Yes, IF you have one unit. — Arcane Sandwich

What counts as one unit? We get to choose.

What counts as one unit? We get to choose. — Banno

"We" as in "who"? The individual members of the species Homo sapiens?

Most people in my world know what 666 means, and so in. — frank

The world of Iron Maiden, you mean?

You kinda learn who when you learn your first language, as you learn to use words like "one" and thereabouts. You are part of a community. Them.

↪Arcane Sandwich
You kinda learn who when you learn your first language, as you learn to use words like "one" and thereabouts. You are part of a community. Them. — Banno

If there is a "Them", then there is an "Us". That, presents itself as different options. Hypothetically:

Option 1) Us vs Them
Option 2) Them vs Us
Option 3) There is no match. There is neither Option One nor Option 2, because this is not to be decided in this context. It does not follow from that, however, that it is not to be decided in any context.

I don't think there is anything more to grasping seven than being able to use it. Hence concepts are no more than being able to work with whatever is in question, and thinking of them as mental items in one's head is fraught with complications. — Banno

This is something h.sapiens can do that no other creature can do. If there’s anything problematic it is the inability to see the significance of that.

This is something h.sapiens can do that no other creature can do. If there’s anything problematic it is the inability to see the significance of that. — Wayfarer

Then I'll just share my own Philosophy of Mathematics with you all, since I have not done that so far (oddly enough, not one of you even stopped to realize that fact). In matters of metaphysics / ontology, I have already told you the following: I am a realist, a materialist, an atheist, and a supporter of scientism. From those four premises, you cannot "get" (deduce) my Philosophy of Mathematics, because it is a "hidden" axiom of the system itself (BTW, this is "the language" {it's more of a dialect, really} that I call: "Axiomatese", as in, "Ontologese", which intended to mimic "Portuguese". Pay no great attention to those facts, as they have a sort of Mind-Flayer-ish tone to them. And I am not a Mind Flayer, of that I am certain. Cogito, ergo sum et res cogitans / extensa) <- Yeah, I just "made that up", so to speak.

And that is my humble point. Some absolute restrictions are necessary in language itself, otherwise communication is not cost-effective. In the terms of Thermodynamics, it would be "too costly for not enough benefit". It would be what is now called "a viable option among many others".

Edited for Clarity.

I'm just trying to convey my intuition on how the problem can be thought about, without resorting to "all in the head", and without resorting to mystical Platonic essences... — hypericin

There's a very good book that can be found online Thinking Being: An Introduction to Metaphysics in the Classical Tradition, Eric S Perl. The explanation of the origin of the Forms is highly illuminating. They're not what nearly everyone says they are.

What counts as one unit? We get to choose.

IDK, something about a cat or a dog seems to strongly suggest that it is a single cat or dog; I am not sure how much "choice" we have in the matter. It's just like how I could refuse to use the word "blue" for my car, but it would in no way cease to "look blue to me" simply because of how I've chosen to speak. The same holds for livestock. There are pastoralists all over the world whose languages, and their domestication of the local fauna, occurred in relative isolation, and I don't know of a single one that divides up the units of what constitutes and individual mammal differently.

This seems to be a choice that is very much constrained by what things are, including how they break down into unified wholes. Good luck cutting a sheep in half, declaring that each half is a unit, and then trying to mate them to get more sheep, for instance.

Plus, the idea that a single male eagle and a single female eagle would cease to be single eagles capable of producing single offspring if the "language community" disappeared seems pretty far fetched. This is what happens if you make philosophy of language your first philosophy.

No doubt, the claim that "you need language to do any philosophy," is true. However, the person who champions a reduction of philosophy to neuroscience will be on similarly strong ground: "no one ever does philosophy without their head." The advocate of phenomenology will likewise argue that no one ever did philosophy without first having experiences and perceptions. Hence, this is not a good way to determine first philosophy.

↪Arcane Sandwich You kinda learn who when you learn your first language, as you learn to use words like "one" and thereabouts. You are part of a community. Them.

As noted above, the language community doesn't seem to choose arbitrarily. In some cases, its choices seem more or less made for it. But the way in which these choices are constrained is exactly what realists are talking about.

This is something h.sapiens can do that no other creature can do. — Wayfarer

Don't be too sure. Our ignorance about what other species can do is astonishing. It wasn't so long ago that scientists questioned whether other animals could even think or be conscious. Anyway, would it really affect your point very much if it turned out that some other animals could do it a little bit?

