# Another Attempt To Understand Identicals

Below are two statements most people would say are true.

1. One plus one equals two. (1 + 1 = 2)
2. “All men are mortal. Socrates is a man. Hence, Socrates is mortal.” ( A = B. C = A. Thus, C = B)
Logically, for a statement to be true, it must be true in all possible domains or worlds and in all possible conditions. The statements given above cannot be verified by these criteria for truth.
In the first instance, 1 + 1 can = 1. My old example is 1 lit match + 1 tank of gas = 1 explosion. For the 1 + 1 to = 2 the 1s must be seen as in some way identical. In a world of the abstract this is easy to imagine. How does it fare in the world of the real?
In the second instance, if only one man could be considered immortal, the syllogism breaks down. The quality of being mortal, B, must in some way retain its identity when being applied to A and C. Otherwise, it could be said that all men are Socrates or that Socrates is all men.
The problem becomes how to account for the necessity of an identical or supposed identical for these statements to have any generally accepted meaning or explanatory value.

Ierrellus - what are ya doin’ man?

1 + 1 = 2 in the same place at the same time. If you want to account for change, then you gotta get a bit more complicated than that. In other words, 1 + 1 = 2 doesn’t fit your word problem, but there is math that does. You just can’t use simple addition when you need an algorithm. But algorithms are still math.

No. The syllogism doesn’t break down - the premise does.

Two entities can be identical for a given purpose. We can’t jettison context and then cry because we don’t know the meaning of a statement.

Faust,
Good and sound rigor. What I’m trying to get across, maybe not to well, is my need to understand the grounds. Wittsgenstein uses the mathematical example as 2 X 2 = 4, then shows how such a statement may have little meaning as a statement for the Chinese. He refers to the ground as “animal”.
My concern is how statements can evolve from such grounds to semantic dualisms and whether or not some constant could be used to correct that. I regret that Dan’s thread on language did not move beyond theories of origins to the problems with word games. I’d like to explore these constants without getting into my customary take on biological precedents.

I think the next question here is how we know something is identical. Houses are very different yet we categorize them all a houses. Things can be identical but in different ways. Function is one form of sameness. A function is perhaps the main effect of the thing in question. But the thing might have many effects so can it have many functions. This sounds odd perhaps because humans think contextually. It has a function in that context. The function of the bat in a baseball game is to use it to hit the ball. The function of it in a burglary is to defend yourself. The fact we see function contextually suggests we only see one function of a thing per context. This is probably because we have specific aims in different contexts so the function of an item is limited to one per aim, context. Even if you have different aims in the same context is the chance of the item being us in all those aims is unlikely or it’s just we forget the previous use of the item. What if an item can have contradicting functions in different contexts? Does this mean we cannot group as identical to other items in the group if both those functions of the two groups are contradictory? No, their not contradictory as even though they can stop each other in the same context it doesn’t matter as only one of those ‘function/uses is needed in that context. In other words such contradictions only arise when you have two functions that contradict each other for the same “aim”. But that is unlikely and if it ever does arise it’ is not a contradiction in value most of the time. That is we value one use over the other at better achieving the aim. The only time we would feel a true contradiction is when you have two uses for the same item or two that contradict each other in that both equally well achieve the aim. However a human could overcome this confusion with the logic that it doesn’t matter which one you choose rather what matters is that you “do” choose one. So we can say as item can have different functions and thus can be categorized as identical in different groups where the included have the same function. We can call this “multifunction identity grouping”.

So that’s function but what other ways can things be identical. Can you think of any? Also perhaps do you have anything to say on what I said on function?

Let’s look at it this way. If something is two then it is made up of ones. One are a specific thing, we can define them as a thing. That’s why their ones. Thus if they can be defined as a thing we can say they with another thing make up two. I’m aware I’m saying something quite obvious but I’m trying to point out are mode of thinking. We are able to define things as making two as we are able to define them as things at all. The thing is we can’t know three if we don’t know two. As two is part of what makes up three. Again these things are obvious but sometimes it’s good to point out the obvious to make things clear.

Ierr -

Russell dispatched with this by separating meaning from significance, to account for the difference between the speaker and the hearer. It just isn’t correct 2 + 2 = 4 becomes meaningless just because the hearer doesn’t understand the language. Translation is just a technical matter. Although I wonder why W chooses mathematics as an example. Certainly it’s not a good one today.

