If "count" is defined as determining the quantity of, then it is an act of measuring. — Metaphysician Undercover

You are saying that counting is the same as measuring, but that can’t be right. Otherwise, what unit of measurement do we use to count? Litres? Metres? Hours? Bananas?

As I said, that's an order, one imagined thing after the other, it's not a quantity. — Metaphysician Undercover

How is it that we can (really) order imaginary things, but we cannot (really) count imaginary things?

Luke, learn how to read! The representations, (which is what we count), exist as symbols. I did not say that the imaginary things exist as symbols. You've taken the sentence out of its context so that it appears possible that I might be saying what you claim to interpret. Though context clearly shows otherwise. This is exactly what I mean, you interpret, and represent what I say, in a totally incorrect (not what I intended), strawman way, solely for the purpose of knocking it down. Your MO, to ridicule, is itself ridiculous. — Metaphysician Undercover

You're just going to gloss over your accusation that I misquoted you, and the fact that I didn't?

I never took your position to be that "imaginary things exist as symbols [and representations]". Quite the opposite. This was, instead, the point I was trying to make and what I was trying to get you to understand. Perhaps you should learn to read.

When counting sheep, the imaginary sheep have no existence other than as imagined sheep. The imagined sheep are representations of real sheep, but they only exist as representations. That is to say, for example:

imaginary things only exist as their symbols or representations, and if we are really counting those symbols or representations, then we are really counting the imaginary things. — Luke

imaginary things have no existence other than their symbols or representations — Luke

There don't need to be any real sheep in order to make the count. One could as easily count unicorns instead of sheep. Or Enterprise captains. Or any other fictional entities.

You then stated that "we can only count representations of the imaginary things, which exist as symbols."
— Luke

That's a false quote. I said "we are not really counting the imaginary things, but symbols or representations of them". You said they only exist as symbols, not I. — Metaphysician Undercover

Nope.

we can only count representations of the imaginary things, which exist as symbols. — Metaphysician Undercover

Luke just seems to be always looking for the easiest ways (mostly fallacious) of making me appear to be wrong, no matter what I say. — Metaphysician Undercover

You don't need my help with that.

You asserted that natural numbers are not countable because they are imaginary:

There is really no reason to attempt to count the natural numbers, when we know that this is impossible because they are infinite. And numbers are not even countable objects in the first place, they are imaginary, so such a count, counting imaginary things, is a false count. Therefore natural numbers ought not be thought of as countable. — Metaphysician Undercover

You then stated that "we can only count representations of the imaginary things, which exist as symbols."

I pointed out that imaginary things have no existence other than their symbols or representations, so counting the symbols or representations is, in fact, counting the imaginary things. For example, counting imaginary sheep is really counting.

You tried arguing that imaginary things cannot exist only as their symbols or representations, and implied that they must have some real existence despite being imaginary. That is, you implied that all representations or symbols (including those of imaginary things) must necessarily represent or symbolise something real.

You then claimed that imaginary things are "a self-contradicting set of ideas". (Perhaps others will appreciate the irony that ideas are also imaginary things.) Presumably this claim was based on your implied, unfounded stipulation that all representations or symbols must necessarily represent or symbolise something real. So it's no wonder that you failed to tell us why imaginary things are self-contradicting ideas.

Then what is (represented by) an "imaginary thing"?
— Luke

A faulty, self-contradicting set of ideas, which has found a place of acceptance in common parlance. Unfortunately, our language is full of these. — Metaphysician Undercover

How is an imaginary thing a self-contradicting set of ideas?

Nothing exists as it's representation, or else we would not call it a representation, it would be the thing itself.. — Metaphysician Undercover

Then what is (represented by) an "imaginary thing"?

Symbols are not imaginary. — Metaphysician Undercover

That's right. I never said they were.

So we are not really counting the imaginary things, but symbols or representations of them
— Metaphysician Undercover

Imaginary things only exist as symbols or representations; that's what makes them imaginary. You therefore acknowledge that we can count imaginary things.
— Luke

Call it counting then if you want — Metaphysician Undercover

I didn't call it counting; you did. You said: "So we are not really counting the imaginary things, but symbols or representations of them."

