93 ideas
| 1627 | Any statement can be held true if we make enough adjustment to the rest of the system [Quine] |
| Full Idea: Any statement can be held true come what may, if we make drastic enough adjustments elsewhere in the system. | |
| From: Willard Quine (Two Dogmas of Empiricism [1953], p.43) |
| 224 | When questions are doubtful we should concentrate not on objects but on ideas of the intellect [Plato] |
| Full Idea: Doubtful questions should not be discussed in terms of visible objects or in relation to them, but only with reference to ideas conceived by the intellect. | |
| From: Plato (Parmenides [c.364 BCE], 135e) |
| 232 | Opposites are as unlike as possible [Plato] |
| Full Idea: Opposites are as unlike as possible. | |
| From: Plato (Parmenides [c.364 BCE], 159a) |
| 8937 | Plato's 'Parmenides' is the greatest artistic achievement of the ancient dialectic [Hegel on Plato] |
| Full Idea: Plato's 'Parmenides' is the greatest artistic achievement of the ancient dialectic. | |
| From: comment on Plato (Parmenides [c.364 BCE]) by Georg W.F.Hegel - Phenomenology of Spirit Pref 71 | |
| A reaction: It is a long way from the analytic tradition of philosophy to be singling out a classic text for its 'artistic' achievement. Eventually we may even look back on, say, Kripke's 'Naming and Necessity' and see it in that light. |
| 1623 | Definition rests on synonymy, rather than explaining it [Quine] |
| Full Idea: Definition rests on synonymy, rather than explaining it. | |
| From: Willard Quine (Two Dogmas of Empiricism [1953], p.26) |
| 15413 | With four tense operators, all complex tenses reduce to fourteen basic cases [Burgess] |
| Full Idea: Fand P as 'will' and 'was', G as 'always going to be', H as 'always has been', all tenses reduce to 14 cases: the past series, each implying the next, FH,H,PH,HP,P,GP, and the future series PG,G,FG,GF,F,HF, plus GH=HG implying all, FP=PF which all imply. | |
| From: John P. Burgess (Philosophical Logic [2009], 2.8) | |
| A reaction: I have tried to translate the fourteen into English, but am not quite confident enough to publish them here. I leave it as an exercise for the reader. |
| 15415 | The temporal Barcan formulas fix what exists, which seems absurd [Burgess] |
| Full Idea: In temporal logic, if the converse Barcan formula holds then nothing goes out of existence, and the direct Barcan formula holds if nothing ever comes into existence. These results highlight the intuitive absurdity of the Barcan formulas. | |
| From: John P. Burgess (Philosophical Logic [2009], 2.9) | |
| A reaction: This is my reaction to the modal cases as well - the absurdity of thinking that no actually nonexistent thing might possibly have existed, or that the actual existents might not have existed. Williamson seems to be the biggest friend of the formulas. |
| 15430 | Is classical logic a part of intuitionist logic, or vice versa? [Burgess] |
| Full Idea: From one point of view intuitionistic logic is a part of classical logic, missing one axiom, from another classical logic is a part of intuitionistic logic, missing two connectives, intuitionistic v and → | |
| From: John P. Burgess (Philosophical Logic [2009], 6.4) |
| 15431 | It is still unsettled whether standard intuitionist logic is complete [Burgess] |
| Full Idea: The question of the completeness of the full intuitionistic logic for its intended interpretation is not yet fully resolved. | |
| From: John P. Burgess (Philosophical Logic [2009], 6.9) |
| 15429 | Relevance logic's → is perhaps expressible by 'if A, then B, for that reason' [Burgess] |
| Full Idea: The relevantist logician's → is perhaps expressible by 'if A, then B, for that reason'. | |
| From: John P. Burgess (Philosophical Logic [2009], 5.8) |
| 15404 | Technical people see logic as any formal system that can be studied, not a study of argument validity [Burgess] |
| Full Idea: Among the more technically oriented a 'logic' no longer means a theory about which forms of argument are valid, but rather means any formalism, regardless of its applications, that resembles original logic enough to be studied by similar methods. | |
| From: John P. Burgess (Philosophical Logic [2009], Pref) | |
| A reaction: There doesn't seem to be any great intellectual obligation to be 'technical'. As far as pure logic is concerned, I am very drawn to the computer approach, since I take that to be the original dream of Aristotle and Leibniz - impersonal precision. |
| 15405 | Classical logic neglects the non-mathematical, such as temporality or modality [Burgess] |
| Full Idea: There are topics of great philosophical interest that classical logic neglects because they are not important to mathematics. …These include distinctions of past, present and future, or of necessary, actual and possible. | |
| From: John P. Burgess (Philosophical Logic [2009], 1.1) |
| 15427 | The Cut Rule expresses the classical idea that entailment is transitive [Burgess] |
| Full Idea: The Cut rule (from A|-B and B|-C, infer A|-C) directly expresses the classical doctrine that entailment is transitive. | |
| From: John P. Burgess (Philosophical Logic [2009], 5.3) |
| 15421 | Classical logic neglects counterfactuals, temporality and modality, because maths doesn't use them [Burgess] |