Hence concepts are no more than being able to work with whatever is in question, and thinking of them as mental items in one's head is fraught with complications. — Banno

I can definitely do without "mental items in one's head," though in fairness that's a somewhat tendentious way of putting it. But I'm wondering whether, by choosing "seven" as our example concept, we haven't picked an outlier. Thinking about "seven", it does seem as if there's nothing left once we enumerate all the things we do with it. Are all concepts like this, though? Don't most concepts include structural parts, often definitionally so? Consider a major chord. I can list all the things we do with such chords, but beyond that I can describe what it is that makes this group of three notes a major chord. Why wouldn't we want to call that description the "concept" of a major chord? You see the difference with "seven" -- there isn't a similar description of what comprises "seven" or makes it what it is.

No doubt, the claim that "you need language to do any philosophy," is true. However, the person who champions a reduction of philosophy to neuroscience will be on similarly strong ground: "no one ever does philosophy without their head." The advocate of phenomenology will likewise argue that no one ever did philosophy without first having experiences and perceptions. — Count Timothy von Icarus

All these things are equally valid; but replace philosophy with knowledge. It applies to all knowledge whether science, philosophy, folk psychology, sports. Difference between different areas of knowledge are what you are talking about and your means of engaging with it. In that sense there are no essential features to any given parts of our knowledge and methods can vary. You don't need some specific foundation to philosophy; you just engage with things your're interested in, usually appealing to methods and insights that have accumulated over the years in those particular areas. The things stated in the quote are a field of interest in and of themselves, one I find interesting, and - from my perspective - in the kind of vein of naturalized epistemology or even Dennett's Heterophenomenology - which are kind of just particular uses of cognitive and brain science. But obviously there are many other fields not related to this. I don't have to view the things in the quote as some kind of foundation for a philosophy. They are just a particular area of philosophy I am interested in as opposed to certain other areas. I am not sure one needs some foundation - but then again, everyone settles into particular ways or habits or inclinations of belief in how they do philosophy. But this is no different to how different scientists or historians have certain inclinations or attractions to certain methods, opinions, ideas - and they don't need to be particularly philosophical about it. I have always been interested in things in the most general sense, in any field - history, nature, music, whatever. Philosophy is naturally interesting so it Was always hanging around. What became my first or top intellectual love though would be in the sciences. I would be dipping into areas of philosophy from random books I came across, random classes I chose to take. Things pop out like say philosophy of science. But then I think the real snowballing came when I start to notice parallels between narratives about how brains work (from neuroscience and cognitive science) and discussions in philosophy - people like Berkeley, Popper, Wittgenstein, others. (Philosophy of mind also obviously takes an interest for similar reasons, or because cogmitive/neural science fails to answer all questions). And I cultivate an interest in how those problems are related or diffused, deflated in a certain way. And thats just an interest, not a concerted attempt at making some foundation - albeit, obviously everything we do (and all knowledge) is actually "founded" in the brain, language and experience inextricably connected. But at the end of the day I am just doing the knowledge I find interesting along my inclinations. And in talking about this in a long paragraph all I am doing is questioning this idea of philosophical foundations as some need.

IDK, something about a cat or a dog seems to strongly suggest that it is a single cat or dog; I am not sure how much "choice" we have in the matter. — Count Timothy von Icarus

Of course, there is ample choice. You can count dogs, mammals, retrievers, brown animals, sick animals, etc. The choice of what counts as a numeric unit is fairly arbitrary.

One can account for this by understanding commissive speech acts. — Banno

You probably mean declarative speech acts. Commissive acts commit the speaker, declarative acts declare things to be so. But this seems to overemphasize speech. Everyone alive was born into a world where the rules of chess and counting were already well established. They are social practices that don't require speech acts to bring them into being.

But suppose they did. Suppose you were defining chess for the first time. The speech acts would specify how the game works. But it seems odd to say that the logic of the game, and all its implications (i.e. the value of the pieces) was somehow contained in the speech. The speech specifies the rules. But the rules are not themselves speech, or language in general.

C.S. Lewis - The Discarded Image — Count Timothy von Icarus

I went back and read this section in its entirety. It is an excellent summary of the difference between intellection and ratiocination, as well as the decline of intellection since the modern period. :up:

You probably mean declarative speech acts. — hypericin

Yeah, my error. i used "Commisive" for acts of commission, much as "declarative", now the term is used for acts of commitment. I'll fix it. Thanks.

You are making much the same point I made to @Joshs earlier. Yes, of course these acts take place and are limited by the circumstances around us. Speech acts are part of a language game, an interaction with the world. So yes, the choice is not arbitrary. Better to count the male and female eagles separately, if your purpose it to breed eagles. An odd choice for your example. But we do sell cattle by lots, not just by individuals, and you could certainly buy half a sheep, in various multiples, from the local butcher when I were a wee lad.

Or consider two drops running down a window pane and coalescing. One plus one makes one.

One might mention gavagai here, but Quine's rabbit takes an approach to language that may be quite foreign for you.

So sure, there is a cat and a dog, and there are two animals. The salient bit is that number is a way of thinking about (talking about, treating, approaching) the animals. Being two things is not strictly a state of the world. nor strictly a thought, but a combination of the two. The dichotomy between realism and idealism is misleading.