I’m not sure I follow. Which semantic dualisms?

Wittgenstein says that saying “two plus two equals four” won’t mean anything to a Chinese speaker, but he’s not talking about grounds making that point. He’s simply saying that the meaning of language comes from its appropriateness to the situation. The mathematical stuff’s in PI, rather than On Certainty. All he really says in OC is that we can give grounds for mathematical assessments, although he holds that the grounds are more the commonality of human experience and usage than any platonic reality. And he argues we say we “know” things when we can give grounds, the same as we say we “doubt” things (philosophers excepted).

In PI he says that mathematical truth is independent of human perception of it, insofar as “people believe 1+1=2” is different from “1+1=2”. If people all believed “1+1=3”, they would be carrying out different operations to us all the time, and they would not engage with what we specifically call mathematics. But since they’re not playing by our rules, we couldn’t really call them wrong - they’re doing something else. So you can see mathematics from that point of view as a pragmatic convention we share. A ruleset. I’d guess that semantic dualisms are therefore part of the flybottle you have to find your way out of. For what it’s worth, I think maths is his shakiest area; as a field, it allows the construction of further insights from within itself, which to my intuition suggests that it’s more than a rule system.

To go back to your OP:

• can “logically, for a statement to be true, it must be true in all possible domains or worlds and in all possible conditions” be verified for all possible domains?

Some good posts here. And thanks, Piensky, for your thoughtful post.
In “On Certainty” Wittsgenstein asks of statements we claim to be true if it makes sense to doubt them. He also gets into the contextual constraints on, and pragmatic value of, such statements, as Piensky notes.
Here’s the quote:
“10. I know that a sick man is lying here? I am sitting at his bedside , looking attentively into his face.–So, I don’t know, then, that there is a sick man lying here? Neither the question, nor the assertion makes sense. Any more than the assertion “I am here”, which I might yet use at any moment, if suitable occasion presented itself.-- Then is “2 X 2 = 4.” nonsense in the same way, and not a proposition of arithmetic, apart from particular occasions? ‘2 X 2 = 4.’ is a true proposition of arithmetic – not ‘on particular occasions’ or ‘always’–but the spoken sentence ‘2 X 2 = 4.’ in Chinese might have a different meaning or be out and out nonsense, and from this is seen that it is only in use that the proposition has its sense.”
I’ve tried to get beyond the subject/object controversy or the liar’s paradox in order to examine what I call identicals. I located these in formal statements of arithmetic and logic. Piensky found their use in the collective nouns of our everyday language. The positing of an identical in the math statements appears necessary for the proposition to function. The identical of collective nouns appears to make sense of our grouping like things into sets. Perhaps identicals function to validate our sense of certainty. If so, it makes sense to me to find out what they are and what they do.

OH,
I realize W. is not talking about the grounds in the example I gave, which I had to correct on rereading. (2 X 2 = 4.) But I can’t help wondering how these contribute to any statement considered “true”.
And, yes, the all possible worlds criterion for what is true might mean that my cat Thai should be aware of mathematical propositions. He could care less. And, as previously stated, I could present a reasonable case for biological precedents for any mental structuring. W. recognizes the ground as “animal”. Without digging that deep, I’d like to explore the ground of posited identicals.
Faust,
What exactly did Russell refute? And how did he do it?
Semantic dualisms–W. says that all propositions that lead to nowhere should be expunged from philosophy. Determinism vs free will, subject vs object, etc.-- the whole way of seeing as polar opposites those things that are simply extensions into further domains or places on the wheels of cycles.

Ierr - Russell explained this problem:

by exactly the means that I described - what we say can have meaning, but may not have significance to the hearer, and an example he used, IIRC, is that of the hearer and the speaker using two different languages. The hearer may very well deem the statement of the speaker meaningful if he knew the language the speaker was using - and this is just a technical consideration. Meaning is not like Brigadoon in the fog - it’s there or it’s not.

Thanks. Sorry that I did not read your post more carefully. I agree with Russell on this.

