my side, for what thats worth. What does that shape mean? is an odd question, except under quite special circumstances.
About music: Yes, theres an up side to non-musical info creeping into our musical experience. When Im working with music, Im certainly grateful that I can place my musical materials theoretically into a larger context. They become richer, and my use of them, hopefully, better.
When you have a grain of table salt and you add more grains of table salt what do you get? More salt. Our terms don't change. And the intuition in a substance metaphysics where particles are ontologically basic is that the world sort of works like this. Yes, we can make many different kinds of things depending on how we combine our pieces, but all the properties of things can ultimately be traced to their physical constituents. In a universe where grains of salt are basic you might be able to make very many different salt structures, salt castles, salt railways, etc., but salt is always salt.
Computation does not seem to work this way. If I start with the input 1 and then add to my input, the prime() function is not going to output more of the same. 1,2, or 3 result in the same output, 1 (true for prime). If we add to our input again we get our first 0. Add more and you get 1,0,1,0,0,0 (5,6,7,8,9,10).
I am not sure if it is a good vehicle for the explanation though. Whenever I have seen explanations of how process deals with superveniance (superengraphment in process) and emergence the examples have been extremely complicated and technical, and I feel like this one might miss something in that you can ask the question "but doesn't it all reduce to dominoes, squares of Turing Machine Tape, etc." I guess the tricky move is in not seeing the substrate as ontologically basic, which is how we tend to think of it.
I don't think this is parallel to the dominoes or language. In fact I think your example is somewhat similar to the idea of shape-meaning, for shape recognition is different from shape meaning (see below).
(Semiotic) Meaning involves the idea that one thing stands for or signifies something else. A sign could be purely conventional, where the the sign and what it signifies have no intrinsic relation. An example of this would be a stop sign, which signifies to drivers that they should stop, yet there is no necessary relation between a stop sign and stopping. At best, your "Trio" is a conventional sign, but I rather doubt that it rises to the level of a conventional sign unless we have some determinate idea of what "art" means. "This is art!" "What do you mean by 'art'?" "I actually have no idea." If its meaning isn't accessible to others, then it doesn't mean anything and is not a conventional sign. But perhaps someone could give a case for what they mean by 'art' in such cases - I will leave this question to the side.
The more important point is that dominoes and language are not merely conventional signs, and therefore even if it can be meaningfully said that the "Trio" is art this does not run parallel to the examples in this thread. Think about Paley's Watchmaker, referenced above. If an alien race discovers the dominoes among our remains 10,000 years from now, they will be able to understand that the dominoes "mean" a decision-procedure for determining whether a number is prime. The physical structure provides this meaning, this capacity, in a way that is not merely conventional.
And if the alien race looks at all of our artifacts of written language, they will to a large extent be able to reproduce the meaning of the language (just as we ourselves have done with dormant languages). The dominoes and language are not purely conventional because the relations between dominoes and the relations between linguistic units are not merely conventional.
Now one might argue that art is high culture and because of this is difficult to explain and recognize. That may be, but I don't think modern art of the type you have described is on par with the dominoes or written language. The relation between the dominoes and prime numbers is altogether different from the relation between "Trio" and "art." Indeed, I would argue that to name the trio "Trio" is more meaningful than predicating of it "art." :razz:
Quoting J
I would argue that it is a subvenient term because someone can come along and understand it. The potential meaning is contained within the physical photocopy. On your reading it would seem that when our race dies out in 10,000 AD the photocopy ceases to be a subvenient term, and then when the alien race deciphers it in 20,000 AD it suddenly becomes a subvenient term again. In one sense this is true, but the pertinent question here is: how is it that the meaning can still be recovered from the physical object after 10,000 years? If what is at stake is merely a matter of human convention, then it couldn't be recovered.
Quoting J
Well, my point was that it is not meaning in the ordinary sense. That's why I gave a dyad to try to explain it:
Quoting Leontiskos
The mental "shape meaning" is perhaps better called shape recognition, and this shape recognition is precisely what constitutes one specification of the physical description of written language. The copy machine recognizes and reproduces shapes and thereby reproduces the subvenient term. You have been objecting that the subvenient term itself has built-in meaning, and therefore it is not the sort of thing upon which meaning supervenes. But have we now agreed that it does not have meaning and that meaning does supervene on this non-meaning term? The point I have been at pains to make is that linguistic meaning supervenes on a subvenient term which is mental, but less mental than linguistic meaning. In this case the less-mental subvenient term is shape recognition.
Quoting J
True. It's also interesting that jazz musicians often testify that knowing the lyrics to a song helps them to play an instrumental cover of the song. For example, Bill Frisell did an album of Beatles covers, and presumably the fact that he knew the words added to the musical quality of the album. Of course one could make more or less of this phenomenon, even to the point of reducing it to the simple question of how accurately the musician is able to mimic the original.
I think what something like Paley's Watchmaker attempts to show is that if only the substrate is ontologically basic then you never end up with watches. Or, in a world full of dominoes with no minds to order them, you never arrive at the domino structure described in the OP. Orderly structures point to ordering minds. As I noted earlier, the order generated within a mind is being infused into material reality.