We, humans, couldn't have abstracted the identity of indiscernibles and self-identity from our sense perception; the existence of space precludes the possibility of two objects (a,b) being identical--no two objects can possibly occupy the same space. On the other hand, the existence of time precludes the possibility of a single object (a) being identical with itself-- no object can maintain the same properties (mass, volume, color, the coordinates of its electrons orbiting the nuclei .etc...) over time. Still, we hold that a=a and a=b ,with certainty.
Where do we get this apparently a priori knowledge of identity then, if not from experience?
Dear Bessat Elmie: your question seems going deeply in our subconscious or unconscious. If I understand your question, from my feeling I suppose that we keep the memory of our birth, in other word we discovered that we are not just one but at least two. Now if in physics the notion of indiscernibility was introduce in statistics for the electrons it was a big error, see “Perturbations and Statistical Distribution of the Thermal Energy” indeed section 5 The most probable distribution and the perturbations -Let us consider the particles ni which occupy the segment i at the time t. We do not know which they are, so the particles are called undistinguishable. Nevertheless it is possible to limit the notion of undistinguishability to this aspect of the phenomena. On the other hand at the microscopic scale we suppose that the particles between them have individuality. Consequently this means that in certain extent it is possible to distinguish them. For example we will assume that the particles have a volume and that two of them cannot occupy the same place at the same time.
Do we have abstracted the identity of indiscernible from the time before our birth it is difficult to say but why not?
"As if smitten by a sword / As if his head were on fire / A bhikkhu should wander mindfully / To abandon identity view" (Samyutta Nikaya)
The two cases presented belong to mathematics, not necessarily to physical reality. They have well defined sense in our imagination, but are quite useful in our every day life. Think about prices, for example.
I suspect you are not appreciating the difference Kant distinguishes between synthetic and analytic a priori. I, like most, I suggest, have a problem with synthetic a priori knowledge but aren't you mainly speaking of the other and your difficulty arises from conflating the two?
Thank you for the question Jan, I have no desire to enter into a discussion here in respect of Kantian idealism however, I was actually thinking of Saul Kripke when I made that remark.
Below may be total nonsense:
It...looks...to...me that you are actually questioning the definition of "a" (and "b", and others) instead of questioning how might "a=a" be possible. If you don't have any problem with, say, Alice at t1 as continuing Alice at t0 and bearing the same name "Alice", then you don't really have a problem with "Alice=Alice". One way to consider is: there were 20 players in a football team ten years ago. Call the football team "FT". Today FT has been filled with another 20 members. Is FT still FT?
I have a vague inclination of thinking that (real-world-related) names reveal the way we partition all the particles in the real world to handle this world. There seems to be not only something about the physical laws that keep particles together but also something about the information load. If we track every particle separately, any language, natural or artificial, will undoubtedly be overwhelmed. So instead we group (and when necessary split) particles into objects. Whenever I know what is a, I know that a=a. When I know what is a and what is b, arguably I would need to define the preciseness of "=". But generally if a is a person and b is also a person, then the two names are of the same partition level, so I would know that a=b when there are enough clues.
Reading the "Begriffsschrift" of Frege, fragment 8: Identity of content, may be helpful.
Taleb Jaberi I cannot find a reliable English translation, so I read a rather suspicious translation in my mother tongue.
I believe in the episode Frege meant that there is a method X to determine a point A expediently named "A", and there is a method Y to determine a point B expediently named "B", and it turns out that the point referred by "A" is exactly the point referred by "B". And, using later his term, "A≡B" means that the reference of "A" is the reference of "B".
It seems that in the episode Frege didn't say if he thinks the two expedient names were expediently about or referring to two points. As I understand, later Frege had to have "sense" to deal with a language-mind relation and have "reference" to deal with a language-world relation. I don't see how this episode in Begriffsschrift answers the question posed?
Xinyuan gu It was a good paraphrase of Frege. You are right, this definition say nothing about "how knowledge of identity is possible", but I though it may makes us more clear about the definition of identity itself. BesideFrege, also Witggenstein recognized the importance of the identity. his speculations about this subject are really interesting in: (1961), Notebooks: 1914-1916, Edited by G. H von Wright and G. E. M Anscombe, translated by G. E. M Anscombe, Harper and Row Publishers.
By the way for a reliable english translation of Begriffsschrift, see: Jean van Heijenoort, From Frege to Gödel, A source book in Mathematical Logic, 1879-1931, , Harvard University Press, 1967.
Taleb Jaberi Thanks very much for mentioning the books. Those would be very helpful for all.
Gerardo Óscar Matía Cubillo , identity and equality are two different concepts.
I think it is a mind-body problem. I am not i if i observe myself from physical point of view at different times but i am i from transcendental view. As to the object they are identical or nonidentical in respect of our inclination into this process and not as they are per se, ipso facto, a priori and the like
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