John Page

Primal:

Sure, sorry I thought I had been clear when posting "Let "Socrates is a man. All men are mortal. Socrates is mortal" be the propositions A, B and C. " The letters refer to the three sentences respectively.

T is True and ~T is False.

IMO we use equivocation when considering these propositions. For example: We will think "Now, what if Socrates is immortal, hmm, in that case he couldn't be a man because all men are mortal" (which uses equivocation of B, the second premise) and we might also think "Socrates can only be immortal if he is not a man" (which uses equivocation of A, the first premise).

Cheers, John

PJPSYCO

I think I'll add my two cents.

The only place I've ever actually seen the terminology A=A is in the derivation of basis of universal definition(generaly refered to as part of the Law of Identity). Simply stated is an object can only have one and only one definition, and that definition cannot be subject to change. This is a simple rule that if we have thingto be communicated A. Then if I say it is object B and you say it is object C, and object B and object C are different objects then my A is not your A. Otherwise it is and we have successfully communicated. So, we say A=A implies True, A not= A implies false. The second half says that A(t1) and A(t2) must refer to the same object (where t1 and t2 are diffeent times). It just means that you must specify that you mean the object at a specific time, or define the parts of the object in flux. Like the fact that I grow is in the defintion of me. To remove it is to improperly define me, unless you specify a time period.

You are doing the mistaken understanding of words must only refer to one object. No, A=A has nothing to do with words. It only has to do with the objects themselves. It would be if someone told you that Vulcan, the roman god, was Vulcan, a guy from Vulcan on Star Trek. They would be wrong. Because these two objects are not the same. The truth of statement is not do they have the same word to communicate them.

John Page

Yes, these objects are beastly little things to tie down, aren't they! Seems they are impermanent so all we are left with is the definitions to which you refer - but they are not objects.

See link here to thread - take a look at what Tyler Durden is trying to push and his reference to multi-valued logics.

Cheers, John

PJPSYCO

I know about the complexity of objects. I was keeping it simple. I see no need to go into the whole story. I could do a 78 page post on the derivations of communication as where we get truth and the following basis and axioms, but that is not required in this thread. The initial post stated that A=A is not true because words can refer to two different ideas. Since A=A has nothing to do with that concept. I covered what I thought was important. No need to put up the whole thing for a little missunderstanding.

John Page

How would you categorize the A's, then?

1. The A's cannot be the objects themselves because this would violate the LOI, we'd be saying, effectively, B=C.
2. The A's cannot be names, for the reasons you just stated - names refer to something else and can be reused.
3. The A's could be symbols - but how does that differ from names. If we take symbols to just be shapes rather than collections of letters they're just pictograms. If we take symbols to be pieces of information then they're just refering to objects in the same way as names.

I have come to the conclusion that objects appear as a result of differences/variations within reality which we detect through our senses. We correlate these differences in qualities and make axioms out of these qualities so we can recognize complex patterns of differences within reality.

Coming back to the OP, then, by repeating the form of a letter we are able to pretend or putting it more bluntly lie to ourselves about uniqueness.

If we say that we are just comparing sets of qualities then uniqueness is implictly denied. However, as you mention in your post we can suppose that each point in spacetime is unique and, using that point of view, track our object's path. But aren;t spacetime coordinates just another set of qualities? Is every point in spacetime necessarily unique?

Cheers, John

Witt

John: Thanks again. I think I'm understanding the rules, but I'm having trouble making them fit with reality.

My pleasure.

Fitting reality, now there's a challenge.

I sent a detailed reply to your post but it dissapeared,
I will try again, I am not especially computer oriented.

Damned machines, !@#$, etc.

Witt: They are 'complete' symbols if they are unique!

John: This is the terminology that threw me initially. Surely a symbol is something that is used to refer to something else (in the pictogram sense, perhaps) and even in information theory a symbol is a unit of information i.e. it implicitly represents something else.

Yes.. symbols, simple or complex..represent.