Things seen as identical, without which our equations would not function and our collective nouns would convey no meaning, may reside in the realm Wittgenstein decribes as “something that lies beyond being justified or unjustified; as it were, as something animal.” (359)
In the following passage W says, “You must bear in mind that the language-game is so to say something unpredictable. I mean: it is not based on grounds. It is not reasonable (or unreasonable).
It is there–like our life.” (559)
Maybe I misinterpret W. from misunderstanding. What I get is that there is a ground for seeing things a certain way that is beyond the need of justification by reason. The “unpredictable” results of language-games could be seen as possible from an evolving potential for more elaborate expressions. Are algorithms grounds? Does asking what identicals are and do invite W’s indictment of “questions that lead to nowhere” and “should be expunged from philosophy?”
Set me straight. It won’t hurt my feelings.

Wittgenstein was a drama queen.

It’s useful to generalise, and it’s reasonable, too. We extract a common partial meaning from particulars. We agree, well enough, on what a word means, and on how much partial meaning is enough to name something.

It’s not even philosophy yet.

Understood. I don’t agree with your assessment of W. So an exploration into the constants from which we glean our ideas of certainty is not philosophical?

It’s pre-philosophical. The distinction is not cut-and-dried, I will admit. But you don;t need much philosophisin’ to understand the process of generalisation. It is patently true that misunderstanding it leads to much Platonic (read: bad) philosophy. The difference between Plato and Wittgy is that both mistook grammar for philosophy - in the former case that led to “meaning” where none existed and in the latter it led to “meaninglessness” where meaning actually dwelt.

My interpretation of On Certainty is that it’s not epistemological, it’s a discourse on why epistemology is barking up the wrong tree.

When we talk of things being true or false, we only practically talk of those things that can be judged by evidence. Statements about events, for example, or experiences. The problem with epistemology is that it tries to apply this to everything. Some “facts” that it considers - the external world exists, it wasn’t created last Thursday, I’ve never walked on the moons of Saturn, and so on - simply can’t be judged so - they’re the “hinge statements” he refers to, our thinking depends on them being true in order to have something to articulate against.

What evidence could you give me that I’ve walked on the moons of Saturn that is more concrete, more reliable, than my knowledge and evidence that I haven’t? If you want absolute definite certainty, you have to have absolutely unimpeachable evidence. There’s no point looking for solid grounds for proof, when there are no solid grounds for doubt either. Seen like that, scepticism is simply a symptom of epistemology, a name we give the chasing of phantoms.

I suspect that identicals probably fall under this groundless hinge statement category. Why is “an apple and an apple and an apple” three apples? Why is “an apple and a pear” two pieces of fruit? How could we talk of it being otherwise?

Thanks, Faust and OH.
Now in defense of this thread–
A. J. Ayer in “Bertrand Russell” (1972) writes “indeed, with the possible exception of his pupil Ludwig Wittgenstein, there is no philosopher of our time who has made such a large difference not only to the treatment of particular philosophical problems but to the way the whole subject is pursued.” In this book Ayer, another of Russell’s students and no mean philosopher himself, outlines ideas W. owes to R. and R. owes to W. He says that “the two diverged philosophically” but that R. “retained great affection for W.” even though R. “could see little merit in his (W’s) later work.” The rift between R. and W. was over justification of “facts”. This is an issue here.
I don’t think Ayer is describing W. as a “drama queen” here and I question why such an indictment would be contributive to an exchange of ideas, even of ideas that radically disagree.
If R. and W. could see this thread, they would probably debate whether or not my term “identicals” refers to an entity or an activity, whether or not those descriptions can allign or be considered mutually exclusive and whether or not the term I use requires justification. So far, the consensus here is that it doesn’t.
Sounds like philosophy to me.

Russell and Wittgensten agree on the truisms you describe, that they need no evidence or justification. They are what they are. I can’t say that epistemology generally errs in this way ot that “identicals” are limited to this classification.

Epistemology is full of it. The “brain-in-a-vat” thought experiments that have kept epistemologists in business for the last few decades are precisely this. Yet no-one says “I’ll be round for dinner next Wednesday, unless it turns out that I’m a brain being kept in a vat, in which case I’ll only think I’m coming round for dinner.”

I don’t think identicals are such a matter, though. I just think they’re an aspect of the way we talk about things, not things in themselves. As such, they require no grounds.

Exactly.