| Full Idea: Classical logic neglects counterfactual conditionals for the same reason it neglects temporal and modal distinctions, namely, that they play no serious role in mathematics. | |
| From: John P. Burgess (Philosophical Logic [2009], 4.1) | |
| A reaction: Science obviously needs counterfactuals, and metaphysics needs modality. Maybe so-called 'classical' logic will be renamed 'basic mathematical logic'. Philosophy will become a lot clearer when that happens. |
| 15403 | Philosophical logic is a branch of logic, and is now centred in computer science [Burgess] |
| Full Idea: Philosophical logic is a branch of logic, a technical subject. …Its centre of gravity today lies in theoretical computer science. | |
| From: John P. Burgess (Philosophical Logic [2009], Pref) | |
| A reaction: He firmly distinguishes it from 'philosophy of logic', but doesn't spell it out. I take it that philosophical logic concerns metaprinciples which compare logical systems, and suggest new lines of research. Philosophy of logic seems more like metaphysics. |
| 15407 | Formalising arguments favours lots of connectives; proving things favours having very few [Burgess] |
| Full Idea: When formalising arguments it is convenient to have as many connectives as possible available.; but when proving results about formulas it is convenient to have as few as possible. | |
| From: John P. Burgess (Philosophical Logic [2009], 1.4) | |
| A reaction: Illuminating. The fact that you can whittle classical logic down to two (or even fewer!) connectives warms the heart of technicians, but makes connection to real life much more difficult. Hence a bunch of extras get added. |
| 15424 | Asserting a disjunction from one disjunct seems odd, but can be sensible, and needed in maths [Burgess] |
| Full Idea: Gricean implicature theory might suggest that a disjunction is never assertable when a disjunct is (though actually the disjunction might be 'pertinent') - but the procedure is indispensable in mathematical practice. | |
| From: John P. Burgess (Philosophical Logic [2009], 5.2) | |
| A reaction: He gives an example of a proof in maths which needs it, and an unusual conversational occasion where it makes sense. |
| 15409 | All occurrences of variables in atomic formulas are free [Burgess] |
| Full Idea: All occurrences of variables in atomic formulas are free. | |
| From: John P. Burgess (Philosophical Logic [2009], 1.7) |
| 9204 | Quine's arguments fail because he naively conflates names with descriptions [Fine,K on Quine] |
| Full Idea: Quine's logical argument against modality presupposes a naïve view of singular terms under which no significant distinction is to be drawn between the use of names and descriptions. | |
| From: comment on Willard Quine (Two Dogmas of Empiricism [1953]) by Kit Fine - Intro to 'Modality and Tense' p. 6 | |
| A reaction: See Idea 9201 for Quine's argument. The question is whether '9' and 'the number of planets' are names or descriptions. The 'number of planets' is not remotely descriptive of 9, so it must be referential. So '9' is a name? Hm. |
| 15414 | The denotation of a definite description is flexible, rather than rigid [Burgess] |
| Full Idea: By contrast to rigidly designating proper names, …the denotation of definite descriptions is (in general) not rigid but flexible. | |
| From: John P. Burgess (Philosophical Logic [2009], 2.9) | |
| A reaction: This modern way of putting it greatly clarifies why Russell was interested in the type of reference involved in definite descriptions. Obviously some descriptions (such as 'the only person who could ever have…') might be rigid. |
| 15406 | 'Induction' and 'recursion' on complexity prove by connecting a formula to its atomic components [Burgess] |
| Full Idea: There are atomic formulas, and formulas built from the connectives, and that is all. We show that all formulas have some property, first for the atomics, then the others. This proof is 'induction on complexity'; we also use 'recursion on complexity'. | |
| From: John P. Burgess (Philosophical Logic [2009], 1.4) | |
| A reaction: That is: 'induction on complexity' builds a proof from atomics, via connectives; 'recursion on complexity' breaks down to the atomics, also via the connectives. You prove something by showing it is rooted in simple truths. |
| 15425 | The sequent calculus makes it possible to have proof without transitivity of entailment [Burgess] |
| Full Idea: It might be wondered how one could have any kind of proof procedure at all if transitivity of entailment is disallowed, but the sequent calculus can get around the difficulty. | |
| From: John P. Burgess (Philosophical Logic [2009], 5.3) | |
| A reaction: He gives examples where transitivity of entailment (so that you can build endless chains of deductions) might fail. This is the point of the 'cut free' version of sequent calculus, since the cut rule allows transitivity. |
| 15426 | We can build one expanding sequence, instead of a chain of deductions [Burgess] |
| Full Idea: Instead of demonstrations which are either axioms, or follow from axioms by rules, we can have one ever-growing sequence of formulas of the form 'Axioms |- ______', where the blank is filled by Axioms, then Lemmas, then Theorems, then Corollaries. | |
| From: John P. Burgess (Philosophical Logic [2009], 5.3) |