John: Now, let me suggest that we only know of things through something called the mind. Our mind can be used to apply the system of logic to things that it knows about - some of which may be objects and others no.

OK.

John: I'm having rather an entertaining conversation with Tyler Durden here who is using someone else's text to argue nominalism.

That's a very interesting thread, entertaining and informative.

John: It strikes me that a set is defined by its criteria for membership and that the set itself is a real object contained within the mind.

I can agree with that. Reality, includes physically existing objects and mental objects, eg. stories, myths, numbers, etc.

John: ..example, there is stuff outside the mind, some of which we might call an instance of a chair. The truthfulness of the statement "A chair has four legs" has no bearing upon the existence of any chair - it needs to be tested against the criteria laid down (in the mind) for something to be considered a chair.

To expand a little further, a set as defined here is a purely mental entity and is a collection of criteria against which sense impressions (not necessarily raw sense impressions) are tested. For example a mind might determine if an object is a chair by examining whether a human body could reasonably rest on it (functional criteria) and whether it had legs (substance criteria).
--------------------------------------------------------------------------------

Yes, and essentialism has it's own problems...even a legless object that can be sat on might fit a particular description of 'chair'.

John: Going back to your OP, then, A represents an abstract entity with A'ness. You have the concept of A in your head, I have the concept of A in my head.

Concrete and abstract objects are represented by our variables.

John: When we agree A=A, then, we are intersubjectively agreeing the concept A.

I interpret your 'intersubjectivity' as 'objectivity'.

John: This being the case, the identity of A is not unique because there are many copies of it.

I don't agree here. That there are copies of the name does not entail copies of what it names.

John: For these reasons I am uncomfortable with the description theory - (ix:Fx) definitely exists but its form can only be mental.

??

John: ..but I'm having trouble making them fit with reality.

The last paragraph of Russell's "On Denoting" linked by Scrambles.

Russell:
"Of the many other consequences of the view I have been advocating, I will say nothing. I will only beg the reader not to make up his mind against the view --- as he might be tempted to do, on account of its apparently excessive complication --- until he has attempted to construct a theory of his own on the subject of denotation. This attempt, I believe, will convince him that, whatever the true theory may be, it cannot have such a simplicity as one might have expected beforehand."

"A logical theory may be tested by its capacity for dealing with puzzles.."

On the last point, Russell writes: (PM page 291)

"I remember the late Prof. De Morgan remarking that all of Aristotle's logic could not prove that 'Because a horse is an animal, the head of a horse is the head of an animal.' "
It must be confessed that this was a merit in Aristotle's logic, since the proposed inference is fallacious without the added premiss E! the head of the horse in question. E.g. it does not hold for an oyster or a hydra.

Witt

John Page

oops!

SlateGreySky

Has anyone referenced the kind of Russellian analysis done here with Fichte's Wissenschaftslehre of 1794?

He's got some earthshaking views on "A=A" in that piece . . . at least I found them to be so.

I'd be very interested in someone's opinion on this.

Dominus Paradoxum

Sorry, but we can't give our opinion if we don't know what he said. So if you could provide a short summary, that would be very helpful.

Note to all: I hope it is clear that here we are discussing the
philosophical notion of identity, i.e., numerical identity, and not identity in the ordinary sense which simply means 'exactly simaler'.

SlateGreySky

Let me preface this by saying that if anyone out there knows Fichte and knows that I'm screwing him up, please correct this post for me.

Fichte notes that "A=A" is a vacuous truth of logic which will not do as a first principle, because even though it seems to hold as an identity statement, one must first posit an "A" with which to begin.

Unless the identity of the "A" is known prior to the statement of self-identity (i.e. "A=A"), the statement of self-identity is devoid of content and therefore of concrete truth.

The self-positing subject, Fichte argues, is the true first principle. That is, replace "A" with "I," and the statement becomes concretely true. In self-positing, the subject (the "I") implies its own existence as an object on which the identity statement is predicated. Thus, the truth of "I=I" is an affirmation verifiable by the subjectivity of the one who posits it as an identity statement.

Thoughts?