In summary, then, the set theoretic 'needs' of physics are surprisingly similar to the set theoretic needs of pure logic. Both disciplines need some set theory to function at all. Both disciplines can 'live' - but live badly - on the meager diet of only predicative sets. Both can live extremely happily on the rich diet of impredicative sets. Insofar, then, as the indispensability of quantification over sets is any argument for their existence - and we will discuss why it is in the next section - we may say that it is a strong argument for the existence of at least predicative sets, and a pretty strong, but not as strong, argument for the existence of impredicative sets.

The similarity between Marxism and neoconservativism might be expressed in the following way: both perspectives say that certain injustices can't be cured under our present system of political democracy and mixed economy. The Marxist concludes that we have to overthrow the present system and the neoconservative concludes that we have to live with the injustices. But they are both wrong.

Philosophers today are as fond as ever of apriori arguments with ethical conclusions. One reason such arguments are always unsatisfying is that they always prove too much; when a philosopher 'solves' an ethical problem for one, one feels as if one had asked for a subway token and been given a passenger ticket valid for the first interplanetary passenger-carrying space ship instead.

In short, analytic statements are statements which we all accept and for which we do not give reasons. This is what we mean when we say that they are true by 'implicit convention'. The problem is then to distinguish them from other statements that we accept, and do not give reasons for, in particular from the statements that we unreasonably accept. To resolve this difficulty, we have to point out some of the crucial distinguishing features of analytic statements (e.g. the fact that the subject concept is not a law-cluster concept), and we have to connect these features with what, in the preceding section, was called the 'rationale' of the analytic-synthetic distinction. Having done this, we can see that the acceptance of analytic statements is rational, even though there are no reasons (in the sense of' evidence') in connection with them.

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I have not attempted in these papers to put forward any grand view of the nature of philosophy; nor do I have any such grand view to put forward if I would. It will be obvious that I do not agree with those who see philosophy as the history of 'howlers', and progress in philosophy as the debunking of howlers. It will also be obvious that I do not agree with those who see philosophy as the enterprise of putting forward a priori truths about the real world (since, for one thing, there are no a priori truths, in my view). I see philosophy as a field which has certain central questions, for example, the relation between thought and reality, and, to mention some questions about which I have not written, the relation between freedom and responsibility, and the nature of the good life. It seems obvious that in dealing with these questions philosophers have formulated rival research programs, that they have put forward general hypotheses, and that philosophers within each major research program have modified their hypotheses by trial and error, even if they sometimes refuse to admit that that is what they are doing. To that extent philosophy is a 'science'. To argue about whether philosophy is a science in any more serious sense seems to me to be hardly a useful occupation. The important thing is that in spite of the stereotypes of science and philosophy that have become blinkers inhibiting the view of laymen, scientists, and philosophers, science and philosophy are interdependent activities; philosophers have always found it essential to draw upon the scientific knowledge of the time, and scientists have always found it essential to do a certain amount of philosophy in their very scientific work, even if they denied that that was what they were doing. It does not seem to me important to decide whether science is philosophy or philosophy is science as long as one has a conception of both that makes both essential to a responsible view of the real world and of man's place in it.

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Part of what makes moral philosophy an anachronistic field is that its practitioners continue to argue in this very traditional and aprioristic way even though they themselves do not claim that one can provide a systematic and indubitable 'foundation' for the subject. Most of them rely on what are supposed to be 'intuitions' without claiming that those intuitions deliver uncontroversial ethical premises, on the one hand, or that they have an ontological or epistemological explanation of the reliability of those intuitions, on the other.

Carnap was driven from Germany by Hitler, and his position has been condemned in the Soviet Union as 'subjective idealism*. Even in the United States, there have been a great many who could not understand this attempt to turn philosophy into a scientific discipline with substantive scientific results, and who have been led to extreme and absurd misinterpretations of the work I have been reporting to you here. Few, perhaps, would have expected traditional empiricism to lead to the development of a speculative theory of ' universal learning machines'; and yet, in retrospect, a concern with systematizing inductive logic has been the oldest concern of empiricist philosophers from Bacon on. No one can yet predict the outcome of this speculative scientific venture. But it is amply clear, whether this particular venture succeeds or fails, that the toleration of philosophical and scientific speculation brings rich rewards and that its suppression leads to sterility.

Even if we consider not words by themselves but rules deciding what words may appropriately be produced in certain contexts — even if we consider, in computer jargon, programs for using words — unless those programs themselves refer to something extra-linguistic there is still no determinate reference that those words possess. This will be a crucial step in the process of reaching the conclusion that the Brain-in-a-Vat Worlders cannot refer to anything external at all (and hence cannot say that they are Brain-in-a-Vat Worlders).

If reason is both transcendent and immanent, then philosophy, as culture-bound reflection and argument about eternal questions, is both in time and eternity. We don't have an Archimedean point; we always speak the language of a time and place; but the rightness and wrongness of what we say is not just for a time and a place.

What I am saying, then, is that elements of what we call "language" or "mind" penetrate so deeply into what we call "reality" that the very project of representing ourselves as being "mappers" of something "language-independent" is fatally compromised from the very start. Like Relativism, but in a different way, Realism is an impossible attempt to view the world from Nowhere. In this situation it is a temptation to say, "So we make the world," or "our language makes up the world," or "our culture makes up the world"; but this is just another form of the same mistake. If we succumb, once again we view the world-the only world we know-as a product. One kind of philosopher views it as a product from a raw material: Unconceptualized Reality. The other views it as a creation ex nihilo. But the world isn't a product. It's just the world.

My own view is that philosophy at its best has always, in every period, included some philosophers who brilliantly represent the moral face of the subject and some philosophers who brilliantly represent the theoretical face, as well as some geniuses whose insights span and unite both sides of the subject. To renounce either the moral ambitions of philosophy or its theoretical ambitions is not just to kill the subject of philosophy; it is to commit intellectual and spiritual suicide.

In closing, I can only apologize for not having given any positive account of either mathematical truth or mathematical necessity. I can only say that I have not given such an account because I think that the search for such an account is a fundamental mistake. It is not that there is nothing special about mathematics; it is that, in my opinion, the investigation of mathematics must presuppose and not seek to account for the truth of mathematics. But this is the beginning of another paper and not the end of this one.

Now, moral philosophers generally prefer to talk about virtues, or about (specific) duties, rights, and so on, rather than about moral images of the world. There are obvious reasons for this; nevertheless, I think that it is a mistake, and that Kant is profoundly right. What we require in moral philosophy is, first and foremost, a moral image of the world, or rather--since, here again, I am more of a pluralist than Kant--a number of complementary moral images of the world.

I might try to save the view that 'future contingents' have no truth value by saying that even present-tense statements have no truth value if they refer to the outcome of events that are so far away that a causal signal informing me of the outcome could not have reached me-now without traveling faster than light. In other words, I might attempt saying that statements about events that are in neither the upper half nor the lower half of my light-cone have no truth value. In addition, statements about events in the upper half of my light-cone have no truth value, since they are in my future according to every coordinate system. So only statements about events in the lower half of my light-cone have a truth value; only events that are in 'my past* according to all observers are determined.