| 15408 | 'Tautologies' are valid formulas of classical sentential logic - or substitution instances in other logics [Burgess] |
| Full Idea: The valid formulas of classical sentential logic are called 'tautologically valid', or simply 'tautologies'; with other logics 'tautologies' are formulas that are substitution instances of valid formulas of classical sentential logic. | |
| From: John P. Burgess (Philosophical Logic [2009], 1.5) |
| 15418 | Validity (for truth) and demonstrability (for proof) have correlates in satisfiability and consistency [Burgess] |
| Full Idea: Validity (truth by virtue of logical form alone) and demonstrability (provability by virtue of logical form alone) have correlative notions of logical possibility, 'satisfiability' and 'consistency', which come apart in some logics. | |
| From: John P. Burgess (Philosophical Logic [2009], 3.3) |
| 15412 | Models leave out meaning, and just focus on truth values [Burgess] |
| Full Idea: Models generally deliberately leave out meaning, retaining only what is important for the determination of truth values. | |
| From: John P. Burgess (Philosophical Logic [2009], 2.2) | |
| A reaction: This is the key point to hang on to, if you are to avoid confusing mathematical models with models of things in the real world. |
| 15411 | We only need to study mathematical models, since all other models are isomorphic to these [Burgess] |
| Full Idea: In practice there is no need to consider any but mathematical models, models whose universes consist of mathematical objects, since every model is isomorphic to one of these. | |
| From: John P. Burgess (Philosophical Logic [2009], 1.8) | |
| A reaction: The crucial link is the technique of Gödel Numbering, which can translate any verbal formula into numerical form. He adds that, because of the Löwenheim-Skolem theorem only subsets of the natural numbers need be considered. |
| 15416 | We aim to get the technical notion of truth in all models matching intuitive truth in all instances [Burgess] |
| Full Idea: The aim in setting up a model theory is that the technical notion of truth in all models should agree with the intuitive notion of truth in all instances. A model is supposed to represent everything about an instance that matters for its truth. | |
| From: John P. Burgess (Philosophical Logic [2009], 3.2) |
| 13986 | Plato found antinomies in ideas, Kant in space and time, and Bradley in relations [Plato, by Ryle] |
| Full Idea: Plato (in 'Parmenides') shows that the theory that 'Eide' are substances, and Kant that space and time are substances, and Bradley that relations are substances, all lead to aninomies. | |
| From: report of Plato (Parmenides [c.364 BCE]) by Gilbert Ryle - Are there propositions? 'Objections' |
| 14150 | Plato's 'Parmenides' is perhaps the best collection of antinomies ever made [Russell on Plato] |
| Full Idea: Plato's 'Parmenides' is perhaps the best collection of antinomies ever made. | |
| From: comment on Plato (Parmenides [c.364 BCE]) by Bertrand Russell - The Principles of Mathematics §337 |
| 15428 | The Liar seems like a truth-value 'gap', but dialethists see it as a 'glut' [Burgess] |
| Full Idea: It is a common view that the liar sentence ('This very sentence is not true') is an instance of a truth-value gap (neither true nor false), but some dialethists cite it as an example of a truth-value glut (both true and false). | |
| From: John P. Burgess (Philosophical Logic [2009], 5.7) | |
| A reaction: The defence of the glut view must be that it is true, then it is false, then it is true... Could it manage both at once? |
| 16150 | One is, so numbers exist, so endless numbers exist, and each one must partake of being [Plato] |
| Full Idea: If one is, there must also necessarily be number - Necessarily - But if there is number, there would be many, and an unlimited multitude of beings. ..So if all partakes of being, each part of number would also partake of it. | |
| From: Plato (Parmenides [c.364 BCE], 144a) | |
| A reaction: This seems to commit to numbers having being, then to too many numbers, and hence to too much being - but without backing down and wondering whether numbers had being after all. Aristotle disagreed. |
| 17738 | Quine blurs the difference between knowledge of arithmetic and of physics [Jenkins on Quine] |
| Full Idea: Quine cannot deal with the intuition that there is a difference in kind between our knowledge of arithmetic and our knowledge of physics. | |
| From: comment on Willard Quine (Two Dogmas of Empiricism [1953]) by Carrie Jenkins - Grounding Concepts 7.5 | |
| A reaction: The endorses this criticism, which she says is widespread. I'm not convinced that there is a clear notion of 'difference in kind' here. Jenkins gets arithmetic from concepts and physics from the world. Is that a sharp distinction? |
| 229 | The one was and is and will be and was becoming and is becoming and will become [Plato] |
| Full Idea: The one was and is and will be and was becoming and is becoming and will become. | |
| From: Plato (Parmenides [c.364 BCE], 155d) |
| 21821 | Plato's Parmenides has a three-part theory, of Primal One, a One-Many, and a One-and-Many [Plato, by Plotinus] |
| Full Idea: The Platonic Parmenides is more exact [than Parmenides himself]; the distinction is made between the Primal One, a strictly pure Unity, and a secondary One which is a One-Many, and a third which is a One-and-Many. | |
