Logicians From The United States

"Secondly, even disregarding the intrinsic necessity of some new axiom, and even in case it has no intrinsic necessity at all, a probable decision about its truth is possible also in another way, namely, inductively by studying its "success." Success here means fruitfulness in consequences, in particular in "verifiable" consequences, i.e. consequences verifiable without the new axiom, whose proofs with the help of the new axiom, however, are considerably simpler and easier to discover, and make it possible to contract into one proof many different proofs. The axioms for the system of real numbers, rejected by the intuitionists, have in this sense been verified to some extent, owing to the fact that analytic number theory frequently allows one to prove number-theoretical theorems which, in a more cumbersome way, can subsequently be verified by elementary methods. A much higher degree of verification than that, however, is conceivable. There might exists axioms so abundant in their verifiable consequences, shedding so much light upon a whole field, and yielding such powerful methods for solving problems, (and even solving them constructively, as far as that is possible) that, no matter whether or not they are intrinsically necessary, they would have to be accepted at least in the same sense as any well-established physical theory."

"The meaning of the world is the separation of wish and fact. Wish is a force as applied to thinking beings, to realize something. A fulfilled wish is a union of wish and fact. The meaning of the whole world is the separation and the union of fact and wish."

"Religions are, for the most part, bad-but religion is not."

"There are other worlds and rational beings of a different and higher kind. The world in which we live is not the only one in which we shall live or have lived."

"I like Islam, it is a consistent idea of religion and open-minded."

"The formation in geological time of the human body by the laws of physics (or any other laws of similar nature), starting from a random distribution of elementary particles and the field is as unlikely as the separation of the atmosphere into its components. The complexity of the living things has to be present within the material [from which they are derived] or in the laws [governing their formation]."

"Either mathematics is too big for the human mind, or the human mind is more than a machine."

"But every error is due to extraneous factors (such as emotion and education); reason itself does not err."

"The completeness theorem, mathematically, is indeed an almost trivial consequence of Skolem 1923a. However, the fact is that, at that time, nobody (including Skolem himself) drew this conclusion (neither from Skolem 1923a nor, as I did, from similar considerations of his own)."

"To every ω-consistent recursive class κ of formulae there correspond recursive class signs r, such that neither v Gen r nor Neg (v Gen r) belongs to Flg (κ) (where v is the free variable of r)."

"Possibly, but my concern is that there not be more things in my philosophy than are in heaven and earth."

"I do not agree with Quine, that there is no analytic-synthetic distinction to be drawn at all. But I do believe that his emphasis on the monolithic character of our conceptual system and his negative emphasis on the silliness of regarding mathematics as consisting in some sense of 'rules of language', represent exceedingly important theoretical insights in philosophy. I think that what we have to do now is to settle the relatively trivial question concerning analytic statements properly so called ('All bachelors are unmarried'). We have to take a fresh look at the framework principles so much discussed by philosophers, disabusing ourselves of the idea that they are 'rules of language' in any literal or lexicographic sense; and above all, we have to take a fresh look at the nature of logical and mathematical truths. With Quine's contribution, we have to face two choices: We can ignore it and go on talking about the 'logic' of individual words. In that direction lies sterility and more, much more, of what we have already read. The other alternative is to face and explore the insight achieved by Quine, trying to reconcile the fact that Quine is overwhelmingly right in his critique of what other philosophers have done with the analytic-synthetic distinction with the fact that Quine is wrong in his literal thesis, namely, that the distinction itself does not exist at all. In the latter direction lies philosophic progress. For philosophic progress is nothing if it is not the discovery of new areas for dialectical exploration."

"Logic chases truth up the tree of grammar."

"Set theory in sheep's clothing."

""Yields falsehood when preceded by its quotation" yields falsehood when preceded by its quotation."

"Life is agid. Life is fulgid. Life is a burgeoning, a quickening of the dim primordial urge in the murky wastes of time. Life is what the least of us make most of us feel the least of us make the most of."

"Necessity resides in the way we talk about things, not in the things we talk about."

"At root what is needed for scientific inquiry is just receptivity to data, skill in reasoning, and yearning for truth. Admittedly, ingenuity can help too."

"Implication is thus the very texture of our web of belief, and logic is the theory that traces it."

"It is within science itself, and not in some prior philosophy, that reality is to be identified and described."

"We cannot stem linguistic change, but we can drag our feet. If each of us were to defy Alexander Pope and be the last to lay the old aside, it might not be a better world, but it would be a lovelier language."