If imaginary things only exist as their symbols or representations, and if we are really counting those symbols or representations, then we are really counting the imaginary things.

Counting symbols or representations is really counting. If you're not counting imaginary sheep to help you sleep, then what would you call it instead of "counting"?
— Luke

I'd say it's ordering, not counting. — Metaphysician Undercover

Why?

It's called "counting sheep" not "ordering sheep". Are you saying we cannot count imaginary things but we can order imaginary things?

How do you account for The Magnificent Seven, The Famous Five, 12 Angry Men, etc.?

They're not called The Magnificent Seventh, The Famous Fifth and 12th Angry Men.

So we are not really counting the imaginary things, but symbols or representations of them — Metaphysician Undercover

Imaginary things only exist as symbols or representations; that's what makes them imaginary. You therefore acknowledge that we can count imaginary things.

But this is not really counting because there are no things being counted. — Metaphysician Undercover

Counting symbols or representations is really counting. If you're not counting imaginary sheep to help you sleep, then what would you call it instead of "counting"?

Yes, dreams have a phenomenological, qualitative aspect (in my experience).

Yes — Shawn

I wouldn't consider that an experience on top of another experience; it's just part of the dream experience. There is something it is like to have a dream, just as there is something it is like to listen to Mozart in reality. This is the distinction I would draw between the two qualia or qualitative experiences.

Let me provide an example:

Listening to Mozart whilst in a dream is what can be called a qualia? — Shawn

Is Mozart on in the background (in reality) while you are asleep, or are you dreaming of hearing Mozart?

I don't understand what having one experience on top of another means.

It seems to me that when one experiences something on top of what is or has been experienced — Shawn

How does one experience something on top of what one experiences?

Namely, the mind can encapsulate the sum total of what space 'feels' like, what sound, 'sounds' like (ever hear music in a dream as if played on a device; but, in a dream), and what food 'tastes' like.

Yet, these, feelings, sounds, and tastes are not entirely qualia. They are actual experiences, reified through the brain's hardware into a phenomenological experience that can be what is called 'dreaming'.

It is intriguing that when one experiences these amalgamates of past experiences that is what one would call a 'qualia'. — Shawn

When you say "these amalgamates of past experiences", are you referring to dreams? If so, then you have already told us that these "are not entirely qualia".

How does one express this in terms of knowledge and language? — Shawn

We could just call them dreams, as you have done in your OP.

Pure water is necessarily the very same thing as H₂O. — Banno

Perhaps, but the question and topic of the OP are not about pure water. @Fooloso4 makes a valid point that H₂O is necessarily water "but water is not necessarily H₂O".

I understand rigid designators to refer to some particular physical object or stuff regardless of the name, so whether that physical stuff is "water" or "H₂O" depends on which stuff is designated.

You want to use "water" for impure H₂O. Go ahead. — Banno

Impure H₂O?

I have stated that language does not require rules — Metaphysician Undercover

Yes, and now we're going round in circles.

The differences in rules are varied. What is legal in some countries is illegal in others. Some philosophies promote violation of the law of excluded middle, some promote violation of the law of noncontradiction. Different languages have developed different grammatical structures. — Metaphysician Undercover

These are not examples of rules of language use, which you appeared to be talking about in your previous post where you said "in language we see competing rules".

Right, some never play chess, because they choose not to. But we really do not have such a choice in the case of language, due to the necessities of nature. — Metaphysician Undercover

What necessity forces you to use language? People can choose not to use language as freely as they can choose not to play chess.

We freely choose whether or not we want to play chess, and if one decides to play, one must adhere to the rules when making moves. — Metaphysician Undercover

I don't see how language is any different. What do you think is learned when one learns a language? Do you think it's just a matter of memorising all the different words without also learning how to use those words? How is learning how to use a word different from learning how to use a pawn?

Luke is doing a fine job — Banno

Thanks Banno :up:

the reality of language, as a fundamentally free and lawless activity — Metaphysician Undercover

Right, in playing a game we must adhere to the rules with all moves. But in language we see competing rules which makes such a thing impossible, so we ought to drop the analogy right there. — Metaphysician Undercover

Does language have no rules or does it have "competing rules"? What "competing rules" does language have?

