Talk:Is logic empirical?

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Contents 1 Reichenbach 2 article? 3 Deletions 4 Dummett's argument; empirical tests of logical laws 5 Deleted material 6 Change to intro para 6.1 Reply 7 Quine's position on revision

[edit] Reichenbach

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)

Point taken. I tried to weaken the sentence in the introduction by adding 'also'. Cheers. -gericault

There are some other adjustments to make, will get to them.- gericaul

The article says "Reichenbach considered one of the anomalies associated with quantum mechanics, the problem of complementary properties. A pair of properties of a system is said to be complementary if each one of them can be assigned a truth value in some experimental setup, but there is no setup which assigns a truth value to both properties. ... Another example of complementary properties are those of having a precisely observed position or momentum."

This is an incorrect statement of the Heisenberg Uncertainty Principle. For a more correct statement see Heisenberg Uncertainty Principle

One statement of the Principle is:

Given something with mass --

   ΔX ΔP ≥ hbar/2

Where the uncertainty in the position of the thing is ΔX, the uncertainty in the momentum of the thing is ΔP and hbar is a basic physical constant of the Universe.

Please notice that in this equation "a precisely observed position..." would mean that uncertainty in the measurement of the position of the thing would be 0 and "a precisely observed ... momentum" would mean that the uncertainty in the measurement of the momentum of the thing would be 0. The entire point of the Uncertainty Principle is that this is impossible.

Notice also that to measure the momentum of something, you have to measure the mass and velocity of the thing in relation to something else. To measure the velocity of something you have to measure its position at one time and its position at a later time. Each of these measurements has a precision assigned to it; real chronometers do not measure time continuously and the time reported by the chronometer must be observed by some method. If the first time is considered 0, then the second time (and elapsed time) will be reported more or less like this: 0.023 ± 0.001 seconds. The '±' here represents the limits of the measuring and reporting devices. The same is true for measurements of position.

The Uncertainty Principle means that talking about the momentum and position of anything carries with it a basic physical connection and a lower limit of measurablity, whatever the precision of the measuring devices involved. The uncertainty in the measurement of the specific momentum of anything at a given time is directly dependent on the uncertainty in the measurement of the position of the thing at the time the momentum is measured. There is no possibility of talking about independent truth values for these two qualities because they are physically tied to each other. This is only important when you are talking about very small things such as electrons. When the thing being observed is bigger (roughly the size of a large atom and above) the Uncertainty Principle limit is so small (relatively) that we can treat momentum and position as if they were two separate physical properties.--Davidkentsnyder (talk) 15:30, 3 May 2008 (UTC)

[edit] article?

In this article, it says, "In a later paper, Variant logics, he [Quine] explicitly repudiates the idea that classical logic is subject to revision." I looked all over for a paper titled "Variant Logics" and found nothing. Google and Google Scholar turned up nothing. I even searching the list of published articles on Quine's website, and did not find a paper of that name. Can someone verify that this paper exists, and is titled correctly? Also, a quotation from the paper that supports the thesis "classical logic is not subject to revision" would be helpful. -- Ramzi

[edit] Deletions

I deleted the following bits of material from User:CSTAR's original text:

1. 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;
2. 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)

[edit] Dummett's argument; empirical tests of logical laws

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)

[edit] Deleted material

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

---

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

and the probability when slit B₂ is open is

(3) The classical (physics) assumption is that when both slits are open then the probability in this case is

(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)

[edit] Change to intro para

CSTAR wrote:

That such a revision might be necessary was suggested by the work of Garrett Birkhoff and John von Neumann on quantum logic.

Doesn't this suggest that Birkhoff and Von Neumann were proposing this revision, ie. that classical logic was wrong and quantum logic should be its replacement? --- Charles Stewart 13:54, 14 Jun 2005 (UTC)

[edit] Reply

Unfortunately, I'm not sure of the history here. However, I'm pretty sure von Neumann/Birkhoff weren't thinking of going whole-hog and revising propositional logic; they were developing a model for dealing with "experimental filters" e.g. a physical process that answers "yes or no"; The yes or no questions are of the nature

1. particle has X-momentum in the interval [a,b]
2. particle energy is in the interval [c,d].

I'm also not sure who used "yes or no" question first. It may have been much later with Finkelstein. Mackey also used the term in his classic book.

BTW My changes to the article text are motivated by the addition (by somebody else) a few weeks ago of Reichenbach's work. I've been trying to figure out the relation between Reichenbach and von Neumann/Birkhoff (actually it's easy technically -- Reichenbach really doesn't have a quantum logic strong enough to do quantum mechanics, just barely enough to give a mesaning to complementarity). Reichenbach doesn't cite vonNeuman/Birkoff even though they preceded him by 8 years.

Reichenbach is however worth mentioning since Putnam was his Ph.D. student at UCLA.

I hope I haven't made the article worse.--CSTAR 14:24, 14 Jun 2005 (UTC)

I see your point now rereading the intro. However, even though the preceding intro may have been better, I don't like the use of "logic" to refer to vnNeumann/Birkhoff. Strictly speaking, they only talk about the semantic domain for a quantum logic. It is as though we referred to a particular semantic domain as the logic for the pi-calculus. Any suggestions? --CSTAR 15:16, 14 Jun 2005 (UTC)

What should we call it? An algebra of observables?

I've made some related changes to Two Dogmas of Empiricism. --- Charles Stewart 16:33, 14 Jun 2005 (UTC)

An algebra of "idempotent" observables is technically accurate. I'll have to run down to the library today or tomorrow to check out the vonNeumann/Birkhoff terminology. Omnès claims that von Neumann referred to these as elementary predicates --CSTAR 16:57, 14 Jun 2005 (UTC)

"Experimental propositions" is what they call them.--CSTAR 23:05, 17 Jun 2005 (UTC)

[edit] Quine's position on revision

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)