Tuesday, January 19, 2021

Space, Time, and Logic

 Causal and sorting processes seem to me to be qualitatively different processes from reasoning. Reasoning involves the knowledge of logical truths and the capacity to be affected by logical truths. Naturalistic processes have causes that are restricted to entities within space and time. But logical truths are not located in space and time. If you believe something because you perceive an entailment, this implies that a) there are entailments, and b) we can perceive them. But since these entailments do not exist in space and time, something other than nature has to exist to enable us to perceive them.

Unless, of course, we recollect perceiving those entailments ina past life, as suggested by Plato. I suppose that's possible, too. 

107 comments:

One Brow said...

But logical truths are not located in space and time. If you believe something because you perceive an entailment, this implies that a) there are entailments, and b) we can perceive them. But since these entailments do not exist in space and time, something other than nature has to exist to enable us to perceive them.

Entailments exist because we create them, by the structure of the model we use to simulate and simplify the world. We can perceive what we have created.

Victor Reppert said...

So, if humans had never evolved, the law of noncontradiction would not be true? Contractions might be true if we had invented logic differently?????

One Brow said...

Victor Reppert,
So, if humans had never evolved, the law of noncontradiction would not be true? Contractions might be true if we had invented logic differently?????

The law of non-contradiction is true only in the model of assigning a single logical value to each statement. When we start out by saying each statement must be either true or false, but never both, we end up saying that a statement may never be both true and false (The Law of Non-Contradiction).

bmiller said...

The law of non-contradiction is true only in the model of assigning a single logical value to each statement.

This is obviously false.

David Brightly said...

Not sure how you are using 'entailment' here. Suppose an entailment is a list of sentences which satisfy a certain relation. Putting this relation to one side for the time being, surely we can say that lists of sentences exist in space and time? They are sequences of sounds, or marks on paper, or bits in computer memory.

What is 'perceiving an entailment'? Suppose a belief is an internal state that guides a body in its interaction with the world and that is expressible in language. Suppose 'perceiving an entailment' means applying a rule of inference like modus ponens to linguistic expressions of beliefs, ie, sentences, arriving at a new expression, and then forming a new belief state that would have that expression. What is there about this process that cannot take place in space and time (and matter for that matter)?

One Brow said...

bmiller,
The law of non-contradiction is true only in the model of assigning a single logical value to each statement.

This is obviously false.


I suppose you could create models that allowed multiple logical values to applied to a single statement where non-contradiction still applied. Fair enough.

bmiller said...

David,

Suppose an entailment is a list of sentences which satisfy a certain relation.

How can an entailment be a list of sentences? In your example, it seems to me, that the 'certain relation' is the entailment. For instance one could say that the existence of sentences entail there was an author of the sentences. Neither the list nor the author is the entailment, it is the relation of the one to the other.

If that is true, and the entailment exists in time and space, we should be able to measure it using scientific methods. It must be extended in space, affect other objects in a measurable way and so on. What scientific instrument should we use to measure this physically existent thing?

Victor Reppert said...

One thing that Lewis (in Miracles, the revised third chapter( notes about ground-and-consequent relationships is that they hold necessarily and always. They are in no way dependent upon the positions of the basic elements of the universe nor are they dependent on the laws of physics in this universe. If the positions of the particles in the universe were different, or if the universe had different physical laws than the ones that obtain in the actual world, modus ponens arguments would still be valid, and those that affirm the consequent would be invalid.

David Brightly said...

There is clearly a sense in which entailment is abstract and non spatiotemporal. We can agree on that I think. I would like to focus on specific instances of entailment. Take 'Socrates is a man', 'All men are mortal', 'Socrates is mortal'. The first two sentences taken together entail the third. For an English speaker. This entailment would not be perceived by a non-English speaker. That's important because it highlights the contingency of the English language. There's no necessity to the English language and Roman alphabet so no necessity that the marks above constitute an entailment. Further, we might write our sentences in a tiny artificial language as xA, *AB, xB. That is, x is A, all As are Bs, x is B. But this reveals that entailments of this form follow a pattern. This pattern can be recognised by a machine. It shows I think that some of the meaning of '*', namely 'all', can be captured syntactically. 'All' supports certain patterns of entailment in English. The above is not an entailment if '*' means the same as 'some'.

Whence, then, comes the sense of necessity to entailments? For further thought perhaps.

bmiller said...

David,

There is clearly a sense in which entailment is abstract and non spatiotemporal.

Given that, do you disagree with in this statement of Victor's?

If you believe something because you perceive an entailment, this implies that a) there are entailments, and b) we can perceive them. But since these entailments do not exist in space and time, something other than nature has to exist to enable us to perceive them.

David Brightly said...

Do I disagree? I'm afraid I do. I would say that 'entailment' is the name we give to certain kinds of pattern we find in sets of sentences. We don't perceive entailment as such. Rather we perceive instances of entailment in spatiotemporal things, viz, spoken and written sentences, just as we recognise patterns in material things like wallpaper.

I think the seeming necessity of entailments lies in the contingent but accepted meanings of certain words. The example above depends on how the word 'all' is used in English. The meanings of the words of our language form a fixed foundation to everything we think. It is only with effort that we can imagine 'all' meaning the same as 'some'. And then the entailment vanishes.

bmiller said...

Rather we perceive instances of entailment in spatiotemporal things, viz, spoken and written sentences, just as we recognise patterns in material things like wallpaper.

So it the term "perceive" that you object to? I suppose that one cannot directly see, hear, taste, feel or smell an entailment, so in that sense we cannot perceive it with our senses. Yet we agree that we can tell when an entailment exists and when it doesn't. So it seems that humans are aware of and react to non spatiotemporal entities.

I think this is the issue Victor is highlighting as a problem for naturalists who insist that everything that exists, exists in space and time.

It may be that our thoughts and language are intertwined but why shouldn't they be? Normally we would want our thoughts to correspond to reality for our own sake and to be able to communicate with others.

It is only with effort that we can imagine 'all' meaning the same as 'some'. And then the entailment vanishes.

I really don't follow your point here. Entailments are relationships of certain propositions. You can change the meanings of words, but do you think doing that means Socrates is immortal?

David Brightly said...

So is it the term "perceive" that you object to? Not at all. 'Perceive' is fine, but I agree it doesn't here mean sensory perception. 'Register' perhaps. The idea is that some spatiotemporal change may occur as a result of 'exposure' to an instance of entailment.

Correction: Yet we agree that we can tell when an instance of entailment exists and when it doesn't. Instances of entailment, I claim, are spatiotemporal.

I don't believe in propositions. At least, not in the sense of sentences in some uber-language that directly captures the way things are or might be. The language of God's thoughts, perhaps. I think that the connection between language and the world is mediated by embodied minds.

By the way, BM, may I wish you a Happy New Year in these trying circumstances and say how much I enjoy these conversations.

bmiller said...

Happy New Year to you too David. I too enjoy our conversations. I have a little more time now that my wife tested positive for Covid and I have to stay away from her. In her case the symptoms are just fatigue and a head cold. She can still can taste and smell.

The idea is that some spatiotemporal change may occur as a result of 'exposure' to an instance of entailment.

Correction: Yet we agree that we can tell when an instance of entailment exists and when it doesn't. Instances of entailment, I claim, are spatiotemporal.


It seems to me that you are implying that instances of entailments can only exist in the mind and this entails (ha!) that those instances therefore must be spatiotemporal because the mind is spatiotemporal. It also seems that you have a strong suspcion that human language does not reflect the real world.

I wonder how one could know that human language does not reflect the real world. Wouldn't one have to know how the "real world" was in order to make that judgement?

Regarding instances of entailments existing only in the mind, then we are back to Victor's question:

So, if humans had never evolved, the law of noncontradiction would not be true?

That question is similar to mine regarding Socrates' immortality wrt your modus ponens example.

David Brightly said...

Hello BM. My good wishes for your wife's speedy recovery.

I'm trying to find a path between Victor's apparent realism and the anti-realism that you detect in me! I do think language reflects the world in some way---it helps explain the success of the species, for example---but I can't go as far as VR does. It doesn't seem plausible to me that we can stand outside the world and compare it with our picture of it. Rather, as we discussed recently, the comparison is between two distinct pictures of the world.