However, a closer look at language use would reveal that it is shaped not by rules, but by freely chosen activities of free willing beings. — Metaphysician Undercover

How is this different to the game of chess? It is not as though people are forced to play chess against their will by the deterministic laws of nature, or that they are physically unable to make illegal moves. Chess is also "shaped...by freely chosen activities of free willing beings", yet it is still a game for all that, and has rules too.

So standards are things which you hold on your own, as opinions, — Metaphysician Undercover

Equivocation. These are different "standards" to those in the context of norms and normativity.

You are just providing evidence here that the "game" analogy fails. — Metaphysician Undercover

How does the analogy fail? Moving pieces wherever you want, irrespective of the rules of the game, is not playing the game.

It's my opinion and belief. It's my opinion that if it hasn't been stated in some form it cannot be a rule, and I believe this. This "must" in your statement, "must be explicitly stated" is normative, because it's a standard of behaviour that I believe in. — Metaphysician Undercover

There is no such "standard"; it is merely your own personal opinion. You don't set the standards or norms all on your own.

Otherwise, where can I find this standard of behaviour? Where is it written? By your own reckoning, a rule cannot exist unless it is explicitly stated, so where is it explicitly stated that a rule must be explicitly stated?

I've told you many times, you are free to use that word however you want. — Metaphysician Undercover

You cannot use that word however you want if you want to be coherent. Your argument is analogous to saying: I can move any chess piece to wherever I like on the board because it's physically possible, therefore chess has no rules. But you can't move the pieces just anywhere if you want to play the game, or if you want to make moves in the game that are permissible/coherent/understood. You seem to think you're making an interesting point about the freedom to make any moves whatsoever, but all we're really interested in are possible moves within the game. This is where the line is drawn between coherent and incoherent. But this line cannot be drawn by you alone. Who told you that?

"Must" is normative here — Metaphysician Undercover

It is your belief or opinion that a rule must be explicitly stated. What's normative about that?

So I see no problem with believing that you use "rule" differently from me, and also believing that a rule must be explicitly stated to qualify as being a "rule". — Metaphysician Undercover

The problem is not with your belief that you and I use the word "rule" differently. The problem, as I have pointed out, is that you contradict yourself with your pair of beliefs that "you can use "rule" however you please", and that "you use "rule" in an incoherent way."

Either I can use "rule" however I please or I cannot. Which is it?

The obvious implication here is that if you want to use the word "rule" in a coherent way, then you cannot use the word "rule" however you please.

So it looks as though language is a game consisting of rules after all.

That's right, you can use "rule" however you please. — Metaphysician Undercover

You can believe that or you can believe that a rule must be explicitly stated. You can't have both. So I trust you've given up on your opinion that rules must be explicitly stated.

What makes a rule a rule is to be explicitly stated (my opinion, notice "I think"). But there is no rule which states that "rule" must be used in this way. — Metaphysician Undercover

Therefore, rules do not have to be explicitly stated.

I think what makes a rule a rule, is to be explicitly stated. — Metaphysician Undercover

There is no rule (used my way) for the use of "rule". — Metaphysician Undercover

Which is it, MU?

Mind=Mind

However, please do not conflate your idiosyncratic way of using "rule" with the philosophically respected way, or you'll be charged with equivocation. — Metaphysician Undercover

What is the "philosophically respected way" of using the word "rule"? Is it that "there are no rules (my use) as to how you ought to use that word"?

How are you supposed to know what to do without being told what to do? — Metaphysician Undercover

I think what makes a rule a rule, is to be explicitly stated. — Metaphysician Undercover

Who told you that this is the only acceptable use of the word "rule"?

The 'rules' are just structures in the way we talk. Before we develop a complex tradition of studying the ways we talk (like trying to clarify what 'truth' means) we have already been using words like 'truth' successfully enough in ordinary contexts. This is the post hoc.

You mention 'imaginary things' which takes for granted what might be called a vague ontology. You also use the word 'exist.' It's not as if these words have clear, uncontested referents. Nor does 'referent' have some clear, uncontested referent. We simply charge ahead, shooting our ambiguous mouths off, taking a certain intelligibility utterly for granted. We can focus a critical 'eye' on some words only by using other words uncritically. This is why it's a matter of making explicit what's mostly automatic and unnoticed (inexplicit). — j0e

Great stuff. Well said.