| From: report of Plato (Parmenides [c.364 BCE]) by Plotinus - The Enneads 5.1.08 | |
| A reaction: Plotinus approves of this three-part theory. Parmenides has the problem that the highest Being contains no movement. By placing the One outside Being you can give it powers which an existent thing cannot have. Cf the concept of God. |
| 221 | Absolute ideas, such as the Good and the Beautiful, cannot be known by us [Plato] |
| Full Idea: The absolute good and the beautiful and all which we conceive to be absolute ideas are unknown to us. | |
| From: Plato (Parmenides [c.364 BCE], 134c) |
| 19492 | Quine is hopeless circular, deriving ontology from what is literal, and 'literal' from good ontology [Yablo on Quine] |
| Full Idea: Quine's advice is to countenance numbers iff the literal part of our theory quantifies over them; and to count the part of our theory that quantifies over numbers literal iff there turn out really to be numbers. | |
| From: comment on Willard Quine (Two Dogmas of Empiricism [1953]) by Stephen Yablo - Does Ontology Rest on a Mistake? XIII | |
| A reaction: This sounds a bit devastating. Presumably it is indeed the choice of a best theory which results in the ontological commitment, so it is not much help to then read off the ontology from the theory. |
| 227 | You must always mean the same thing when you utter the same name [Plato] |
| Full Idea: You must always mean the same thing when you utter the same name. | |
| From: Plato (Parmenides [c.364 BCE], 147d) |
| 223 | If you deny that each thing always stays the same, you destroy the possibility of discussion [Plato] |
| Full Idea: If a person denies that the idea of each thing is always the same, he will utterly destroy the power of carrying on discussion. | |
| From: Plato (Parmenides [c.364 BCE], 135c) |
| 210 | It would be absurd to think there were abstract Forms for vile things like hair, mud and dirt [Plato] |
| Full Idea: Are there abstract ideas for such things as hair, mud and dirt, which are particularly vile and worthless? That would be quite absurd. | |
| From: Plato (Parmenides [c.364 BCE], 130d) |
| 220 | The concept of a master includes the concept of a slave [Plato] |
| Full Idea: Mastership in the abstract is mastership of slavery in the abstract. | |
| From: Plato (Parmenides [c.364 BCE], 133e) |
| 211 | If admirable things have Forms, maybe everything else does as well [Plato] |
| Full Idea: It is troubling that if admirable things have abstract ideas, then perhaps everything else must have ideas as well. | |
| From: Plato (Parmenides [c.364 BCE], 130d) |
| 219 | If absolute ideas existed in us, they would cease to be absolute [Plato] |
| Full Idea: None of the absolute ideas exists in us, because then it would no longer be absolute. | |
| From: Plato (Parmenides [c.364 BCE], 133c) |
| 228 | Greatness and smallness must exist, to be opposed to one another, and come into being in things [Plato] |
| Full Idea: These two ideas, greatness and smallness, exist, do they not? For if they did not exist, they could not be opposites of one another, and could not come into being in things. | |
| From: Plato (Parmenides [c.364 BCE], 149e) |
| 16151 | Plato moves from Forms to a theory of genera and principles in his later work [Plato, by Frede,M] |
| Full Idea: It seems to me that Plato in the later dialogues, beginning with the second half of 'Parmenides', wants to substitute a theory of genera and theory of principles that constitute these genera for the earlier theory of forms. | |
| From: report of Plato (Parmenides [c.364 BCE]) by Michael Frede - Title, Unity, Authenticity of the 'Categories' V | |
| A reaction: My theory is that the later Plato came under the influence of the brilliant young Aristotle, and this idea is a symptom of it. The theory of 'principles' sounds like hylomorphism to me. |
| 212 | The whole idea of each Form must be found in each thing which participates in it [Plato] |
| Full Idea: The whole idea of each form (of beauty, justice etc) must be found in each thing which participates in it. | |
| From: Plato (Parmenides [c.364 BCE], 131a) |
| 218 | Participation is not by means of similarity, so we are looking for some other method of participation [Plato] |
| Full Idea: Participation is not by means of likeness, so we must seek some other method of participation. | |
| From: Plato (Parmenides [c.364 BCE], 133a) |
| 213 | Each idea is in all its participants at once, just as daytime is a unity but in many separate places at once [Plato] |
| Full Idea: Just as day is in many places at once, but not separated from itself, so each idea might be in all its participants at once. | |
| From: Plato (Parmenides [c.364 BCE], 131b) |
| 216 | If things are made alike by participating in something, that thing will be the absolute idea [Plato] |
| Full Idea: That by participation in which like things are made like, will be the absolute idea, will it not? | |
| From: Plato (Parmenides [c.364 BCE], 132e) |
| 215 | If things partake of ideas, this implies either that everything thinks, or that everything actually is thought [Plato] |
| Full Idea: If all things partake of ideas, must either everything be made of thoughts and everything thinks, or everything is thought, and so can't think? | |