Regarding LNC. So, if humans had never evolved, the law of noncontradiction would not be true? It's tempting to see the LNC as 'in the objects', as it were. It looks like a fact about grass that it can't be both green and not green. But it's not a law of physics or any natural science. Unlike the law of gravity, say, it doesn't explain how the world works in any way. Its only contribution is to argumentation. If our inferences lead us to P&¬P we conclude that we have made a false assumption, as in reductio ad absurdum, or that we have made some sort of mistake, an invalid inference, say. Yes, all statements of the form P&¬P are formally false in any representational language, but if we hadn't evolved we wouldn't be making statements or arguments that appealed to LNC.

bmiller said...

Thanks for the well wishes.

Sure. Humans wouldn't be discussing LNC if humans had never existed, but before humans existed grass was not both green and not green in the same sense at the same time was it? Scientists assume that the laws of nature we witness now applied in the past and will also apply into the future. Photosynthesis didn't change when humans came on the scene did it?

It doesn't seem plausible to me that we can stand outside the world and compare it with our picture of it.

Since we are in the world, any picture of the world we have cannot be from outside the world, even the picture that the world as unknowable for someone inside the world.
But what fact tells us that since one cannot stand outside the world it means that we cannot know the world as it is?

But it's not a law of physics or any natural science. Unlike the law of gravity, say, it doesn't explain how the world works in any way.

I'd say LNC is foundational to the laws of physics or natural science. In that sense, the sense that we wouldn't have noticed physical laws without LNC, I would argue that it actually does play a part in explaining how the world works.

David Brightly said...

One last shot before we agree to disagree. Ex falso quodlibet. From a contradiction anything follows. The demonstration of this starting from P&¬P and deriving an arbitrary Q strikes me as an exercise in pure thought. For there are no contradictions in nature for P&¬P to denote.

Likewise the proof by reductio ad absurdum that there is no rational square root of 2. It starts by assuming that there is such a rational root, p/q in lowest terms (ie, no common factor) and showing that both p and q are divisible by 2 in contradiction with the no common factor assumption. Again, an exercise in pure thought because what we show is that there are no such numbers for p and q to denote. What then do the letters mean? I can remember finding this rather disconcerting when I encountered it for the first time as a teenager. We seem to wander off into unreality only to return with a prize about reality!

bmiller said...

We may have to end up agreeing to disagree, but I'm more interested in finding out what exactly we disagree about. I seem to be missing where you are coming from.

Both of your latest examples involve reductio ad absurdum. In both of those cases we are asked to assume that the argument being proposed is false and examine the logical consequences if that were so. At the beginning of each exercise we are supposed to suspend judgement until the exercise is complete. In both cases we are supposed to realize that the consequences that follow are rationally distasteful.

Certainly at the end of the exercise we realize that the premises were faulty/meaningless and in that sense we wandered off into unreality although unwittingly at the time. But we gain information about the world using this method all the time. The Monty Hall Problem is an example of making a guess, checking the consequences and using that information to re-calibrate. Just because we chose door #1 and the prize wasn't behind it doesn't mean all is lost. It just means we've eliminated a formerly live possibility.

Again, an exercise in pure thought because what we show is that there are no such numbers for p and q to denote. What then do the letters mean? I can remember finding this rather disconcerting when I encountered it for the first time as a teenager. We seem to wander off into unreality only to return with a prize about reality!

Is the fact that we can imagine something to be real and it turns out to be impossible for it to be real that is so disconcerting? To me, this is just the process of elimination and is not worrying at all.

David Brightly said...

Let me summarise a bit. I am struggling with Victor's realism with regard to logical phenomena like LNC and entailment. He says they are there outside of space and time yet we have a necessarily non-natural faculty to perceive them. I think it's far too easy to make this kind of argument. It takes but a few sentences but offers no purchase for critique and leaves one hungry for more. I ask myself, Can a question about the nature of thought---for that's how I see it, though I may be wrong---be so readily answered? Or are we perhaps speaking metaphorically? In what analogical sense is LNC or an entailment a thing and in what analogical sense is it perceivable? In anti-realist spirit I gave some reasons for thinking that instances of entailment might be patterns in sentences that we---and suitably designed machines---could recognise. And that LNC is a habit of thought that saves us from the explosion of ex falso quodlibet which vitiates the distinction between truth and falsity without which we fail to survive. And if reductio ad absurdum is a formal sentence juggling then we are spared from finding referents for the terms therein.

bmiller said...

I ask myself, Can a question about the nature of thought---for that's how I see it, though I may be wrong---be so readily answered? Or are we perhaps speaking metaphorically? In what analogical sense is LNC or an entailment a thing and in what analogical sense is it perceivable?

I think Victor's assertion is that LNC is extra-mental and also non-physical. He could be wrong. It seems you think it's only a mental concept, but don't directly challenge him on this aspect. I think that's where I'm confused.

We are talking about LNC, so it must be a thing of some sort. We've agreed it's not the sort of thing that we can perceive with our 5 senses or with scientific instruments so it has to be another sort of thing. There are non-naturalist philosophies that can account for this sort of thing, so it's not a problem for them. No analogies are necessary. Victor thinks it's a problem for naturalists.

Also, I don't think that referring to entailments as patterns that we recognize changes the basic problem. Patterns have no extension in space, weight, taste etc any more than entailments do and so we are faced with the same issues regardless of whether they are useful for survival or not.

David Brightly said...

Regarding LNC again, to explain what it is you have to talk, I think, about sentences and truth, where truth is some relation between language and the world, though this is disputed in some quarters. Victor's Contradictions might be true if we had invented logic differently????? rather suggests that he might accept that LNC, regardless of its status as a entity, was a necessary feature of any natural language worth its salt, and I'd have to agree with the plausibility of that.

Again, I think we must distinguish between a pattern as an abstraction and instances of that pattern. Think of the scale of C major played on a piano. That has extension in time and 'extension' in the frequencies of vibration of air. It's just as real and material as the piano itself. I have an app on my phone that recognises (sometimes!) tunes I sing to it. We shouldn't see the material world as containing just objects (substances) with properties. It contains these things in certain arrangements. And the arrangements are just as real and as recognisable as the things. After all, a thing is usually just parts (smaller, simpler things) in some arrangement, usually involving physical contiguity, and recognising the thing requires recognising the arrangement.

If this makes sense it's but a small step to seeing entailments as patterns in sets of materially realised sentences.

bmiller said...

Sounds like you're arguing for immanent realism rather than anti-realism full stop.

David Brightly said...

Well, maybe. This seems to me not so much a debate about the nature of universals, rather an attempt to shift the conceptual boundary between the material and the immaterial, or the spatiotemporal and the non-spatiotemporal, at any rate.

bmiller said...

It sounds like what you're describing is the inter-relationship of form and matter.

We shouldn't see the material world as containing just objects (substances) with properties. It contains these things in certain arrangements.

This sounds like it could have almost come from an A-T philosopher allowing for a few quibbles. The arrangements (forms) don't exist in the Platonic realm, but are immanent in the instances of things.

David Brightly said...

And in sets of instances, and sets of sets, and so on?

Can the form of the scale of C major be immanent in eight diachronic non-substantial events?

bmiller said...

Depends on the point of reference doesn't it?

A sentence has words as it's material part and the arrangement as it's formal part. Likewise a paragraph has sentences as its material part and the arrangement of the sentences as the formal part. Change the arrangement and the meaning changes or becomes meaningless.

David Brightly said...

Could then the light and dark dots below be matter in the form of an entailment?

Socrates is a man
All men are mortal
Socrates is mortal

Could they constitute or be an entailment? Does this give us reason to think that Victor's claim in the OP that entailments do not exist in space and time might be wrong?

bmiller said...

Socrates is mortal
All men are mortal
Socrates is a man

Same words, same sentences, same light and dark dots. Same amount of ink, photons, lumens, etc. If they could be weighed, they would weigh the same. Is this an entailment?

David Brightly said...

No, different paragraph?

bmiller said...

So the arrangement of the sentences (which have no physically measurable differences) make them different things.

The arrangement of the sentences exist in your mind. I could have read them top to bottom while you read them bottom to top. Where does the entailment physically exist?

David Brightly said...

The two arrangements do have a physically measurable difference. We can't translate and/or rotate (or even reflect) the one into the other.

