Ontological Relativity | |||

Quine (W.V.) | |||

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**BOOK ABSTRACT: **None.

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- Epistemology is concerned with the foundations of science. Conceived thus broadly, epistemology includes the study of the foundations of mathematics as one of its departments. Specialists at the turn of the century thought that their efforts in this particular department were achieving notable success: mathematics seemed to reduce altogether to logic. In a more recent perspective this reduction is seen to be better describable as a reduction to logic and set theory. This correction is a disappointment epistemologically, since the firmness and obviousness that we associate with logic cannot be claimed for set theory. But still the success achieved in the foundations of mathematics remains exemplary by comparative standards, and we can illuminate the rest of epistemology somewhat by drawing parallels to this department.
- Studies in the foundations of mathematics divide symmetrically into two sorts, conceptual and doctrinal. The conceptual studies are concerned with meaning, the doctrinal with truth. The conceptual studies are concerned with clarifying concepts by defining them, some in terms of others. The doctrinal studies are concerned with establishing laws by proving them, some on the basis of others. Ideally the obscurer concepts would be defined in terms of the clearer ones so as to maximize clarity, and the less obvious laws would be proved from the more obvious ones so as to maximize certainty. Ideally the definitions would generate all the concepts from clear and distinct ideas, and the proofs would generate all the theorems from self-evident truths.
- The two ideals are linked. For, if you define all the concepts by use of some favored subset of them, you thereby show how to translate all theorems into these favored terms. The clearer these terms are, the likelier it is that the truths couched in them will be obviously true, or derivable from obvious truths. If in particular the concepts of mathematics were all reducible to the clear terms of logic, then all the truths of mathematics would go over into truths of logic; and surely the truths of logic are all obvious or at least potentially obvious, i.e., derivable from obvious truths by individually obvious steps.
- This particular outcome is in fact denied us, however, since mathematics reduces only to set theory and not to logic proper. Such reduction still enhances clarity, but only because of the interrelations that emerge and not because the end terms of the analysis are clearer than others. As for the end truths, the axioms of set theory, these have less obviousness and certainty to recommend them than do most of the mathematical theorems that we would derive from them. Moreover, we know from Gödel’s work that no consistent axiom system can cover mathematics even when we renounce self-evidence. Reduction in the foundations of mathematics remains mathematically and philosophically fascinating, but it does not do what the epistemologist would like of it: it does not reveal the ground of mathematical knowledge, it does not show how mathematical certainty is possible.

- "Sosa (Ernest) & Kim (Jaegwon), Eds. - Epistemology - An Anthology", and in
- "Kornblith (Hilary) - Naturalizing Epistemology".

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- What tends to confirm an induction? This question has been aggravated on the one hand by Hempel's puzzle of the non-black
__non-ravens___{1}and exacerbated on the other by Goodman's puzzle of the grue__emeralds___{2}. I shall begin my remarks by relating the one puzzle to the other, and the other to an innate flair that we have for natural kinds^{3}. Then I shall devote the rest of the paper to reflections on the nature of this notion of natural kinds^{4}and its relation to science. - Hempel's puzzle is that just as each black raven tends to confirm the law that all ravens are black, so each green leaf, being a non-black non-raven, should tend to confirm the law that all non-black things are non-ravens, that is, again, that all ravens are black. What is paradoxical is that a green leaf should count toward the law that all ravens are black.
- Goodman propounds his puzzle by requiring us to imagine that emeralds, having been identified by some criterion other than color, are now being examined one after another and all up to now are found to be green. Then he proposes to call anything
*grue*that is examined today or earlier and found to be green or is not examined before tomorrow and is blue. Should we expect the first one examined tomorrow to be green, because all examined up to now were green? But all examined up to now were also grue; so why not expect the first one tomorrow to be grue, and therefore blue? - The predicate "green," Goodman
__says___{5}, is*projectible*; "grue" is not. He says this by way of putting a name to the problem. His step toward solution is his doctrine of what he calls__entrenchment___{6}, which I shall touch on later. Meanwhile the terminological point is simply that projectible predicates are predicates p and q whose shared instances all do count, for whatever reason, toward confirmation of [All p are q]. - Now I propose assimilating Hempel's puzzle to Goodman's by inferring from Hempel's that the complement of a projectible predicate need not be projectible. "Raven" and "black" are projectible; a black raven does count toward "All ravens are black." Hence a black raven counts also, indirectly, toward "All non-black things are non-ravens," since this says the same thing. But a green leaf does not count toward "All non-black things are non-ravens," nor, therefore, toward "All ravens are black"; "non-black" and "non-raven" are not projectible. "Green" and "leaf" are projectible, and the green leaf counts toward "All leaves are green" and "All green things are leaves"; but only a black raven can confirm "All ravens are black," the complements not being projectible.

- Also in "Kornblith (Hilary) - Naturalizing Epistemology",
- And in "Schwartz (Stephen P.), Ed. - Naming, Necessity and Natural Kinds".
- Photocopy filed in "Various - Papers on Identity Boxes: Vol 15 (Q-R)".
- For Notes, see "Funkhouser (Eric) - Notes on Quine, “Natural Kinds”".

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- Blue: Text by me; © Theo Todman, 2019
- Mauve: Text by correspondent(s) or other author(s); © the author(s)

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