| From: Plato (Parmenides [c.364 BCE], 132c) |
| 217 | Nothing can be like an absolute idea, because a third idea intervenes to make them alike (leading to a regress) [Plato] |
| Full Idea: It is impossible for anything to be like an absolute idea, because a third idea will appear to make them alike, and if that is like anything, it will lead to another idea, and so on. | |
| From: Plato (Parmenides [c.364 BCE], 133a) |
| 214 | If absolute greatness and great things are seen as the same, another thing appears which makes them seem great [Plato] |
| Full Idea: If you regard the absolute great and the many great things in the same way, will not another appear beyond, by which all these must appear to be great? | |
| From: Plato (Parmenides [c.364 BCE], 132a) |
| 1628 | If physical objects are a myth, they are useful for making sense of experience [Quine] |
| Full Idea: 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. | |
| From: Willard Quine (Two Dogmas of Empiricism [1953], p.44) |
| 15851 | Parts must belong to a created thing with a distinct form [Plato] |
| Full Idea: The part would not be the part of many things or all, but of some one character ['ideas'] and of some one thing, which we call a 'whole', since it has come to be one complete [perfected] thing composed [created] of all. | |
| From: Plato (Parmenides [c.364 BCE], 157d) | |
| A reaction: A serious shot by Plato at what identity is. Harte quotes it (125) and shows that 'character' is Gk 'idea', and 'composed' will translate as 'created'. 'Form' links this Platonic passage to Aristotle's hylomorphism. |
| 15846 | In Parmenides, if composition is identity, a whole is nothing more than its parts [Plato, by Harte,V] |
| Full Idea: At the heart of the 'Parmenides' puzzles about composition is the thesis that composition is identity. Considered thus, a whole adds nothing to an ontology that already includes its parts | |
| From: report of Plato (Parmenides [c.364 BCE]) by Verity Harte - Plato on Parts and Wholes 2.5 | |
| A reaction: There has to be more to a unified identity that mere proximity of the parts. When do parts come together, and when do they actually 'compose' something? |
| 15849 | Plato says only a one has parts, and a many does not [Plato, by Harte,V] |
| Full Idea: In 'Parmenides' it is argued that a part cannot be part of a many, but must be part of something one. | |
| From: report of Plato (Parmenides [c.364 BCE], 157c) by Verity Harte - Plato on Parts and Wholes 3.2 | |
| A reaction: This looks like the right way to go with the term 'part'. We presuppose a unity before we even talk of its parts, so we can't get into contradictions and paradoxes about their relationships. |
| 15850 | Anything which has parts must be one thing, and parts are of a one, not of a many [Plato] |
| Full Idea: The whole of which the parts are parts must be one thing composed of many; for each of the parts must be part, not of a many, but of a whole. | |
| From: Plato (Parmenides [c.364 BCE], 157c) | |
| A reaction: This is a key move of metaphysics, and we should hang on to it. The other way madness lies. |
| 13259 | It seems that the One must be composed of parts, which contradicts its being one [Plato] |
| Full Idea: The One must be composed of parts, both being a whole and having parts. So on both grounds the One would thus be many and not one. But it must be not many, but one. So if the One will be one, it will neither be a whole, nor have parts. | |
| From: Plato (Parmenides [c.364 BCE], 137c09), quoted by Kathrin Koslicki - The Structure of Objects 5.2 | |
| A reaction: This is the starting point for Plato's metaphysical discussion of objects. It seems to begin a line of thought which is completed by Aristotle, surmising that only an essential structure can bestow identity on a bunch of parts. |
| 10929 | Aristotelian essence of the object has become the modern essence of meaning [Quine] |
| Full Idea: The Aristotelian notion of essence was the forerunner of the modern notion of intension or meaning. ...Meaning is what essence becomes when it is divorced from the object of reference and wedded to the word. | |
| From: Willard Quine (Two Dogmas of Empiricism [1953], §1) | |
| A reaction: Quine first wants to jettison de re necessity (essence of the object), by shifting it to de dicto necessity (necessity in meaning), but he subsequently rejects that as well, presumably because he doesn't even believe in meanings. |
| 15847 | Two things relate either as same or different, or part of a whole, or the whole of the part [Plato] |
| Full Idea: Everything is surely related to everything as follows: either it is the same or different; or, if it is not the same or different, it would be related as part to whole or as whole to part. | |
| From: Plato (Parmenides [c.364 BCE], 146b) | |
| A reaction: This strikes me as a really helpful first step in trying to analyse the nature of identity. Two things are either two or (actually) one, or related mereologically. |
| 15420 | De re modality seems to apply to objects a concept intended for sentences [Burgess] |
| Full Idea: There is a problem over 'de re' modality (as contrasted with 'de dicto'), as in ∃x□x. What is meant by '"it is analytic that Px" is satisfied by a', given that analyticity is a notion that in the first instance applies to complete sentences? | |