David Brightly said...

Also, the ordering of the symbols top left to bottom right is indeed an arbitrary convention, as are the shapes of the letter forms and much else about language. But this is not to say that the practice of the convention is deeply mental and cannot be physically realised. Optical character recognition programs for example

bmiller said...

OCR seems to serve the same purpose as eyeglasses do to a scribe. The scribe (human) is actually doing the work.

Also, the ordering of the symbols top left to bottom right is indeed an arbitrary convention, as are the shapes of the letter forms and much else about language. But this is not to say that the practice of the convention is deeply mental and cannot be physically realised.

Right. The same 3 physical sentences on paper mean 2 different things depending on the order a person reads them. For instance, if they were written on a roll of paper, the meaning would vary depending on which direction you rotated the roll or would be meaningless if you didn't speak English.

If someone spoke the 3 sentences to you rather than wrote them, it would be the same syllogism wouldn't it? Yes, there is a physical aspect to speaking and hearing rather than reading and seeing, but the material aspects are completely different. Yet the same syllogism is perceived in your mind. We have eyes to see and ears to hear, but what physical sense organ perceives the syllogism?

David Brightly said...

Where does the entailment physically exist? In the physical symbols. But to perceive it a mind or machine has to process the symbols in some conventional order. Temporal order in the case of speech. I instance OCR to show that such conventions can be observed by machines.

If someone spoke the 3 sentences to you rather than wrote them, it would be the same syllogism wouldn't it? In one sense, obviously not. Sounds are different from marks on paper or dots on a screen. In another sense, yes. There is 'sameness of pattern', isomorphism, realised in distinct media. In a further sense, also yes. Present sentences translated into German, say. I suspect our ordinary use of language is a bit sloppy in making this distinction, but we usually manage to communicate successfully. Maybe not so much when doing philosophy!

What physical sense organ perceives the syllogism? If 'perceive' means undergoes some internal change when presented with the syllogism, as suggested above, then presumably the brain. Tons of evidence that brains are good at recognising patterns in the neural signals supplied by sensory organs, and by extension, patterns in the external environment.

bmiller said...

Maybe not so much when doing philosophy!

HA! Agreed.

I don't think an AT philosopher would disagreement that knowledge of a thing is normally gained through the senses. He would say that the material thing is not actually present in the mind, but instead the form of the thing. But the intellect does not directly come into contact with the thing, but only abstracts the thing's form from the sense stimulation.

That is why the syllogism is the same regardless of the physical means of transmitting it whether one reads it (by sight or touch), hears it, smells it or tastes it.

David Brightly said...

Yes, I appreciate that that is the Thomistic doctrine. Although I'm not comfortable with the jargon and would not speak in those terms, it seems to me that we are saying similar things.

But the intellect does not directly come into contact with the thing, Agreed.

but only abstracts the thing's form from the sense stimulation. I would say 'recognises a pattern' rather than 'abstracts the things form' but the two ideas are nearby.

We will disagree about the nature of the intellect. You think of it as an immaterial thing with various powers, I think of it more as an activity within my nervous system which gets its powers from the structure and properties of said system.

Having encountered Thomism relatively late in life I tend to think of it as a foreign language. I'm like Quine's field linguist trying to figure out what gavagai might mean.

He would say that the material thing is not actually present in the mind, but instead the form of the thing. But here I hit a difficulty. I think of the form of a thing as definite and complete. The information about a thing arriving at my senses is incomplete, so what my intellect abstracts from this must also be incomplete so can at best be an approximation to the form of a thing. Yet I understand the doctrine says it is necessarily one and the same form that exists both in the thing itself and in the intellect, quoting from Feser's Aquinas, p 153. Is this right?

bmiller said...

Yes, I'd say we're close to the same idea but separated by language.

We will disagree about the nature of the intellect. You think of it as an immaterial thing with various powers, I think of it more as an activity within my nervous system which gets its powers from the structure and properties of said system.

The reason the Aristotle considered the intellect as non-material is because it processes non-material things, specifically universals, not just instances of universals. It's a uniquely human thing and separates humans from animals. So you and I are able to talk about syllogisms in general and not just this or that particular syllogism.

Yes, under AT the intellect is a thing that is doing something. But you seem to be defining the intellect as an activity rather than the seat of an activity. That doesn't seem to fit our ordinary language. Otherwise why would we speak of intellectual activity? Activity is just the description of something in motion and it seems to be reifying motion.

But here I hit a difficulty. I think of the form of a thing as definite and complete. The information about a thing arriving at my senses is incomplete, so what my intellect abstracts from this must also be incomplete so can at best be an approximation to the form of a thing. Yet I understand the doctrine says it is necessarily one and the same form that exists both in the thing itself and in the intellect, quoting from Feser's Aquinas, p 153. Is this right?

For some reason I can't access my Kindle version of the book, but let me go from memory.
What you've described about abstracting the form from a particular thing would not be considered an act of the intellect. Animals can do what you described. But animals cannot grasp the concept of this particular thing, say a snake, as having "snakeness" which all snakes have. Each individual instance of a snake will be an imperfect instance of "snakeness" yet we an intellectually recognize it.

I suppose we are at the problem of universals now.

David Brightly said...

Is this helpful?

bmiller said...

Thanks David. That was helpful.

In the meantime I was able to get my old tablet fired up and was able to access my Kindle copy. And so, I'll have to amend what I wrote.

Feser used cats and "catness". In context then, he would say that all cats are a combination of form and matter. The form is the same (a universal) for all cats, and it's each cat's instantiation with matter that makes them different and imperfect.

I think the problem with concluding that since there are no "perfect" cats to perceive that there can be no perfect form of catness is that we must perceive catness somehow in the thing in order to know that the thing is indeed a cat and not something else.

How can the form of catness exist in 2 places at the same time? Could it be the same way that the same Socrates syllogism can exist in 2 books at the same time?

David Brightly said...

I think I have been misled by phrases like 'the form of the thing'. The definite article implies uniqueness. And on p157 Feser says For the reasons just stated, material things cannot possess more than one form precisely because they are material, and intellects can do so precisely because they are not. Surely he should have said substantial form here? The substantial form cat and the accidental forms black and male presumably coexist in a black tomcat?

On p145 he quotes St Thomas: "the active intellect...causes the phantasms received from the senses to be actually intelligible, by a process of abstraction". In other words, it strips away all particularizing or individualizing features of a phantasm so as to produce a truly universal concept or 'intelligible species', leaving you, for instance, with the idea not just of this or that particular cat, but of 'catness' in general, of that which is common to all cats. The abstract concept is then stored in the 'possible intellect'.

This appears to be an account of how an intellect acquires the (substantial) form cat, or equivalently how the form cat comes to exist in the intellect, or indeed, how we learn the concept cat. There is an assumption here that catness in the material cat and catness in the intellect are identical. That's why the intellect has to be immaterial. If it were material and had catness in it it would be a cat. But we saw earlier that our syllogism could exist in both dots on a screen and in air vibrations in radically different but isomorphic ways. Couldn't an isomorph of catness, something that played a role in recognising cats, reacting to cats, and maybe thinking about cats be present in a material intellect, without the intellect becoming a cat? This raises difficult questions as to how we understand 'form'.

bmiller said...

Hi David,

Sometimes discussing things like this with an amateur like me will mislead you. Hope you don't mind when I get things wrong. It's been a while since I've been deep into that book.

I read somewhere that Averroës spent 7 years reading Aristotle (on his own and not officially) before he got an "aha" moment and started writing his commentaries, that Aquinas mostly agreed with much later.

But we saw earlier that our syllogism could exist in both dots on a screen and in air vibrations in radically different but isomorphic ways. Couldn't an isomorph of catness, something that played a role in recognising cats, reacting to cats, and maybe thinking about cats be present in a material intellect, without the intellect becoming a cat? This raises difficult questions as to how we understand 'form'.

I would say the the syllogism is a different kind of thing than a cat. The picture of a cat or a video of a cat would be more analogous to the syllogism in the book or hearing someone state the syllogism. I can pet an actual cat, but I can't pet an actual syllogism. I can throw water on a picture of a cat or the ink on a page with a syllogism and both will be destroyed. Not so with a real cat or a real syllogism. Those both point to the real thing, but aren't the real thing.

David Brightly said...

