Before I dealt with this bird I didn't realize there was a branch of mathematicians called 'formalists' who have this unusual way of looking at everything. That they can't see the fallacy of their thinking is unusual, but there are many means of dodging logic
it fails conspicuously in subnuclear physics to explain the 2-slit experiment
This is the BIG QUESTION that you can expect to face endlessly. That this doesn't refute the law of identity, only that we haven't found the proper identity, is never entertained. According to this view we can't be certain of anything except that the law of identity is invalid in this case. The contradiction of this view is never examined because contradictions are never valid except when he says they are, never when you say they are.
my ability to be both happy and not(happy) that my mother has died. It is just one of several mathematical descriptions of how elements in well-formed sets behave. As such, it does not constitute the entire warp and weave of the universe. It is a useful tool for many purposes, it is not a ghost that inhabits every corner of the universe.
Here is another one. When you are talking reality, he will talk mathematics. When you talk mathematics, he will shift to ephemeral things like emotions. That way neither of you will ever be on the same 'domain of discourse' no matter how hard you try to land it there.
Chomsky level
Chomsky? Pardon me while I go puke. Just say commie idiot and be done with it.
Kindly just answer the question: is "This sentence is FALSE" FALSE? If we assume the sentence is FALSE, (as you say, because it is contradictory), than upon evaluation, we find it declares itself to be TRUE, which we must believe, because we declared it to be FALSE. If it is true, it must therefore be FALSE, therefore, it must be TRUE...are you getting the drift here? Contradiction does not necessarily just mean FALSE--it could mean you cannot get a value. You hang up if you try. You are using a loose and inadequate notion of contradiction as if it were ubiquitous. It is not, it is quite easy to have validly formed predicates that are neither TRUE nor FALSE in any formally acceptable sense. That is what most of 20th century formal mathematics was about.
I liken it to a forebrain problem like sociopaths. They either get it or they don't. You either see the contradiction (speaks against itself) here or you don't. You cannot make someone see a contradiction. You cannot make a person acknowledge a contradiction. That this didn't invalidate all that logic proved was also brushed aside. That this this conundrum is meaningless was never considered, it becomes the holy grail. Then I asked him if fallacies were invalid. He said yes. The conversation stopped. If a person can commit a fallacy and still think he is thinking, there is no hope.
I wish you luck.
A BI-PHOTON DE BROGLIE WAVELENGTH has been directly measured in an interference experiment for the first time. In the early days of quantum mechanics, Louis de Broglie argued that if waves could act like particles (photoelectric effect) then why couldn't particles act like waves? They could, as was borne out in numerous experiments (the double-slit experiment for electrons was voted the "most beautiful" experiment in a recent poll—see Physics World, Sept 2002). In fact intact atoms in motion and even molecules can be thought of as "de Broglie waves." Molecules as large as buckyballs (carbon-60) have been sent through an interferometer, creating a characteristic interference pattern (see Update 579, www.aip.org/enews/physnews/2002/split/579-1.html).
The measured wavelength for a composite object like C-60 will in part depend on the internal bonds of the molecule. What then if the corporate object is a pair of entangled photons? One of the more fascinating predictions made regarding quantum entanglement (Jacobson et al., Physical Review Letters, 12 Jun 1995) was the suggestion that the de Broglie wavelength for an ensemble consisting of N entangled photons (each with a wavelength of L) would be L/N. This proposition has been verified now by physicists at Osaka University (Keiichi Edamatsu, 81-6-6850-6507, eda@mp.es.osaka-u.ac.jp) for the case of two entangled photons. The daughter photons were created by the process of parametric down-conversion, in which an incident photon entering a special crystal will split into two correlated photons. These photons are then sent through an interferometer (see figure at http://www.aip.org/mgr/png/2002/169.htm).
The resultant interference pattern shows that the photons behave as if they acted as a single entity with a wavelength half that for either photon alone, a feature which might improve the sharpness of future quantum lithography (the narrowness of lines on a circuit board being no better than the wavelength of light used in the fabrication process). But since the parent photon already had this shorter wavelength, what will have been gained by splitting the photon in half? The advantage will come when, at some point in the future it will be possible to generate entangled photons from non-entangled photons of the same wavelength, a process called hyper-parametric scattering. (Edamatsu et al., Physical Review Letters, 18 November 2002)
This is the BIG QUESTION that you can expect to face endlessly. That this doesn't refute the law of identity, only that we haven't found the proper identity, is never entertained.
If the law of identity works all the time, than, pardon my french--it works all the time. If it doesn't work all the time, than it is not ubiquitous, yes or no? Oh, but wait, you say, SOMEDAY, we will discover just the correct way to turn our heads so that we see that it works for the 2-slit.
Now that's a devastating argument, isn't it? The fact is that one buckyball goes through two visibly separated slits at the same time. This nakedly violates Identity using very simple structures that you can easily draw venn diagrams around. So unless you want to claim that buckyballs can't be elements of sets when you figure out how to "see" this as NOT a violation of the law of identity, you will have also thrown out the rest of classical physics.