| From: John P. Burgess (Philosophical Logic [2009], 3.9) | |
| A reaction: This is Burgess's summary of one of Quine's original objections. The issue may be a distinction between whether the sentence is analytic, and what makes it analytic. The necessity of bachelors being unmarried makes that sentence analytic. |
| 15419 | General consensus is S5 for logical modality of validity, and S4 for proof [Burgess] |
| Full Idea: To the extent that there is any conventional wisdom about the question, it is that S5 is correct for alethic logical modality, and S4 correct for apodictic logical modality. | |
| From: John P. Burgess (Philosophical Logic [2009], 3.8) | |
| A reaction: In classical logic these coincide, so presumably one should use the minimum system to do the job, which is S4 (?). |
| 12188 | Contrary to some claims, Quine does not deny logical necessity [Quine, by McFetridge] |
| Full Idea: Nothing in Quine's argument seems to be said directly against the view that the propositions of logic are necessary truths, ..though Crispin Wright has represented him as saying this at the end of 'Two Dogmas'. | |
| From: report of Willard Quine (Two Dogmas of Empiricism [1953]) by Ian McFetridge - Logical Necessity: Some Issues §3 | |
| A reaction: Quine famously denies that logical truths are merely a matter of convention, so the question is, if he believes in logical necessity, what does he think is the basis of it? Answers, as always, on a postcard. |
| 15417 | Logical necessity has two sides - validity and demonstrability - which coincide in classical logic [Burgess] |
| Full Idea: Logical necessity is a genus with two species. For classical logic the truth-related notion of validity and the proof-related notion of demonstrability, coincide - but they are distinct concept. In some logics they come apart, in intension and extension. | |
| From: John P. Burgess (Philosophical Logic [2009], 3.3) | |
| A reaction: They coincide in classical logic because it is sound and complete. This strikes me as the correct approach to logical necessity, tying it to the actual nature of logic, rather than some handwavy notion of just 'true in all possible worlds'. |
| 15090 | Quine's attack on the analytic-synthetic distinction undermined necessary truths [Quine, by Shoemaker] |
| Full Idea: Quine's attack on the analytic-synthetic distinction sought to contract, if not to empty, the class of truths that are called necessary. | |
| From: report of Willard Quine (Two Dogmas of Empiricism [1953]) by Sydney Shoemaker - Causal and Metaphysical Necessity I | |
| A reaction: The thought was that absolutely everything, including, for example, basic logic, became potentially revisable. See the last section of Quine's paper. |
| 15422 | Three conditionals theories: Materialism (material conditional), Idealism (true=assertable), Nihilism (no truth) [Burgess] |
| Full Idea: Three main theories of the truth of indicative conditionals are Materialism (the conditions are the same as for the material conditional), Idealism (identifying assertability with truth-value), and Nihilism (no truth, just assertability). | |
| From: John P. Burgess (Philosophical Logic [2009], 4.3) |
| 15423 | It is doubtful whether the negation of a conditional has any clear meaning [Burgess] |
| Full Idea: It is contentious whether conditionals have negations, and whether 'it is not the case that if A,B' has any clear meaning. | |
| From: John P. Burgess (Philosophical Logic [2009], 4.9) | |
| A reaction: This seems to be connected to Lewis's proof that a probability conditional cannot be reduced to a single proposition. If a conditional only applies to A-worlds, it is not surprising that its meaning gets lost when it leaves that world. |
| 9383 | Metaphysical analyticity (and linguistic necessity) are hopeless, but epistemic analyticity is a priori [Boghossian on Quine] |
| Full Idea: Quine showed the vacuity of the metaphysical concept of analyticity and the futility of the underwritten project - the linguistic theory of necessity. But that doesn't effect the epistemic notion of analyticity needed for a priori knowledge. | |
| From: comment on Willard Quine (Two Dogmas of Empiricism [1953]) by Paul Boghossian - Analyticity Reconsidered Concl | |
| A reaction: This summarise Boghossian's view, that a priori knowledge is still analytic, once we get clear about analyticity. See Idea 9368 for his two types of analyticity. Horwich attacks the view. |
| 12424 | Quine challenges the claim that analytic truths are knowable a priori [Quine, by Kitcher] |
| Full Idea: The last section of Quine's article challenges the claim that analytic truths are knowable a priori. | |
| From: report of Willard Quine (Two Dogmas of Empiricism [1953]) by Philip Kitcher - The Nature of Mathematical Knowledge 04.5 | |
| A reaction: That is, Quine does not deny that there are truths which rest entirely on meaning. It is a 'dogma of empiricism' that the a priori can be equated with the analytic (and the necessary). |
| 9338 | Quine's objections to a priori knowledge only work in the domain of science [Horwich on Quine] |
| Full Idea: Quine's arguments provide no reason to doubt the existence of a priori knowledge outside the domain of science. | |