The notion of "first philosophy" is somewhat antiquated. Aristotle appears to have been obsessed with hierarchy - perhaps it was the only tool he had at hand. More recent thinking might be a bit more holistic - we can do ethics without a complete epistemology or metaphysics; indeed, we probably have no choice about this. Arguing about what comes first is superficial.

But language is a common ground for all philosophy - amongst other things - so having a good grounding in how it works might be helpful.

The choice of what counts as a numeric unit is fairly arbitrary. — hypericin

Yep.

C.S. Lewis - The Discarded Image
— Count Timothy von Icarus

I went back and read this section in its entirety. It is an excellent summary of the difference between intellection and ratiocination, as well as the decline of intellection since the modern period. :up: — Leontiskos

It is interesting to consider the relevance of Kahneman's distinction between fast and slow thinking to Lewis' discussion of intellectus and ratiocination.

Kahneman's work suggests that Lewis' claim that intellection (fast thinking) is higher, is rather questionable.

- Intellection isn't fast thinking. I thought we already addressed this in the past?

Everyone alive was born into a world where the rules of chess and counting were already well established. — hypericin

Sure. What remains is that being a bishop is a way of treating that piece of wood, being a dollar coin is a way of treating that piece of metal and being two animals is a way of treating that cat and dog.

it seems odd to say that the logic of the game, and all its implications (i.e. the value of the pieces) was somehow contained in the speech. — hypericin

Yep. it's the doing that has import here. There needn't even have been an explicit speech act that commissioned the practice. What's salient is the idea that we can count something as something new or different, and build on that.

I'm wondering whether, by choosing "seven" as our example concept, we haven't picked an outlier. — J

Seven only exists as part of an extended language game that includes one and two and a few other things. And a chord is dependent on the scale in which it sits. The first, third, fifth and seventh sound distinctly different, as does a minor chord.

But I'm not clear as to what you are getting at. If you understand that the major is the root, third and fifth, while the seventh chord is the root, third, fifth and seventh note of the scale, is there again something more that is needed in order to have the concept of major and seventh?

In a sense perhaps putting your fingers on the right strings to produce each? The doing?

Yep. it's the doing that has import here. — Banno

If that's the import, then what's the export? What does it "get out of it", in economic and/or thermodynamic terms, and/or systemic terms?

And a chord is dependent on the scale in which it sits. The first, third, fifth and seventh sound distinctly different, as does a minor chord.

But I'm not clear as to what you are getting at. If you understand that the major is the root, third and fifth, while the seventh chord is the root, third, fifth and seventh note of the scale, is there again something more that is needed in order to have the concept of major and seventh?

In a sense perhaps putting your fingers on the right strings to produce each? The doing? — Banno

If you want to talk about Math & Music, then we need more musical concepts here. I would suggest incorporating rhythm, harmony and melody as mathematical and musical concepts into this specific aspect of the discussion.

But I'm not clear as to what you are getting at. If you understand that the major is the root, third and fifth, while the seventh chord is the root, third, fifth and seventh note of the scale, is there again something more that is needed in order to have the concept of major and seventh? — Banno

No, exactly that. I think that is (with a couple of technical tweaks) the concept of a major chord. But I thought you were saying that we didn't have such a concept, only the various things we can do with said chord.

What remains is that being a bishop is a way of treating that piece of wood, — Banno

OK, but the annoying question is, "Wouldn't it have to follow that 'being a piece of wood' is a way of treating Object A [specify space-time coordinates here]?"

Not sure I'm following you.

So the Major is the root, third and fifth. It's that string, that string, and that string - and usually the root, again. That's a doing. Then you slide it up and down the fretboard, and set it out in tab or notation. More doing.

if someone blithely says that the major is the root, third and fifth, but doesn't play or listen, do they understand the concept of a major chord? Does an AI have the concept, becasue it can form the words?

On the other hand, if someone can form the shape and slide it up and down the fretboard, but can not tell us about thirds and fifths, do they "have" the concept?

The concept is what we do, and that includes the conversation.

"Wouldn't it have to follow that 'being a piece of wood' is a way of treating Object A" — J

Yep. This counts as a piece of wood.

But here I am relying on the grammar of the demonstrative, with all that this implies. This is shown.

Humans seem to have evolved to the point of both constructing and exploring mathematics. The counting numbers arise from observations and abilities to distinguish. In my opinion none of math exists in some Platonic realm independent of human brains. These are ideas, not physical objects. — jgill

Sure humans evolved, and so too the ability to count, speak, tell stories and much else besides. But that doesn't mean that Frege's 'metaphysical primitives' such as integers and logical principles, can be legitimately depicted as a result of evolution. The aim of evolutionary theory is to explain the origin of species, not an epistemology.