Hi BM,

Not at all. We are both amateurs. And I don't think Feser, though a professional, is always as careful as he could be :-( Your story about Averroës chimes nicely with my earlier remark that understanding Thomism requires learning a language.

I think the correspondence would be between our syllogism and the (substantial) form of the cat. Both are abstract, immaterial things which can inhere in matter and give us physical things like marks on paper and real felines. In both cases it seems we have to add accidental forms as well, but I guess we can disregard these. And both can exist 'in the intellect'. But we disagree as to how the latter existence might be understood.

Thomism prides itself on its direct realism. The intellect is in contact with the world as it is, largely because one and the same substantial forms exist both in the intellect and in matter. But it strikes me as rather too convenient that the forms turn out to be exactly those aspects of the world that interest us! It could equally be that we find in the world just what our language gives us words for and that we ignore the rest of its complexity. Biology explains how organisms fall not on a continuum but into discrete clumps we call species with similarities within clumps and dissimilarities between clumps. So there are cats and there are dogs. It's not clear to me that this requires that there be in addition the form of cats and the form of dogs.

bmiller said...

I think the correspondence would be between our syllogism and the (substantial) form of the cat. Both are abstract, immaterial things which can inhere in matter and give us physical things like marks on paper and real felines.

Then does the substantial form of the cat inhere in a picture of a cat in the same book as the syllogism? I can draw cats and I can sing of cats but neither the picture or the song are real cats I think. If the ink drawing of a cat is not a cat, then why should we think that writing an English sentence in ink creates an instance of a syllogism rather than a depiction of one?

But it strikes me as rather too convenient that the forms turn out to be exactly those aspects of the world that interest us! It could equally be that we find in the world just what our language gives us words for and that we ignore the rest of its complexity.

I'm having trouble understanding your point of view here. Let me ask some questions.

Do you think language (however it came about and is now) blinds us to aspects of the world? If so, what aspects would those be? Or does language make us see things that aren't there. Again what are those things?

Biology explains how organisms fall not on a continuum but into discrete clumps we call species with similarities within clumps and dissimilarities between clumps. So there are cats and there are dogs. It's not clear to me that this requires that there be in addition the form of cats and the form of dogs.

OK yes, biology tells us that organisms along the lines of discrete types rather than a continuum. But what do you think is the difference among the terms species, clumps, types and forms? How are any of these terms distorting our view of reality?

One Brow said...

Do you think language (however it came about and is now) blinds us to aspects of the world? If so, what aspects would those be? Or does language make us see things that aren't there. Again what are those things?

At the very least, languages interpret the world for us in different ways, causing different perspectives. People who don't have the word for "green" in their language have fewer associations they make toward things that are green. I studied some German and a very small amount of Russian, but I could still sense the difference in how they cause their speakers to see the world, vs. my native English. Have you studied a foreign language, and if so, didn't you notice that?

But what do you think is the difference among the terms species, clumps, types and forms?

Species -- an imprecise method of categorizing individuals by looking for viable offspring

Clumps -- I'm guessing he's referring to something like "populations", groups of individuals that can generally interbreed and interact with each other to do so

Types -- That's your term, but if I were to interpret it, I'd say ecological niches, which may be filled similarly by distantly related species (the wolf type, the herd type, etc.)

Forms -- an attempt to group together individuals by some common characteristics

David Brightly said...

Then does the substantial form of the cat inhere in a picture of a cat in the same book as the syllogism? Technically, no. But there is surely enough 'cat-patternedness' in the picture to make it recognisably of a cat rather than something else. Discreteness versus continuum again.

Why should we think that writing an English sentence in ink creates an instance of a syllogism rather than a depiction of one? Can we depict an abstraction? What would a depiction of the form cat look like? After all, we can only draw pictures of material things, and pace the cubists, from a specific point of view. But maybe some syllogisms could be depicted with a Venn diagram?

I think language reflects our species interests and the size and complexity of the repertoire of patterns we typically have the capacity to learn. So some features of the world are sufficiently insignificant for us that we ignore them. Here's a somewhat contrived example. We have the word 'crows feet' for wrinkles at the corner of the eye. But other skin wrinkles say in the palms and fingers have no specific term. Maybe cosmeticians have one, but that would illustrate my point. Likewise the shapes of clouds perhaps, though clearly meteorologists have a larger vocabulary than the rest of us. Or think of the complex bending and branching geometries of trees. Some of us can recognise tree species from those little silhouettes published in guidebooks. The only words we have to classify these myriads of possibilities are the small number of species names themselves

I wouldn't say that words distort our view of reality. I think they constitute it. (The view not the reality!) Who in the past thought that today in the Anglosphere we would be wrangling over the meaning of 'man' and 'woman' :-(

bmiller said...

I wouldn't say that words distort our view of reality. I think they constitute it. (The view not the reality!) Who in the past thought that today in the Anglosphere we would be wrangling over the meaning of 'man' and 'woman' :-(

Ha!. That's a whole different kettle of fish. However, as a Brit once said “What’s in a name? That which we call a rose - By Any Other Name would smell as sweet.”

I think it's true to say that language expresses the ideas we have in our mind. I don't know how anyone (sane, sober and logically ept) that is using their mind can conclude those ideas do not reflect reality. It may be the case they are being fooled, but the only way they could determine otherwise would be to step outside of their minds.

Can we depict an abstraction?

I think when we write or draw pictures we are depicting the ideas or rather the content of our ideas in our mind.
Can we depict an idea? Maybe with a picture of Socrates with a light bulb over his head? But the light bulb is not really a picture of an idea, but is used to convey the idea of an idea.

But I disagree that we can only draw pictures of material things. I can draw a picture of a unicorn which is not a materially existing entity and other people would recognize it. Language, writing, drawing are means of exchanging or storing ideas, not instantiations of anything other than a instance of a medium to convey an idea.

David Brightly said...

I agree that language expresses the ideas we have in our mind. I like talk of 'ideas'. But surely most of those ideas reflect the appearances of reality to us, as when, say as children we learn to classify the appearances of animals into the appearances of cats, dogs, cows, etc. This because we have no direct contact with animals themselves---their informed matter if you will---but only with the appearances they make on our senses. This is not to say that the appearances are arbitrary, that we can choose them or construct them at will. They are still part of the causal nexus of reality.

We may get into deep water very quickly on this, but here is a picture of a very material unicorn enclosed by a material fence. It's just that there are no such creatures. All unicorns are animals; all animals are material; all unicorns are material. But there are no unicorns. I agree that language, writing, drawing are a means of exchanging and storing ideas. That's how they are used. But can't they be instances of patterns too? The letterform 'a' in all its manifestations is surely a pattern---a circle touching a vertical stroke on the right. Ish!

bmiller said...

Here is a snippet from Feser's Philosophy of Mind: an Introduction that is relevant to our discussion.

This because we have no direct contact with animals themselves---their informed matter if you will---but only with the appearances they make on our senses.

And this is pretty much the theory of forms. It's not the entire combination of form and matter that exists in our mind (or it would get crowded in there very soon), but the form of the thing that is translated from the sense organs to the mind. We can call them patterns, but patterns by themselves have no physicality.

A syllogism can be communicated to us via speech without any written words. Or silently through written words. If a syllogism were a materially existing object like a cat, then we would have to conclude that it both was a noise and was not a noise, or that it was squiggles on paper and not squiggles on paper. Like the Cheshire cat?

bmiller said...

Wouldn't you say that patterns contain information and things that don't contain information are not patterns?

It seems we can't get away from the term "form" since that is the root of the word information. Formula is the arrangement of steps to produce something. If you are informed, you now have acquired information. If you form an idea, you have taken potentially meaningless things and arranged them into something intelligible. And so on.

David Brightly said...

Regarding Feser's argument from his mother's picture. It's a good argument. But it leaves out the possibility that neural 'representations' could be more than mere passive 'objects' to be interpreted by something else. They could be active in the sense that when stimulated they trigger bodily movement of some appropriate sort. Isn't this what intentionality, 'aboutness', comes down to?

