Neurath's Boat

Logical truth and logical consequence

As GFA notes, there has come to be something of a sentiment that logical consequence is a more fundamental notion than logical truth. He cites Read and Etchemendy; Dummett also takes this view (I've been reading Dummett's Frege: Philosophy of Language). GFA questions how anybody can say this when the two are (usually) equivalent; usually you can translate a logical truth into the claim that some consequence relation holds, and vice versa.

GFA does note a couple of exceptions to this equivalence. It is not exactly an exception, but is perhaps also relevant that in providing a minimal basis for a logical system, it is possible to give only rules of inference and no axioms (in fact, this is often done; the logic I'm teaching in my intro class this semester is a "natural deduction" system which uses this approach). On the other hand, it is not possible to give only axioms; some rule of inference is always needed ("axiomatic" systems normally have modus ponens, as well as some sort of substitution rule; substitution rules may be a special case, but modus ponens is clearly a rule of logical consequence). At least, the only way to give a purely axiomatic system would be to make every logical truth an axiom.

Whether all of this suffices to make consequence the more "fundamental" notion, I'm not sure. I am by nature very suspicious of claims that anything is more fundamental than anything else. On the other hand, I sympathize with some of the motives for saying that consequence is the more fundamental notion. Dummett notes that the 20th century saw quite a bit of controversy over the status of logical truths; whether they could be understood to be "analytic" (whatever that means anyway; another issue that was much fought over) and what status they did have if they couldn't be classified as analytic. Dummett seems to consider this largely ink spilled in vain (certainly nothing much was ever settled by all these debates), and also thinks there wouldn't have been so much fuss over it if people had been thinking in terms of consequences rather than logical truths. Perhaps there is more of an intuition that a logical truth needs to be about something, that something needs to make it true, than there is any corresponding intuition regarding logical consequences.

If such an intuition has indeed been a source of frivolous worries, then the equivalence of logical consequence and logical truth ought to be enough to undermine the intuition; if logical truth and logical consequence are equivalent, then it's possible, even if not compulsory, to give a reductive account of the former in terms of the latter, so intuitions that special explanations of logical truths are needed should already be undermined. But they're not precisely equivalent; as GFA's examples show, and as mine may also show, logical consequence is an ever so slightly broader notion. This surely wouldn't justify any extravagant metaphysical thesis that logical consequences are built into the structure of reality in a way that logical truths are not, but of course I don't myself think any extravagant metaphysical theses are ever justified, and if Dummett is right the great benefit of focusing on logical consequence is that such a metaphysical thesis has no intuitive appeal anyway. If we set aside such metaphysical concerns, though, we do seem to be left with a meaningful sense in which consequence is more fundamental. Still, perhaps the terminology is less than ideal, since the word "fundamental" has so many associations with the metaphysical concerns.

Carnap on Heidegger

So, I'm continuing to try to put together a paper on the motivation and significance of Carnap's criticism of Heidegger in his "Overcoming Metaphysics."  As I see it, the core is not so much the verification principle as Carnap's anti-authoritarianism; he rejected metaphysics as being an attempt to claim the authority of Truth for value judgments, and considered Heidegger an important contemporary representative of such authoritarian trends.

Part of this project requires me to get a much better grip on Heidegger.  After all, Carnap himself spent a long time studying Heidegger before he first presented his anti-Heidegger polemic.  However, I find Heidegger extremely hard to understand (probably far more so than Carnap did, since Carnap was familiar with Husserl and the neo-Kantians and the general German philosophical scene which he shared with Heidegger).  I've tried reading Heidegger's own writings before, and haven't gotten much out of them, so before attempting that again I'm trying to find other readings that might help me figure out what he's really trying to say.

To that end, I've been reading Husserl's introduction to phenomenology, but I have also found that very hard to follow.  Tracing things back further, I looked up some Brentano, which seemed easier to follow, but didn't seem to help much with understanding Husserl.  Probably I should read some neo-Kantian stuff, or perhaps work from the other direction and read some Sartre, since I never found Sartre as hard to follow as some other continental thinkers.  Maybe seeing what Sartre tries to do with Heidegger will give me more of an idea of what Heidegger could have been up to.