(Interestingly, in a parallel domain, the linguist Noam Chomsky co-authored a book, Why Only Us?, which looks at why h.sapiens alone possess language ability. 'They focus on the cognitive and computational mechanisms underlying language, particularly Chomsky’s concept of the "Merge" operation, which allows humans to generate infinite expressions from a finite set of elements. They critique simplistic Darwinian explanations for language evolution and emphasize the role of internal cognitive structures over external social or cultural factors. The book combines insights from linguistics, biology, and cognitive science to propose that language is a byproduct of a small genetic mutation rather than a gradual adaptation, challenging traditional narratives about its development' (from jacket description). In other words, an evolutionary leap that enabled a faculty that resulted in exponential differences from non-language-using primates.)

If you can count out seven things, do additions that result in or use seven, double and halve seven... what more is there that you are missing, that is needed before you can be said to have grasped seven?

I don't think there is anything more to grasping seven than being able to use it. Hence concepts are no more than being able to work with whatever is in question, and thinking of them as mental items in one's head is fraught with complications. — Banno

It would indeed be a complication, if that is what had been suggested. But Plato dismisses any such idea:

Is there such a thing as health? Of course there is. Can you see it? Of course not. This does not mean that the forms are occult entities floating ‘somewhere else’ in ‘another world,’ a ‘Platonic heaven.’ It simply says that the intelligible identities which are the reality, the whatness, of things are not themselves physical things to be perceived by the senses, but must be grasped by thought. — Thinking Being, Eric D Perl

Nor are concepts 'in the head' but more like rational principles. But the ability to count and infer is nevertheless indispensable to rational ability, and that is indubitably facilitated by the highly-developed hominid forebrain that we possess. That is what is at issue: the ontological status of such objects of reason (where 'object' is used metaphorically, e.g. 'the object of thought' ) and the ability of reason to grasp them. I don't see how it can be plausibly denied, as either denying it or advocating it relies on the very faculty which is subject of the discussion.

So the Major is the root, third and fifth. It's that string, that string, and that string - and usually the root, again. That's a doing. Then you slide it up and down the fretboard, and set it out in tab or notation. More doing.

if someone blithely says that the major is the root, third and fifth, but doesn't play or listen, do they understand the concept of a major chord? Does an AI have the concept, becasue it can form the words?

On the other hand, if someone can form the shape and slide it up and down the fretboard, but can not tell us about thirds and fifths, do they "have" the concept? — Banno

This is tricky. I want to say that a major chord is not "that string, that string, and that string." If I'd given such an answer back in school, I would have flunked, at any rate. We both know that the term describes three notes, sounded simultaneously, that stand in a certain relation to each other. That's what I'm calling "the concept."

It sounds like you've moved to talking about what it would take to have that concept, and here we're in agreement. Someone who doesn't listen, someone who only goes up and down the fretboard, and "someone" who is an AI do not have the concept, quite right. But I thought you were saying that "concept" itself is doing no useful work here, and I'm still not seeing that.

"Wouldn't it have to follow that 'being a piece of wood' is a way of treating Object A"
— J
Yep. This counts as a piece of wood.

But here I am relying on the grammar of the demonstrative, with all that this implies. This is shown. — Banno

So the "counts as" locution stops with the demonstrative? If I could give a sufficiently accurate set of coordinates for the location of the object we "count as" a piece of wood, along with a chemical description, wouldn't we have to pursue the matter further? "'Being at [coordinates] and consisting of [chemical analysis]' is a way of treating Object A-prime"? And you can see where this is going . . . right into the realm where you can't use demonstratives at all, or at least not in any ordinary-language way.

I'm not trying to refute this way of talking, I just want to understand what it commits me to.

That is what is at issue: the ontological status of such objects of reason — Wayfarer

Is that an objection to my proposal?

I'll go over the first part of the argument, again, since it's a while it was addressed and it answers what you have said. But let's move away from numbers for awhile.

We can set up a domain of discourse that contains Alice, Bob and Charlie. Alice and Bob are brave. Charlie isn't.

Simple logic tells us that since Alison Bob are brave, something is brave. That's a first order application of existential generalisation. We can fiddle with the grammar and say things like since something is brave, there are brave things, or braveness exists. Doing this does not commit us to there being anything "in the world" except Alice and Bob and Charlie. Our domain of discourse, and our ontological commitment, remains unchanged.

It sounds like you've moved to talking about what it would take to have that concept — J

Well, yes, in that to have the concept and the concept amount to the same thing... the actions performed.

Again, it's not that someone can play various major chord, record and read them, and recognise them when they hear them, and yet not have, or not understand, what a major chord is, because they are missing something more... the concept.

So the "counts as" locution stops with the demonstrative? — J

All language stops with showing and doing.

But again, I don't think I've quite understood your point.