Having been brought up on Meccano and Lego and later the natural sciences, when I first encountered the theory of 'form' I thought it meant something like 'structure'. This piece goes here, another piece goes there, and so on. The form says where the pieces go. This would seem to go at least some way towards accounting for the principles of life in living substances. But this does not seem to be what we get from following the process of abstraction from phantasms alluded to above. In fact, I don't understand how the abstraction process gets started. For it seems the active intellect must know in advance what counts as a 'particularising feature'. But let's concede this. We seem to arrive at what I can only call cat-shapedness. But how does a mere cat-shapedness amount to a principle of life in a cat? I think the notion of 'form' here is being made to do more work than it can bear. Having said this, the Thomistic account of abstraction does bear a vague resemblance to theories of learning in neural networks, both natural and artificial. It seems that you can 'train' a prepared neural network to distinguish between photos of cats and dogs. The process is analogous to a child learning when to use 'cat' and 'dog' by being rewarded or corrected by a parent. But it's hard to make clear in what sense the forms cat and dog are 'in' the networks other than that the networks respond correctly with high probability. There is however a vague sense in which all the doggy and kitty particulars within the training examples have been 'smeared away' to leave just two 'centres'. The interesting aspect of this if it's remotely right is its metaphysical implications. For it's saying that nature merely throws up individuals without regard to essence. It's we who do the classification, passing it on quasi-deterministically from one generation to the next. It's just that nature tends to produce clumps for evolutionary and ecological reasons, and we can learn to distinguish the clumps fairly easily. Except for all those beetles...

Isn't it a characteristic of abstractions that they can be instantiated in different 'media'? C major can be a sequence of sounds or marks on paper or keys on an instrument. Have you come across the idea of a mathematical group? If not, my apologies, the WP articles are not particularly easy introductions.

There is no information in chaos (Genesis), and no pattern. So there must be a connection.

bmiller said...

But let's concede this. We seem to arrive at what I can only call cat-shapedness. But how does a mere cat-shapedness amount to a principle of life in a cat? I think the notion of 'form' here is being made to do more work than it can bear.

If "form" meant "shape" in AT then of course you'd be right.

When trying to understand AT philosophy there are unique challenges that very difficult to deal with disregarding any historical, political or religious bias against it. The first is that it introduces some basic concepts that one must become very comfortable with in order to understand the following concepts. That is par for the course for most new subjects, but the problem is that the terms it uses (at least in English) have other normal meanings that muddy the waters. Act, potency, form, matter all have very technical meanings in the philosophy and even if you are sympathetic to it, you can easily get lost while discussing it due to that fact. That problem was further exacerbated due to famous and influential people like Leibniz borrowing some of the terms and using them in his physics theories in a similar but different manner (potential energy for instance).

So it's easy to think "shape" when an AT philosopher uses "form". But form is more than just shape. It's akin to the nature of a thing making it the kind of thing it is. Matter on the other hand can potentially be anything ("for you are dust and to dust you will return"). Hydrogen and oxygen combine to form water with a new nature that is neither O or H2 but H2O. The physical shape is only part of what makes water the thing it is.

We can distinguish between a cat and something merely shaped like a cat by observing how it behaves, how it smells, how it feels and so on....it's nature in other words. How do we explain the difference between a live cat and a dead cat? AT says that the nature of the material has changed. It no longer is the form of a cat, or no longer has the nature of a cat, but something else....cat corpse or whatever.

Regarding AI, my understanding of it is that we are merely using machines to do what we normally do manually but in a more efficient manner just like we do with all other machines. The machines do what we design them to do and they do what we want unless we made a design mistake or the machine malfunctioned. An abacus allows us to count more efficiently, but our minds are really doing the work.

Isn't it a characteristic of abstractions that they can be instantiated in different 'media'? C major can be a sequence of sounds or marks on paper or keys on an instrument. Have you come across the idea of a mathematical group? If not, my apologies, the WP articles are not particularly easy introductions.

I have a technical background but it's more practical and so didn't require mathematics to study groups. But again I think we disagree about what is being instantiated when we sing, read music or point to series of keys on the piano. If C major is a series of sounds in a particular order then a picture of a treble cleft with circles is not C major but is a representation of C major to convey the idea of C major to someone who can read music.

bmiller said...

But it leaves out the possibility that neural 'representations' could be more than mere passive 'objects' to be interpreted by something else. They could be active in the sense that when stimulated they trigger bodily movement of some appropriate sort. Isn't this what intentionality, 'aboutness', comes down to?

Sorry. I don't understand this at all. Are you referring to the picture as a neural representation? Because the point Feser is trying to make is that a picture, just the material object taken by itself, can convey any number of things so it could be "about" a lot of different things (indeterminate). So a purely material thing lacks determinate content. So it follows that if thoughts were purely material things then they too would lack determinate content and conversely if they do contain determinate content, they cannot be purely physical.

David Brightly said...

We agree there is a language difficulty. But Ed Feser is writing for a contemporary audience. He says, In other words, it strips away... as quoted above. Do Thomistic thinkers ever elaborate further on this? Why stop at the species cat when further stripping gets us to mammal, then animal?

Doesn't a representation generally have something in common with what it represents? Some shared pattern or form? Else it ceases to be re+presentative and becomes a mere association. The symmetries of an equilateral triangle and the permutations of three objects (both spatiotemporal) instantiate the one abstract group.

As you say, some straggly bunch of neurons qua bits of matter have no intrinsic intentionality, no determinate content. But suppose said neurons become active when I see my mother, and suppose they are connected via further neurons to muscles so that I say 'Hello, Mum'. Don't they then have a degree of 'aboutness'?

bmiller said...

He says, In other words, it strips away... as quoted above. Do Thomistic thinkers ever elaborate further on this? Why stop at the species cat when further stripping gets us to mammal, then animal?

It took me a while to realize you were quoting from the Feser's Aquinas so I was confused for a while. But I found the passage. I think Feser stopped at "catness" because that was merely the example he was using to illustrate the point. He was talking about cats, not a mixture of mammals or animals.

Doesn't a representation generally have something in common with what it represents?

Yes, but what is the picture representing? It could be representing a thousand different things but we can't know which one or all just from the materially existing picture. But at least some representations in the mind are about a specific determinate thing. So the argument goes, the mind cannot be the merely and wholly physical.

This is actually more of a contemporary philosophical problem than an AT philosophical argument. HERE is a more detailed academic paper that lays it out, including the distinctions AT has with it.

Here's a quote from the beginning summarizing James Ross:
“Some thinking (judgment) is determinate in a way no physical process can be. Consequently, such thinking cannot be (wholly) a physical process.”2

As you say, some straggly bunch of neurons qua bits of matter have no intrinsic intentionality, no determinate content. But suppose said neurons become active when I see my mother, and suppose they are connected via further neurons to muscles so that I say 'Hello, Mum'. Don't they then have a degree of 'aboutness'?

I suppose you could program some cameras and a computer to recognize your Mum and say Hello. But that was you doing the work of the determination (by design), not the pieces of glass, metal silicon and electricity. If material stuff has no intentionality and you are only material stuff, then you cannot have intentionality either. This is why Feser says that what follows is eliminative materialism which denies intentionality altogether and assumes it's an illusion.

David Brightly said...

Hi BM. We seem to have become engaged on about three different fronts! Let's try to get back to the immateriality or otherwise of entailments. In the meantime, regarding James Ross's argument I have some thoughts in a comment thread at Ed F's blog.

David Brightly said...

Here is a little thought experiment. You have a bag containing some tokens. Tokens are either square or round and coloured red or white. Suppose all the round tokens are red. Suppose also that your only language is the predicate calculus, but nobody taught you the rules of inference. But happily you have the proof assistant app PeeAye on your phone. You know ∀x.round(x)-->red(x) is true of the contents of the bag. You put your hand in the bag and draw out a token but don't look. You can feel it's round. Can you infer anything more? No, you don't know any rules of inference. But PeeAye does! You type in the above universally quantified formula and then round(a). It responds red(a). You check. It's right! Now you pull out a square token. You tell the app square(b). It says ⟂, a special symbol that means it can't help. You shrug your shoulders and try again. After a while you begin to trust the app. It's like an oracle. It doesn't always tell you the colour of the token, but when it does it's always right. Now imagine the phone and app internalised in your head. When you say 'PeeAye: round(a)' to yourself you hear 'red(a)' in its electronic voice. And you trust it. It's never wrong. Ok, it's all very far-fetched, but isn't this somewhat like how it feels when we make inferences?

bmiller said...

