Talk:Is Logic Empirical?

message: Although Reichenbach's project was distinct from the later quantum logical approaches in two main ways, (1) 3-valued logic and not quantum logic (2) Classical logic has not been shown to be false but rather unsatisfactory for building the quantum mechanical language, the core idea that somehow there is an uneasy realtionship between classical logic and quantum mechanics is present. Furthermore, "The Philosophical Foundations of Qunautm Mechanics" preceeds Quine's work and as such deserves recognition for noting this tension.-- gericault  
I'll see if I can dig up something on Quine's Variant logics. I have the belief that Quine eventually refused to budge from Classical logic, but for the life of me I can't recall why. I'd like to get to the bottom of this as well.
:Reichenbach's book Philosophic Foundations of Quantum Mechanics was published in 1944.  The Birkhoff-von Neumann paper was published around 1936. Though the inclusion in this article of Reichenbach's work is definitely justified, the emphasis I think is now too biased in that direction. --CSTAR 23:14, 22 May 2005 (UTC)
thread_title: Reichenbach

message: I deleted the following bits of material from User:CSTAR's original text:
#He summarised Putnam using analogy: for example as the laws of mechanics or of general relativity, and in particular that what physicists have learned about quantum mechanics;
#Note that the formal laws of a physical theory are justified by a process of repeated controlled observations; this from a physicist's point of view is the meaning of the empirical nature of these laws.
-- Charles Stewart 23:12, 13 Nov 2004 (UTC)
thread_title: Deletions

message: I don't understand Dummett's argument about distributivity being necessary for truth tables to work. Either that, or the argument is trivial. Of course, if you assume that a propositional variable is bivalent and the connectives are given by the usual truth tables, then the logic is distributive.
Also, I think it should be possible to give in this article  the details of why projections as propositions is true empirically. CSTAR 04:04, 14 Nov 2004 (UTC)
thread_title: Dummett's argument; empirical tests of logical laws

message: The following materail from the Hans Reichenbach section requires more work. It doesn't adequately explain the role of 3-valued logic and probability.
-- I don't think there is anything wrong in the details here, but it would be diffucult to give a full explanation without overwieghting Reichenbach's portion of this article. There is a lot more that could be said,
(1) brief explanation of the 2 slit experiment and the role of probabilities
(2) Further explanation of why classical logic allows us to infer the wroing probabilities
(3) brief introduction of 3 valued logic and then how it blocks the inference (more fully)
(4) The distinction between exhaustive and restrictive languages
(5) The Bohr-Heisenberg view
(6) Why prefer 3VL to the BH view
This is basically an overview of the book though. This would all be interesting and I would write something up if it is thought to be worthwhile (and would love the input of others)
Cheers 
gericault
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The double-slit experiment plays a central role in highlighting the disadvantages of classical logic. Reichenbach suggests that if our language is classical, then unless we make adjustments to it (as in the case of the Bohr-Heisenberg view) we will infer the wrong probabilities, or the picture in which the observation in the 2-slit case is a sum of the single slit cases.
(1) Let us consider the events B1 = “The particle passes through slit B1” and B2 = “The particle passes through slit B2”
(2) The probability of appearing at a location C when just B1 is open is  
: \operatorname{P}(B_1) \times \operatorname{P}(C|B_1). 
and the probability when slit B2 is open is 
:\operatorname{P}(B_2) \times \operatorname{P}(C|B_2).
(3) The classical (physics) assumption is that when both slits are open then the probability in this case is
::  \mbox{(CP) } [\operatorname{P}(B_1) \times \operatorname{P}(C|B_1)] +  [\operatorname{P}(B_2) \times \operatorname{P}(C|B_2)] 
(i.e. we observe a sum of the single slit cases).          
(4) If a particle reached the screen then (i) if B1, then ~B2 and if  B2, then ~B1 (ii) if ~B1, then  B2 and if ~B2, then B1
 
(5) From (i) and (ii) in classical logic we can infer that B1 v B2 holds which entails CP, the wrong account of the probabilities (or the sum of the single slit cases). It was classical logic that allowed us to go from (i) and (ii) to B1 v B2 and so arrive at the problematic (CP). 
Three-valued logic of course rejects bivalence, that every meaningful statement has one of {T, F} as truth-values. 3VL introduces a third value ‘I’ which is taken to mean indeterminate. As such the truth tables change and the valid inferences change. As it turns out we can’t infer B1 v B2 from (i) and (ii). In 3VL when (i) and (ii) are true ‘B1 v B2’ can be indeterminate. So it is not legitimate in general to infer ‘B1 v B2’, and so the incorrect probability. In such cases the suggestion is that propositions like “the particle has passed through B1 or B2” (or has a definite trajectory) are genuinely, or irreducibly indeterminate. 
--CSTAR 04:20, 3 Jun 2005 (UTC)
thread_title:  Deleted material 

message: The article currently states:
In Philosophy of Logic (the chapter titled "Variant Logics"), Quine explicitly repudiates the idea that classical logic is subject to revision.
In the second edition (1986) there is no chapter titled "Variant Logics", but Chapter 6 carries the title "Deviant Logics". Among the "deviant" logics discussed is Birkhoff and von Neumann's logic. Quine makes it quite clear he is not enthusiastic about this and other logics as a replacement for truth-functional logic: "a serious loss of simplicity", "the handicap of having to think within a deviant logic". This is, however, a far cry from explicit repudiation of the idea that classical logic is subject to revision. On the contrary, in the next chapter, "The Ground of Logical Truth", on page 100, Quine writes: "Logic is in principle no less open to revision than quantum mechanics or the theory of relativity." And further on: "But this circumstance does not distinguish logic from vast tracts of common-sense knowledge that would generally be called empirical." The quoted sentence thus appears to somewhat misrepresent Quine's position: logic is open to revision, but the paradoxes of quantum mechanics are not a compelling reason for revision – the disadvantages outweigh the advantages.  --Lambiam 10:23, 4 May 2008 (UTC)
thread_title:  Quine's position on revision 

message: logic and the process of logic in the universe simply does not apply, it's illogical to be logical in our universe as everything points to the radical (as in the human explanation of everything: we are only binary) Markthemac (talk) 00:37, 29 April 2010 (UTC)
thread_title:  look at nature