"I regard Quine as one of our most stimulating philosophers."

"How are we to adjudicate among rival ontologies? Certainly the answer is not provided by the semantical formula "To be is to be the value of a variable"; this formula serves rather, conversely, in testing the conformity of a given remark or doctrine to a prior ontological standard."

"Nonbeing must in some sense be, otherwise what is it that there is not? This tangled doctrine might be nicknamed Plato's beard; historically it has proved tough, frequently dulling the edge of Occam's razor."

"Wyman's overpopulated universe is in many ways unlovely. It offends the aesthetic sense of us who have a taste for desert landscapes."

"Modern empiricism has been conditioned in large part by two dogmas. One is a belief in some fundamental cleavage between truths which are analytic, or grounded in meanings independently of matters of fact, and truths which are synthetic, or grounded in fact. The other dogma is reductionism: the belief that each meaningful statement is equivalent to some logical construct upon terms which refer to immediate experience. Both dogmas, I shall argue, are ill-founded. One effect of abandoning them is, as we shall see, a blurring of the supposed boundary between speculative metaphysics and natural science. Another effect is a shift toward pragmatism."

"The word 'definition' has come to have a dangerously reassuring sound, owing no doubt to its frequent occurrence in logical and mathematical writings."

"Our argument is not flatly circular, but something like it. It has the form, figuratively speaking, of a closed curve in space."

"No particular experiences are linked with any particular statements in the interior of the field, except indirectly through considerations of equilibrium affecting the field as a whole."

"Even a statement very close to the periphery can be held true in the face of recalcitrant experience by pleading hallucination or by amending certain statements of the kind called logical laws. Conversely, by the same token, no statement is immune to revision. Revision even of the logical law of the excluded middle has been proposed as a means of simplifying quantum mechanics; and what difference is there in principle between such a shift and the shift whereby Kepler superseded Ptolemy, or Einstein Newton, or Darwin Aristotle?"

"As an empiricist I continue to think of the conceptual scheme of science as a tool, ultimately, for predicting future experience in the light of past experience. Physical objects are conceptually imported into the situation as convenient intermediaries—not by definition in terms of experience, but simply as irreducible posits comparable, epistemologically, to the gods of Homer. For my part I do, qua lay physicist, believe in physical objects and not in Homer's gods; and I consider it a scientific error to believe otherwise. But in point of epistemological footing the physical objects and the gods differ only in degree and not in kind. Both sorts of entities enter our conception only as cultural posits. The myth of physical objects is epistemologically superior to most in that it has proved more efficacious than other myths as a device for working a manageable structure into the flux of experience."

"The issue over there being classes seems more a question of convenient conceptual scheme; the issue over there being centaurs, or brick houses on Elm Street, seems more a question of fact. But I have been urging that this difference is only one of degree, and that it turns upon our vaguely pragmatic inclination to adjust one strand of the fabric of science rather than another in accommodating some particular recalcitrant experience. Conservatism figures in such choices, and so does the quest for simplicity."

"Tactically, conceptualism is no doubt the strongest position of the three; for the tired nominalist can lapse into conceptualism and still allay his puritanic conscience with the reflection that he has not quite taken to eating lotus with the Platonists."

"A fancifully fancyless medium of unvarnished news."

"Creatures inveterately wrong in their inductions have a pathetic but praiseworthy tendency to die before reproducing their kind."

"I have free will, but not of my own choice. I have never freely chosen to have free will. I have to have free will, whether I like it or not!"

"If it is really true that you cannot resist them, then you are not sinning of your own free will and hence (at least according to me) not sinning at all."

"There is nothing like a naturalistic orientation to dispel all these morbid thoughts of "sin" and "free will" and "moral responsibility.""

"Medical opinions differed as to the cause of this "humor" disease."

"From what little was known about the subject, insincerity itself was regarded as another form of psychosis but one which was exceedingly rare."

"Humor could not flourish in a wholly serious and rational atmosphere."

"Metaphysical problems about "mind" versus "matter" arise only from epistemological confusions."

"Of course the falsity of the fact that you believe it is red implies that you don't believe it is red. But this does not mean that you believe it is not red!"

"I believe that either Jupiter has life or it doesn't. But I neither believe that it does, nor do I believe that it doesn't."

"Why should I worry about dying? It's not going to happen in my lifetime!"