| From: comment on Willard Quine (Two Dogmas of Empiricism [1953]) by Paul Horwich - Stipulation, Meaning and Apriority §10 | |
| A reaction: This rather ignores Quine's background view of thoroughgoing physicalism, so that the domain of science is the domain of nature, which is the domain of everything. See his naturalising of epistemology, for example. Maths is part of his science. |
| 9337 | Science is empirical, simple and conservative; any belief can hence be abandoned; so no a priori [Quine, by Horwich] |
| Full Idea: Quine says scientific beliefs follow empirical adequacy, simplicity and conservatism; science and rationality support this view; hence any hypothesis can be abandoned to increase simplicity; so no scientific belief is a priori. | |
| From: report of Willard Quine (Two Dogmas of Empiricism [1953]) by Paul Horwich - Stipulation, Meaning and Apriority §10 | |
| A reaction: [Compressed] I just don't accept this claim. If science wants to drop simple arithmetic or the laws of thought, so much the worse for science - they've obviously taken a wrong turning somewhere. We must try to infer God's logic. |
| 9340 | Logic, arithmetic and geometry are revisable and a posteriori; quantum logic could be right [Horwich on Quine] |
| Full Idea: I think logic, arithmetic and geometry are subject to Quine's empirical revisability argument: quantum logic may turn out to be the best overall theory; so these things are justified a posteriori. | |
| From: comment on Willard Quine (Two Dogmas of Empiricism [1953]) by Paul Horwich - Stipulation, Meaning and Apriority §11 | |
| A reaction: Not much of an argument, because 'quantum logic' may also turn out to be a will-o'-the-whisp. Until it is established (which I doubt, because quantum theory is so poorly understood), I think we should be highly suspicious of the Quinean view. |
| 1620 | Empiricism makes a basic distinction between truths based or not based on facts [Quine] |
| Full Idea: One dogma of empiricism is that there is some fundamental cleavage between truths that are analytic, or grounded in meanings independently of facts, and truths which are synthetic, or grounded in fact. | |
| From: Willard Quine (Two Dogmas of Empiricism [1953], p.20) |
| 1629 | Our outer beliefs must match experience, and our inner ones must be simple [Quine] |
| Full Idea: The outer edge of our empirical system must be kept squared with experience; the rest, with all its elaborate myths and fictions, has as its objective the simplicity of laws. | |
| From: Willard Quine (Two Dogmas of Empiricism [1953], p.45) |
| 19488 | The second dogma is linking every statement to some determinate observations [Quine, by Yablo] |
| Full Idea: Quine's second dogma of empiricism is the reductionism that finds every statement to be linkable by fixed correspondence rules to a determinate range of confirming observations. | |
| From: report of Willard Quine (Two Dogmas of Empiricism [1953]) by Stephen Yablo - Does Ontology Rest on a Mistake? V | |
| A reaction: Quine's response to this is to embrace holism about theories, instead of precise connections with Humean impressions. I'm thinking that Lewis disagrees with Quine, when his Humean supervenience rests on a 'mosaic' of small qualities. |
| 1625 | Statements about the external world face the tribunal of sense experience as a corporate body [Quine] |
| Full Idea: My suggestion, following Carnap, is that our statements about the external world face the tribunal of sense experience not individually but only as a corporate body. | |
| From: Willard Quine (Two Dogmas of Empiricism [1953], p.41) |
| 1626 | It is troublesome nonsense to split statements into a linguistic and a factual component [Quine] |
| Full Idea: My present suggestion is that it is nonsense, and the root of much nonsense, to speak of a linguistic component and a factual component in the truth of any individual statement. | |
| From: Willard Quine (Two Dogmas of Empiricism [1953], p.42) | |
| A reaction: I take the language and its subject matter to be obviously separate, but it is right that we can't separate these two components within a sample of language. |
| 7317 | 'Renate' and 'cordate' have identical extensions, but are not synonymous [Quine, by Miller,A] |
| Full Idea: It is easy to see that intersubstitutability salva veritate is not a sufficient condition for synonymy. 'Renate' (with kidney) and 'cordate' (with heart) can be substituted in a purely extensional language, but are plainly not synonymous. | |
| From: report of Willard Quine (Two Dogmas of Empiricism [1953]) by Alexander Miller - Philosophy of Language 4.2 | |
| A reaction: This seems to be a key example (along with Hesperus, and many others) in mapping out synonymy, meaning, analyticity, sense, reference, extension, intension, and all that stuff. |
| 1621 | Once meaning and reference are separated, meaning ceases to seem important [Quine] |
| Full Idea: Once theory of meaning and of reference are separated it is a short step to recognising as the primary business of theory of meaning simply the synonymy of linguistic forms and analyticity of statements; meanings themselves may be abandoned. | |
| From: Willard Quine (Two Dogmas of Empiricism [1953], p.22) | |