I'm not sure what you think I should conclude.

One makes successful judgements in a similar/same manner that a successful app does? But that should be unsurprising since someone programmed the app to do just that, in fact you may have been the programmer yourself.

David Brightly said...

Regardless of how it got to be the way it is, the phone running peeaye is wholly material. The story suggests that making an inference/perceiving an entailment needs no more immateriality than the use of language does. There is therefore no special argument 'from reason'.

bmiller said...

Regardless of how it got to be the way

Why should we disregard this?

David Brightly said...

Well, we have to address the question eventually. But do you see how we have changed a metaphysical problem into a historical one? Inference is no longer beyond the power of matter, as it were. The question becomes, Can matter on its own get organised this way? Nagel discusses this 'two question' analysis in Mind and Cosmos.

bmiller said...

This is a true story.

A man in Colorado arranged a shotgun to point at the door of his warehouse and rigged the trigger to pull when the door was opened. Someone was shot entering the door.

He was killed by a shotgun blast or you could say he was killed by the shotgun/string/door/aiming fixture all of which was purely material....regardless of how it got to be that way. Do you think the booby-trap intentionally killed the man? The judge ruled otherwise.

I think this is a similar situation as someone using an app to accomplish something.

bmiller said...

Or maybe we could change the question to: What was the booby-trap inferring when it shot the man?

Did the booby-trap infer that it was an unauthorized person entering the door? It must have since an authorized person would have known there was a booby-trap.

So the logic it used was:
a) No door opening, non-authorized person not entering, don't shoot.
b) Door opening non-authorized person entering shoot.

David Brightly said...

The judge did well. But I'm not sure I understand the connections here. I don't think my story outsources any intentionality to the phone. I'd never suggest that phones have intentionality or intentional states. What I am suggesting is that inference and intentionality are independent: you can have things that have or can do both, either, and neither. The significant thing about inference and logic generally is that it is independent of the meanings of the sentences that the logical constants connect. For example, ¬(P∨Q) has the same truth value as (¬P)∧(¬Q) regardless of the meanings of P and Q and indeed regardless of their truth values. So moving from the first to the second is a matter of spotting the pattern of connectives and sentences in the first and rearranging to get the second. The same goes for rules of inference. Modus ponens says that given that P is true, and that (P-->Q) is true, then we can (validly) infer that Q is true, regardless of the meanings of P and Q. The meanings of the connectives are at one with the rules of inference they participate in. For example, there is no modus ponens like rule for ∨. If P is true and P∨Q is true (which it must be if P is true) it doesn't follow that Q is true. The rule for ∨ is this: if (P ∨ Q) is true and ¬P is true then infer Q is true. Applying rules of inference thus turns out to be a rather shallow business of pattern matching and substitution. Which is why it can be done by symbol manipulation machines like suitably programmed computers with zero intentionality and no grasp of the meaning we place on the symbols.

bmiller said...

So you agree that the booby-trap is inferring that an un-authorized person was entering the building as witnessed by the gunshot, right?

David Brightly said...

No, certainly not! I don't see anything going on that looks remotely like inference. Not in the sense of a kind of mental or speech act. And not in the sense of pattern matching and rearranging in symbol sequences that I'm advocating here. I could say that digestion is going on in the shotgun because it takes in cartridges and then eliminates the products of a chemical reaction. But you'd know I'd be joking.

bmiller said...

The arrangement is doing the same thing as a logic circuit. It changes it's output state when an input changes states. But more importantly, it is making a judgement in the same/similar way the designer wanted it to, as if he was armed and waiting for intruders.

David Brightly said...

I would think that to make a judgement is to decide on the truth or falsity of a sentence. Whether a material system can do this is not the issue. I make no claims as to whether a material system might be intentional (4.25 PM above). What I'm claiming is that making an inference, that is so generating a new sentence from a set of old sentences that we would judge that the new sentence is true if the old ones are, can, perhaps surprisingly, be done mechanically. The shotgun arrangement isn't in the business of making new sentences from old. It's not an inference maker in that sense at all. I rather suspect that you and Victor (going back to his firm commitment in the OP) will think that my conception of making an inference is impoverished or otherwise inadequate.

bmiller said...

The booby-trap could be modeled as an inverter in a digital logic circuit with an associated truth table. A stands for "Door Open" Q stands for "Don't Shoot", 0 for False, 1 for True. Here it is:

A Q
0 1
1 0

In fact, can't we design a digital logic circuit for any truth table?

Here is Modus ponens:
p q p → q
T T T
T F F
F T T
F F T

It isn't surprising that people design and build tools to aid their tasks at all. Why should we be surprised when we design a tool that actually does what it was designed to do? The designer of the modus ponens circuit expects the one's and zero's to follow the truth table pattern or it's broken.

The shotgun arrangement isn't in the business of making new sentences from old. It's not an inference maker in that sense at all.

If that's the case, then neither is the combinational logic circuit built from the modus ponens truth table, right?

David Brightly said...

Aha! I see the problem. I have got you confused between logical connectives and rules of inference. They are not the same thing. The arrow symbol → which I sometimes write as --> for quickness denotes the logical connective called material implication. It's usually read as 'implies'. Its truth table (and only connectives have truth tables) is the one you gave, viz

p q p→q
T T    T
T F    F
F T    T
F F    T

Note that the only row in the table with p and p→q both T (the first one) has q also T. So we can read the table from right to left as it were: if p→q is T and p is T then q must also be T. This gives us the rule of inference for → which is modus ponens. Rules of inference are often displayed vertically because they are tiny arguments

p is true
p→q is true
---------------
q is true

and we usually leave out the 'is true'. This can also be written horizontally to save space,

p, p→q ⊦ q

Read this as 'from (the truth of) p together with (the truth of) p→q infer (the truth of) q'. Similarly, from the truth table of ∨ (or),

p q p∨q
T T    T
T F    T
F T    T
F F    F

reading again from right to left there is just one row (the third) in which p∨q is T and p is F and in this q is T. So we get another rule of inference, boringly called '∨-elimination',

¬p is true (ie, p is false)
p∨q is true
---------------
q is true

See how the truth tables of the connectives are functions of two inputs to one output so can be implemented in electronic 'logic' circuits. But inference is about reading the tables from right to left, ie, inverting the functions. Trouble is, the functions are many-to-one (three input pairs have output T in both tables above), so they don't have inverses. Hence inference cannot be expressed functionally and cannot be computed by logic circuits.

Phew! Hope that makes sense.

bmiller said...

So I should infer that computers that are composed of logic circuits are incapable of inference?

David Brightly said...

No, because they have also have memory and iteration which enables search.

bmiller said...

I think there is no difference as long as I add a clock to my logic circuit.

Memory consists of flip-flops which consist of logic gates with particular truth tables just like the "imply gate" above. Iteration is just a clock that triggers those flip-flops in addition to all the other gates with truth tables to enable the next state. The door opening triggering the next state of the booby-trap could be considered a clock pulse.

David Brightly said...

Backtrack to 12:21 PM:

DB: The shotgun arrangement isn't in the business of making new sentences from old. It's not an inference maker in that sense at all.

BM: If that's the case, then neither is the combinational logic circuit built from the modus ponens truth table, right?

You're right. A circuit implementing the --> truth table is not an inference maker. It operates on truth values themselves (binary 0/1, on/off, voltage high/low, etc) not on sentences that may have truth values. So arguing that the shotgun setup implements --> is not going to persuade me that it does make inferences. Further, I'm not sure why you are trying to persuade me that your shotgun assembly amounts to a computing device at all. Is the idea to deflate the whole concept to nothing by showing that anything anywhere can be thought as such?

Perhaps I am jumping the gun in calling certain material things 'inference-makers'. Because we can see the same patterns in their behaviour as we find in our own inferential behaviour, this seems to me a reasonable way to speak. But let me instead call them mere 'inference-mimickers'. In the discussions of James Ross's argument at EF's blog some critics were reluctant to grant that pocket calculators actually add. They preferred to say that they merely mimic addition. I think Ross himself and also Ed Feser take this line. Would you accept my calling the PeeAye app an inference mimicker?

bmiller said...

David,

I'm trying to see what you think is actually being done by using various examples. It seems to me you think that a computer is doing something fundamentally different than doors, strings and shotguns arranged in a certain manner.