I did pick up a book on Nietzsche's influence on the early 20th century German left wing, particularly the Expressionists.  That's also useful for my general thesis, as I find Carnap's approving comments on Nietzsche supportive of my interpretation of Carnap as anti-authoritarian.  Nietzsche's criticisms of metaphysics were certainly directed at the way metaphysicians tried to derive authority from Truth, and the appropriation of Nietzsche by other early 20th century leftists shows that Carnap could easily have picked up on that feature of Nietzsche through his leftist cohorts.

Anyway, suggestions from others are of course welcome.

GF-A's bleg

This looks like a very interesting book to me.  I was, sadly, not able to find much by way of problems (though the sentence of Heidegger's which Carnap made fun of was "Das Nichts selbst nichtet;" the manuscript mysteriously and consistently omits the "selbst").  I did find the very end rather rushed and under-argued; it occurred to me that surely Carnap and Neurath could admit that any statement or set of statements could be incorporated into unified science, but claim that pragmatic concerns made it undesirable to do so with metaphysical claims.  This makes the criterion less forceful, of course, but it is not clear that it makes the criterion entirely worthless.  In any event, I found the manuscript quite interesting and plausible, and it made me think I should look at some of the material in the Carnap archives at some point.  I recommend it to anyone interested in the history of analytic philosophy.

Another important day

I had to be told by Richard Zach that today was the birthday of two of the greatest philosophers of the 20th century, possibly the two greatest, Rudolf Carnap and Bertrand Russell.  They also died the same year, a year which would have been an unmitigated tragedy for philosophy were it not for my own birth just before it ended.

The most important work of both philosophers was in philosophical logic, and while logic continues to be a going concern with fascinating new work being done all the time, I tend to think that some of the most important lessons of the early 20th century explosion in logic are being forgotten.  Both more and less can be done with logic than earlier philosophers naively thought, yet modern philosophers, even having all taken their mandatory graduate courses in symbolic logic, continue to try to do what cannot be done, or insist on the impossibility of what has already been done.

Logical symbols can be made to represent anything.  Really anything.  There's no right way to interpret a set of logical symbols; their interpretation is utterly up to us, and if even with that freedom we find it tricky to match up what we're trying to interpret with a given set of symbols, we can just invent more.  Other sets of symbols, with seemingly different sets of rules, can do exactly the same thing as the sets of symbols we're gotten in the habit of using.  Proofs of this are plentiful.

Thus, logic cannot reveal to us the structure of any part of reality.  Completely different logical structures can represent the same reality exactly as well.  That is the sense in which logic does less than some had hoped; there is no legitimate a priori metaphysics.  But there are consequences of this fact.  The extent to which logic can't capture the structure of reality is the extent to which we can't represent the structure of reality; this limitation of logic is not an invitation for "semantic glue" to stick our words to the things they represent, in Putnam's mocking phrase, nor for anything else extra-logical to do the job.  Logic is the story of structures.  If logic says two structures which seem completely different amount to the same thing, then they really do, and one's intuition that one structure is correctly representing reality while the other isn't simply has to be an illusion.  Again, there are in many cases proofs of the equivalence of intuitively different structures, proofs whose validity nobody questions.  If their validity isn't questioned, the consequences must be accepted.

A tiny example of how the great logicians were more perceptive on that point than many since; Carnap used "=" for the biconditional in his Logical Syntax of Language.  Most philosophers since have not done so, because of an intuition that "=" should be used to represent the things on either side being the same, in a stronger sense than logical equivalence.  But logical equivalence means possession of the same truth value, and truth values are ultimately what complete wffs represent.  In what sense are "1+1" and "2" the "same thing" in "1+1=2," such that the left and right formulas in "(p->p)=(pv~p)" are not the same thing?  Certainly some such difference could be built into a system, but in the standard interpretation it is not.  Even logicians seem to attribute spooky properties to identity these days, when they of all people should know better (some of Kripke's work is afflicted with this problem).

Anyway, enough ranting.  Some of us are trying not to forget the lessons of the new logic, and we should celebrate those who helped discover those lessons.  Happy May 18th!