[FOM] Progress in Philosophy

[Studtmann, Paul]

The question as to whether there is progress in philosophy immediately faces two philosophical questions: (1) what is progress? and (2) what is philosophy?  Philosophers no doubt will disagree as to whether there is genuine progress in philosophy as a result of their different answers to these questions.  Now, in some sense of progress and some sense of philosophy I think it is absurd to deny that philosophy makes progress.  As some people on this list have already pointed out philosophers and philosophical thinking, whatever those might be, have led to conceptual innovations, new insights, etc.  Just imagine the course of intellectual progress without Aristotle, Descartes, Spinoza, Leibniz, Russell, Frege, and so on.

 

There is, however, another sense of progress that is called to mind by Godel's comments about philosophy, and it is far from clear that philosophy has made progress in that sense.  When Godel compares philosophy to mathematics in Babylonian times, he seems to be suggesting that philosophy is capable, though perhaps only in the distant future, of some kind of systematic body of theory that is as well-established as mathematics, or, if one is not quite so optimistic, perhaps as well-established as some branches of empirical science, for instance psychology.  Godel's sentiment, by the way, is not unique to Godel -- many of the most famous philosophers thought the same thing and indeed developed methodologies and instituted research programs that they thought would place philosophy on a firm theoretical footing.  I have in mind at least the following philosophers (I mention their programs in parentheses): Plato (dialectic), Aristotle (science and its cousins as outlined in the Topics and Posterior Analytics), Descartes (the method of doubt), Spinoza (the geometrical method), Hume (the empiricist method), Kant (the critical philosophy), Husserl (the phenomenological method), Wittgenstein (the linguistic turn), Frege/Russell (The method of analysis).  Of course, no one now thinks that any of these methods came anywhere close to establishing some body of well-established theoretical doctrine.  But one should not infer from our awareness of their failings that the philosophers in question were not extremely serious about their programs.  The suggestion that Kant was not extremely serious about the prospects for the Copernican Revolution in philosophy could only come from someone who hasn't read much Kant.

 

Now, I am a philosophical optimist.  I hold out hope that philosophers can indeed establish positive, substantive philosophical results, though I won't say how I think that they can do this.  But for those on this list who are interested in how close philosophy is to doing this, I think the following line of thought is useful to consider.  As far as I can tell, there is no dispute among mathematicians about whether certain sentences are theorems in classical or intuitionist mathematics.  The matter is capable of decisive proof.  How?  Well, proof.  If the sentence is provable from the axioms in question using the logical rules licensed by the type of mathematics in question, then the sentence is a theorem.  And hence, we have at least that sort of knowledge, i.e. the knowledge that such and such a sentence is provable in such and such a system.  But now to the philosophical question: which mathematical system, classical mathematics or intuitionist mathematics, is correct?  

 

Notice that I have used the word 'correct' in order to ask the philosophical question, and some will object to the use of such a word.  But to the extent that one is interested in doing philosophy rather than mathematics, one must use some word or concept not definable within mathematics.  So if you as a philosopher object to that word, substitute it with another word more to your liking, perhaps 'true', or if you like 'corresponds to the numbers', or some such.  But everyone should be clear -- refusing to use any such words and insisting on using only those words definable within some mathematical theory effectively eliminates the possibility of doing philosophy. This is an instance of the no philosophy in no philosophy out doctrine.

 

With a philosophical question in front of us, we can now ask whether Godel's optimism is naïve. How?  Well, let us ask whether we are close to having settled the philosophical debate between the intuitionist and the classical mathematicians.  Indeed, perhaps we can rehash the arguments that have been carried out on this list so as to see whether any of them decisively settle the matter.  I am quite serious about this.  The debate between proponents of classical mathematics and proponents of intuitionist mathematics is certainly one of the most fundamental debates in the philosophy of mathematics.  So if anyone thinks that philosophy has developed to the point that we can have systematic well-confirmed theoretical knowledge as to whether classical or intuitionist mathematics is the correct mathematics, or, if one is tempted to go meta-philosophical at this point and would prefer to think that philosophy has developed to the point that we have systematic knowledge that questions as to the correctness of some form of mathematics make no sense or are somehow defective, then I want to see the arguments.  

 

Now, I do not deny that there are arguments that people have made.  Philosophers are awfully clever at providing arguments.  Indeed, we have seen several such arguments on this list.  But the arguments do bring to mind the (probably apocryphal) tales of Medieval philosophers engaging in fisticuffs over the universals debate.  One cannot help but get the impression that the arguments eventually end in two philosophers glaring at each other as if each cannot believe that the other is so dense as to accept some philosophical thesis that is patently absurd.  What would really make Godel's claims about philosophical progress plausible, (and I must admit, though Godel no doubt read philosophy, it seems to me that his optimism really must be the result of not having studied the history of philosophy nearly well enough), would be the existence of arguments or other considerations that the experts in the field of philosophy would agree settle one of the fundamental debates in the philosophy of mathematics.  So, once again, I reiterate my challenge: let's hear the arguments.  Or, if one prefers, one can provide some methodology, (or indeed, I would be satisfied with a mere suggestion as to what such a methodology might look like) that would, if carried out properly, settle the debate.  

 

 

Paul Studtmann