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.

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.

On another possible world or another planet a word might be associated with much the same stereotype and much the same criteria as our term 'water', but it might designate XYZ and not H₂O. At least this could happen in a prescientific era. And it would not follow that XYZ was water; it would only follow that XYZ could look like water, taste like water, etc. What 'water' refers to depends on the actual nature of the paradigms, not just on what is in our heads.

To successfully adjudicate ethical problems, as opposed to 'solving' them, it is necessary that the members of the society have a sense of community. A compromise that cannot pretend to be the last word on an ethical question, that cannot pretend to derive from binding principles in an unmistakeably constraining way, can only derive its force from a shared sense of what is and is not reasonable, from loyalties to one another, and a commitment to 'muddling through' together.

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.

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Let me close with a picture. My picture of our situation is not the famous Neurath picture of science as the enterprise of reconstructing a boat while the boat floats on the open ocean, but it is a modification of it. I would change Neurath's picture in two ways. First, I would put ethics, philosophy, in fact the whole culture, in the boat, and not just 'science', for I believe all the parts of the culture are inter- dependent. And, second, my image is not of a single boat but of a fleet of boats. The people in each boat are trying to reconstruct their own boat without modifying it so much at anyone time that the boat sinks, as in the Neurath image. In addition, people are passing supplies and tools from one boat to another and shouting advice and encouragement (or discouragement) to each other. Finally, people sometimes decide they don't like the boat they're in and move to a different boat altogether. (And sometimes a boat sinks or is abandoned.) It's all a bit chaotic; but since it is a fleet, no one is ever totally out of signalling distance from all the other boats. There is, in short, both collectivity and individual responsibility. If we hanker for more, is that not our old and unsatisfiable yearning for Absolutes?

To me it seems clear that the descriptions of human life we find in the novels of Tolstoy or George Eliot are not mere entertainment; they teach us to perceive what goes on in social and individual life. And such descriptions require the many subtle distinctions that ordinary language has made available to us. The question of the relevance or irrelevance of “how we speak” is not just a question for philosophers, although it is that too. It is a question for philosophers because once ordinary language is laughed out of the room, philosophical theories are no longer held responsible at all to the ways we actually speak and actually live; but it is a question for more than just philosophers because, at bottom, contempt for ordinary language is contempt for all the humanities.

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.

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.

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What we have is a device for producing sentences in response to sentences. But none of these sentences is at all connected to the real world. If one coupled two of these machines and let them play the Imitation Game with each other, then they would go on 'fooling' each other forever, even if the rest of the world disappeared! There is no more reason to regard the machine's talk of apples as referring to real world apples than there is to regard the ant's 'drawing' as referring to Winston Churchill.

Even though the model referred to satisfies the theory, etc., it is 'unintended'; and we recognize that it is unintended from the description through which it is given (as in the intuitionist case). Models are not lost noumenal waifs looking for someone to name them; they are constructions within our theory itself. and they have names from birth.

The problem with all this--the problem I discussed in the first lecture--is that if the causes/background conditions distinction is fundamentally subjective, not descriptive of the world in itself, then current philosophical explanations of the metaphysical nature of reference are bankrupt.

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.