Thanks Sam. An interesting paper and I found myself agreeing with some of it. However, I think the main thesis of the article is undermined by the quotes presented by the author (on p.85 of the article) that get dismissed a little too easily, imo. The same quotes from Part II of PI:

365. If concept formation can be explained by facts of nature, shouldn’t we be interested, not in grammar, but rather in what is its basis in nature? —– We are, indeed, also interested in the correspondence between concepts and very general facts of nature. (Such facts as mostly do not strike us because of their generality.) But our interest is not thereby thrown back on to these possible causes of concept formation; we are not doing natural science; nor yet natural history a since we can also invent fictitious natural history for our purposes.

"If concept formation can be explained by facts of nature..." The main thesis of the article is the rejection of this possibility. But Wittgenstein does not appear to rule it out. He states only that it is not of philosophical interest, or is not a philosopher's goal/purpose to discover.

366. I am not saying: if such-and-such facts of nature were different, people would have different concepts (in the sense of a hypothesis). Rather: if anyone believes that certain concepts are absolutely the correct ones, and that having different ones would mean not realizing something that we realize — then let him imagine certain very general facts of nature to be different from what we are used to, and the formation of concepts different from the usual ones will become intelligible to him.

Here W rejects the idea that "certain concepts are absolutely the correct ones", as though nature carved herself at the joints for us and we just pinned labels within those ready-made contours. But I think the paper may go too far the other way in suggesting (if I recall it correctly) that our language is therefore independent from nature or self-contained. This would seem to undermine the author's references to "the method", or to comparing propositions with reality, because what difference could such a comparison make if our concepts were unaffected by reality?

Yes, my point was that hinges need not be expressed, and can therefore be non-linguistic. I think I responded to your post before you edited and added "and all propositions can be stated", so it seems we agree.

See OC 103 and 159.

There is no proof of anything, and I can prove it!

So, in this case "I know..." means that I have learned how to use the word hand. The same can be said of 2+2=4, in some contexts it can makes sense to say it's true, other contexts not so much. I don't know what Wittgenstein would say about this. OC 10 doesn't give enough information. — Sam26

I find no ambiguity in OC 10 regarding this. Wittgenstein plainly states that "2x2=4" is a true proposition, irrespective of any and all contexts (occasions, times):

is "2x2=4"...not a proposition of arithmetic, apart from particular occasions? "2x2=4" is a true proposition of arithmetic—not [only] "on particular occasions" nor "always"

Moreover, Wittgenstein never edited his thoughts in OC, it's just a rough draft. — Sam26

It's easy to disregard the parts that don't fit with your interpretation, but that's not very charitable to Wittgenstein. At any rate, it seems unusually specific to be classed as a careless error. Taken as what W intended to say, it also appears consistent with (and perhaps a precursor to) his latter remarks on mathematical propositions, e.g. 340, 350, 651-658.

The fact that it doesn't make sense to doubt Moore's propositions, seems to also hold for the mathematical proposition 2+2=4. Can I doubt that it's true that 2+2=4. It seems senseless to doubt it. — Sam26

If it were the result of Wittgenstein's philosophy that hinge propositions are neither true nor false, have you considered that this might not be because they are indubitable, but because they are usually non-propositional (except for W's exposition of them)? If memory serves, I believe that Daniele Moyal-Sharrock regards hinges as non-propositional.

I'm more interested in Sam's exposition than in tedious chitchat. — Banno

I must have mistaken this for a philosophy forum discussion. I didn't realise it was Sam's blog.

If you wish to understand, you might benefit from a wee bit of charity, instead of the tedious "gotcha". — Banno

The same charity that has been afforded to @Fooloso4, you mean?

Of course it is true that 2+2=4. No one here doubts that. — Banno

Did you change your opinion in the interim? Because you and Sam claimed earlier that mathematical propositions can be neither true nor false:

That 12x12=144 is not subject to doubt; it could not be false, and hence is outside our considerations of true and false... — Banno

I think Sam's earlier suggestion that @Fooloso4 should start his own analysis in another thread. instead of offering his interpretation in this discussion, needs to be seriously re-considered.