When I point out that a computer is designed to do a certain thing you say you don't consider the fact that it was designed to be part of the metaphysical question of what it does. I don't understand why not.

This is an example:
Because we can see the same patterns in their behaviour as we find in our own inferential behaviour, this seems to me a reasonable way to speak.

We see the patterns in their behavior because we put them there and know how to read them back. Or should I say we assign some ideas to some physical states and arrange physical things to change physical states per our design and then examine the final physical state and therefore the idea we assigned to that state.

The way you present this is as if we should think it is a surprising discovery when it is being used in the way the designer intended. The thing came to be in the first place because it was designed and built for a purpose. How it this not part of the metaphysical question about what the thing is doing?

So if you want to assign "inference mimicker" to your app you're welcome to. I would call it a tool to aid a person interested in performing inference. It may also be useful in setting up my next booby-trap ;-)

bmiller said...

BTW:

jumping the gun

Ha!..just caught that!

David Brightly said...

Yes, I think that it's common-sense to say that computers do something different from what doors, etc, do, and No, I don't see a metaphysical issue in questions about what material things do. Doors swing on their hinges. Computers run programs. We know what these sentences mean.

I'm certainly not surprised that artifacts do what they are designed to do. If I gave the impression otherwise then that's down to expressing myself badly. What I am a bit surprised by is the seeming shallowness of the concept of inference. It's not the deep and mysterious thing---outside of time and space according to Victor---that it unreflectively may seem. At least, that's the drift of what I've been trying to argue here. But then I remember as a teenager when computers were becoming known about, though few people had seen one, that I found it hard to believe that they could do that stuff we called arithmetic that had taken us so long to pick up in the primary school. Later on doing arithmetic lost its mystery too.

Jumping the gun maybe but not jumping the shark I hope!

bmiller said...

Jumping the gun maybe but not jumping the shark I hope!

At least we're getting some exercise :-) Not that easy with the Covid restrictions.

Isn't ontology considered part of metaphysics? That's what I'm getting at when I think we need to consider where a thing came from and why to answer the question of what it is and what it's doing. If someone didn't know a computer's purpose he would use it for the wrong purpose.

What I am a bit surprised by is the seeming shallowness of the concept of inference. It's not the deep and mysterious thing---outside of time and space according to Victor---that it unreflectively may seem. At least, that's the drift of what I've been trying to argue here.

Yes, I get your point. You think a computer is doing the same thing that a human is doing. When it's running a program it is thinking just like a human is doing. I think that is where the disagreement lies.

I don't think a computer is doing the same thing a human is doing. I think it's doing something more like what an abacus is doing. It helps a human do what he wants in a faster or more efficient manner than he could do without the tool. The beads are not "adding" or "subtracting" numbers as they are slid side to side any more than my grocery list is "remembering" what I want to buy at the store. In both of these cases, it is not the material things doing the things of the mind, but the mind designing an aid to think and remember more efficiently. It does that by encoding some idea into material stuff, manipulating that stuff in a manner determined by the mind and decoding after the manipulation.

David Brightly said...

I agree that a computer and an abacus are both tools invented as prostheses for human limitations. But there is a big difference. An abacus cannot add without a human calculator moving the beads and executing an algorithm. The abacus has no internal 'arithmetic dynamic' of its own. But the computer does (my argument at EF). The human calculates by moving the beads on the abacus but he predicts the weather by having the computer calculate.

But I wouldn't say that when a computer is running a program it is thinking just like a human. I don't claim that computers think. Just that one aspect of human cognition, inference, looks computational, or at any rate looks achievable in suitably arranged matter in space and time. And that, for me, demystifies it somewhat.

bmiller said...

I don't think the complexity of the mechanism changes the basic thing it does.

What if I designed an abacus that moved beads after I punched in numbers in a keypad and finally pressed a "+" or "-" button? I crank a wheel causing other wheels to start turning, and bead movers move on linear rails. At the end of the process, I read out the final state of the beads or a even bead reader mechanism with an output to a LED display. Is the abacus now adding because my hands are not physically touching the beads?

It seems to me that this demystifies what calculators and computers are doing.

David Brightly said...

Well, I'm not sure that it comes down to complexity. Has to be complexity of the right sort. I'm no expert on the abacus but from my reading of the WP entry it appears to serve as a register for intermediate results in a calculation, a prosthesis for our very limited short term memory for digit sequences. The operator has to know how to add single digit numbers, or at the very least, how to move the beads to effect single digit additions (with carries), even if he doesn't understand what he is doing as arithmetic. He has to 'internalise' a procedure for working the abacus, or maybe he could refer to a flowchart or an instruction manual of some sort. It seems to me reasonable to say that the operator working the abacus is doing addition. Even if the operator is a human who doesn't understand addition, or a mechanism that has the procedure built into it. Both the operator on its own and the abacus on its own are not up to the job. But in combination they are.

bmiller said...

David,

There is clearly a sense in which entailment is abstract and non spatiotemporal. We can agree on that I think. I would like to focus on specific instances of entailment.

Going back to the beginning, then perhaps where we are talking past each other.
This from Merriam Webster:

instantiate verb
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in·​stan·​ti·​ate | \ in-ˈstan(t)-shē-ˌāt \
instantiated; instantiating
Definition of instantiate
transitive verb

: to represent (an abstraction) by a concrete instance


According to this definition, I've been focusing on the abstraction and it seems to me that you've been focusing on the representation by a concrete instance. So a calculator can represent addition by supplying a concrete instance, but it is not addition itself since addition itself is an abstraction.

Does this look right to you?

David Brightly said...

Yes, so far so good!

bmiller said...

So entailment per se is abstract. It is non spatiotemporal.
Like LNC?

bmiller said...

So, if humans had never evolved, the law of noncontradiction would not be true?

One Brow said...

bmiller,
So, if humans had never evolved, the law of noncontradiction would not be true?

If humans never existed, the Law of Non-contradiction would be non-existent.

David Brightly said...

Hello BM. Putting LNC to one side for a minute, Yes, entailment per se is abstract. So is injustice. We don't rail against injustice the abstraction as such, but rather particular concrete instances of injustice in space and time. Injustices, plural, conveys this. Victor isn't arguing as far as I'm aware for our contact with the non-spatiotemporal from our awareness of abstractions in general. For him there's something special about entailments compared to, say, injustices. A particular---I guess I can't say concrete---individual entailment is itself a non-spatiotemporal thing that we can perceive. I think I can see why one might think this. We seem to be talking about relations between words and sentences or even those mysterious things propositions, and these seem already to contain a good dollop of abstraction. I guess a parallel argument could be made from our contact with number and arithmetic, and we have touched upon this just lately. On the other hand, without the sentences of an entailment written in front of me, or spoken to me, or just 'heard' in the head all in the here and now, there is no determinate entailment to be perceived. Because it's exactly the read or heard words that determine the entailment in question.

bmiller said...

I think we've come back to a certain aspect we've discussed before.

I will point out that if the exact same entailment is transmitted to a mind in a voice, a Power Point slide or a Braille book, then that particular entailment cannot be a merely material entity since it is present in so many different material things. But you see no problem with this and your philosophy of materialism. It seems to me then, that apparently your version of materialism allows for hylomorphism since you see a distinction between the material component of a thing and it's form (or pattern).

If that's the case, then I'm not sure what we disagree about.

David Brightly said...

...then that particular entailment cannot be a merely material entity. But it's an entity of some sort, Yes? This is a point of difference between us. Despite 'entailment' being grammatically a noun I'm very reluctant to grant that an entailment is an entity of any kind. Much more akin to arrangement as discussed above at 9:52 AM. But then it seems rather grandiose to say that if I notice that my wife has changed the arrangement of the furniture in the living room then I must be in contact with something beyond time and space. And is it a deep metaphysical puzzle if the furniture next door is in the same arrangement? I prefer to think not.

bmiller said...

I wonder what you think an entity is and what a noun is then.

You and I both recognize the same "entailment" conveyed by the sound, touch and sight of the different material media and so we have both been able to separate the media from the message. Yet it seems you're saying that this thing we both recognize as existing does not exist.

That doesn't make sense to me.

David Brightly said...

Suppose we have a stack of five coins on the table. Is there a stack entity in addition to the five coin entities? I'd say not. The noun 'stack' denotes a way of arranging things rather than a thing itself. But the stack exists. To deny this is to deny the existence of the coins or the way they are arranged, and that would be false. Likewise 'row', 'square', 'pile', 'scattering', 'pyramid', 'queue', and others. Can't 'entailment' behave analogously?

bmiller said...

Please define entity.

bmiller said...

In this example you stated that a stack of coins existed. So if an entity is an existent thing then the stack of coins is an entity. What is the material part of this particular stack? Coins. So we have formal and material explanation for this entity. They are not separate entities but all make up the single entity "stack of coins".

bmiller said...

Likewise I may have a "stack of bricks". In this case there is one entity with the material aspect of it being bricks rather than coins while the formal aspect is "stack".

But when we ask ourselves what is common between a stack of coins and a stack of bricks, the answer is stack isn't it? It's not the material aspect of the 2 different stacks, but immaterial "stack" aspect of them.

bmiller said...

To be honest, I don't know what you're getting at.

If you want to say that a "stack of coins" can't exist without there being coins in a stack then OK.

I don't get this at all:
Is there a stack entity in addition to the five coin entities?

Who has implied this is the case?

David Brightly said...

I guess I am nibbling away at the idea that entailments are entities existing outside space and time. Largely because I can't make sense of this. I can't offer a decent definition of 'entity'. Maybe 'substance', as I understand it, or 'object' gets close. I don't think 'existent thing' will do because there is just as much vagueness in that term as in 'entity'. I think we might proceed by means of examples and looking at how words are used. Often we can agree that sentences are true when we can't really say (in other words) what they mean!

A further point I want to make about the terms I brought up above is that they are composable. We can take four stacks of five coins, place them on the table at the corners of a square and then we have a square of stacks of coins. Repeat at random places on the table and we have a scattering of squares of stacks of coins. My difficulty in seeing this as an entity is now compounded. Yet we can still make an existential statement, There is a scattering of squares of stacks of coins on the table, and we'd agree it's true, I hope.

Let's call these words nouns of arrangement. When we say, 'There is a stack of books on the shelf' we are saying,
  1. There are some books
  2. They are on the shelf
  3. They are stacked up.
We can analyse away the noun 'stack' by describing an arrangement. But nouns of arrangement are useful for describing composed arrangements. An arrangement is always an arrangement of somethings, even if the somethings turn out to be themselves arrangements of simpler somethings. Thus we can say, There is a row of stacks of books on the shelf. The arrangement is row-of-stack, as it were, and the arranged objects are books, but that's not how we say it in English. Unfortunately, the way we do say it in English leads us to think there may be row and stack entities or objects.

So my proposal is that 'entailment' is a noun of arrangement. This is at least plausible in so far as (written) words are sequences of letters, sentences are sequences of words, and entailments are sequences of sentences, subject to further conditions.

bmiller said...

If your definition of "entity" is only something that exists within space and time then of course something outside of space and time cannot be an "entity". But the dictionary doesn't necessarily confine English users to just that sense.

Here's the first result from Google:
Merriam Webster:

en·​ti·​ty | \ ˈen-tə-tē , ˈe-nə- \
plural entities
Definition of entity
1a : BEING, EXISTENCE
especially : independent, separate, or self-contained existence
b : the existence of a thing as contrasted with its attributes
2 : something that has separate and distinct existence and objective or conceptual reality
3 : an organization (such as a business or governmental unit) that has an identity separate from those of its members


The Cambridge English Dictionary also lists adjectives often used with the term entity such as: abstract entity, autonomous entity, and biological entity.

The fact that there is no physical spatio-temporal component associated with what we both understand to be an "arrangement", doesn't mean it doesn't have existence. If it didn't objectively exist, then maybe one or the other of us would notice it, but not both of us (along with the rest of the human race).

I'll admit if one limits oneself to only thinking physical objects have existence, then "arrangement" is a perplexing topic. I don't think calling it a noun changes things much.

David Brightly said...

The fact that there is no physical spatio-temporal component associated with what we both understand to be an "arrangement"..

Hmmm. You've lost me now. All my recent examples have been spatial in that they are about spatial arrangements of objects at some time, stacks, rows, etc, it's just that they aren't objects themselves, even though the language we use in talking about them is the language of objects. I say that these arrangements are real and we can make objectively true statements using the nouns 'stack', 'row', etc, yet there are no stack and row entities either in spacetime or outside it. This is Ockham's razor: entia non sunt multiplicanda sine necessitate.

bmiller said...

All my recent examples have been spatial in that they are about spatial arrangements of objects at some time, stacks, rows, etc, it's just that they aren't objects themselves,

We switched from entity to object? I think object refers only to material things.

I agree they aren't objects since that implies they have material existence. If "arrangements" are real and have existence but aren't objects what kind of existence do they have?

I say that these arrangements are real and we can make objectively true statements using the nouns 'stack', 'row', etc, yet there are no stack and row entities either in spacetime or outside it.

I think I asked before What are your definitions of noun and entity?
There are many different types of things these terms encompass so there is much room for ambiguity.

David Brightly said...

If "arrangements" are real and have existence but aren't objects what kind of existence do they have? I don't think squares have any existence at all but we could use graph paper or rulers and protractors to show that four coins really, truly were arranged in a square.

What are your definitions of noun and entity? For entity how about individual? A noun is a word that can be preceded by 'a' or 'the' to denote an individual of some kind.

bmiller said...

I don't think squares have any existence at all..

But a thing that doesn't exist in any way is just nothing. I don't think nothing can be called a square, stack or anything else for that matter.

I say that these arrangements are real and we can make objectively true statements using the nouns 'stack', 'row', etc, yet there are no stack and row entities either in spacetime or outside it.

I don't know what these objectively true statements could be about if they depend crucially on denoting nonexistent individuals.

David Brightly said...

Consider: the points (0,0), (1,0), (1,1), and (0,1) form a square or are in a square in the Cartesian plane, Yes? But there's nothing there. And I haven't specified a distance unit, the location of the origin, or the orientation of the plane in space. What can I be talking about? It would seem that space is filled with countless squares and other figures some of which we haven't names for or have yet to imagine. But you knew straight away when I listed the coordinates what I was talking about. This suggests to me that 'square' denotes a relationship that may hold between any four positions in space. And by a species of linguistic 'extension' the term for the relation comes to be applicable to any set of four concrete things whose location in space satisfies the relation. Of course, this explanation builds on a related phenomenon whereby multiple individuals under some connecting relation are denoted by a singular term---couple, quartet, herd, platoon, company, collection, etc, etc, etc.

bmiller said...

But there's nothing there

If there is nothing there in any aspect of existence and then neither I nor anyone else would know what you were talking about. Nothing is the complete absence of existence. The fact that you are talking about something means that this something you are talking about has some form of existence.

David Brightly said...

The fact that you are talking about something means that this something you are talking about has some form of existence.

I don't think this principle holds. I could tell you all about my sister-in-law, Phoebe, where and when she was born, where she went to school, who she married, and so on. You'd understand it all. But I have no sister-in-law.

If there is nothing there in any aspect of existence and then neither I nor anyone else would know what you were talking about.

Accepting this principle for sake of argument, are you then saying,

1. There is nothing there and therefore you don't know what I'm talking about (modus ponens),

or

2. You do know what I'm talking about and therefore there is something there? (modus tollens)

I'm guessing (2), but what is it that's there?

bmiller said...

But I have no sister-in-law.

In this case your fictional SIL exists as a fictional person. Not nothing.


Regarding your 2 questions:
I'm claiming you are making a category mistake.

If you can talk about it, it is not nothing (per Parmenides).
But if you could talk about nothing (which is not possible) your speech would have no content.

David Brightly said...

The adjective 'fictional' is applicable to books and films and statements given to the police, but not to people. You could look into the biography of every person that ever was and you would find that at no time were they ever fictional.

The unit square and Phoebe appear to be counterexamples to Parmenides, then. There is nothing there yet we can talk about them.

bmiller said...

Well it seems you're making nothing out of something. That's a switch.

This is most likely the reason we're talking past each other. I suspect this is a good place to stop.

David Brightly said...

OK. Thank you for engaging with this. Has helped me get some ideas clearer. Much appreciated. DB