| A reaction: I can't buy the abandonment of meaning, because when I introspect my own speech there is clearly what I want to say formulating in my mind before the words are settled. |
| 9371 | Analytic statements are either logical truths (all reinterpretations) or they depend on synonymy [Quine] |
| Full Idea: Analytic statements fall into two classes: 'no unmarried man is married' typifies the first class, of logical truths; it remains true under all reinterpretations. 'No bachelor is married' is analytic if synonyms replace synonyms, and there's the problem. | |
| From: Willard Quine (Two Dogmas of Empiricism [1953], §1) | |
| A reaction: Boghossian emphasises this passage. In other papers Quine argues that logical truths also cannot be purely analytic, although he does not deny that there are logical truths. |
| 1622 | Did someone ever actually define 'bachelor' as 'unmarried man'? [Quine] |
| Full Idea: How do we find that 'bachelor' is defined as unmarried man? Who defined it thus, and when? Not the lexicographer, who is a scientist recording antecedent facts. | |
| From: Willard Quine (Two Dogmas of Empiricism [1953], p.24) | |
| A reaction: All mid-20th C philosophy of language is too individualistic in its strategy. Eventually later Wittgenstein sank in, and socially agreed meanings for 'water' and 'elm'. |
| 9366 | Quine's attack on analyticity undermined linguistic views of necessity, and analytic views of the a priori [Quine, by Boghossian] |
| Full Idea: Quine's attack on analyticity devastated the philosophical programs that depend upon a notion of analyticity - specifically, the linguistic theory of necessary truth, and the analytic theory of a priori knowledge. | |
| From: report of Willard Quine (Two Dogmas of Empiricism [1953]) by Paul Boghossian - Analyticity Reconsidered §I | |
| A reaction: Note that much more would be needed to complete Quine's aim of more or less eliminating both necessity and the a priori from his scientific philosophy. Quine was trying to complete a programme initiated by C.I. Lewis (q.v.). |
| 14473 | Quine attacks the Fregean idea that we can define analyticity through synonyous substitution [Quine, by Thomasson] |
| Full Idea: Quine's attack argues against the Fregean attempt to define 'analyticity' in terms of synonymy - where analytical truths are logical truths ('unmarried men are unmarried'), or become logical truths by synonymous replacement ('bachelors are unmarried'). | |
| From: report of Willard Quine (Two Dogmas of Empiricism [1953]) by Amie L. Thomasson - Ordinary Objects 02.1 | |
| A reaction: This is a very helpful explanation of what is going on in Quine. Why won't philosophers explain clearly what they are attacking, before they attack it? |
| 7321 | The last two parts of 'Two Dogmas' are much the best [Miller,A on Quine] |
| Full Idea: The arguments of the final two sections of 'Two Dogmas' have received more acceptance than the arguments of the first four sections, which are now generally acknowledged to be unsuccessful. | |
| From: comment on Willard Quine (Two Dogmas of Empiricism [1953]) by Alexander Miller - Philosophy of Language 4 Read | |
| A reaction: The early sections are the 'circular' argument against analyticity; the later parts are further discussions of the concept. We don't have to take Miller's word for this, but it is a useful pointer when reading the paper. |
| 8803 | Erasing the analytic/synthetic distinction got rid of meanings, and saved philosophy of language [Davidson on Quine] |
| Full Idea: Erasing the line between the analytic and the synthetic saved philosophy of language as a serious subject by showing how it could be pursued without what there cannot be: determinate meanings. | |
| From: comment on Willard Quine (Two Dogmas of Empiricism [1953]) by Donald Davidson - Coherence Theory of Truth and Knowledge p.158 | |
| A reaction: Note that this comes from the most famous modern champion of one of the main theories of meaning (as truth-conditions). Did anyone ever believe in reified objects called 'meanings'? |
| 17737 | The analytic needs excessively small units of meaning and empirical confirmation [Quine, by Jenkins] |
| Full Idea: Quine rejects the analytic on the grounds that it assumes a smaller unit of meaning than a total theory, and he does not think it makes sense to talk about such smaller units of meaning because there are no smaller units of empirical confirmation. | |
| From: report of Willard Quine (Two Dogmas of Empiricism [1953]) by Carrie Jenkins - Grounding Concepts 7.5 | |
| A reaction: A very helpful account of the famous Quine argument, showing how it arises out of his particular holistic view of empiricism. |
| 1624 | If we try to define analyticity by synonymy, that leads back to analyticity [Quine] |
| Full Idea: In defining analyticity an appeal to meanings seems natural, but that reduces to synonymy or definition. Definition is a will-o'-the-wisp, and synonymy is best understood by a priori appeal to analyticity, so we are back at the problem of analyticity. | |
| From: Willard Quine (Two Dogmas of Empiricism [1953], p.32) | |
| A reaction: Quine is full of these over-neat sceptical arguments, saying everything is circular, or can never get started. Compare Aristotle's benign circle of virtuous people and virtuous actions. |
| 222 | Only a great person can understand the essence of things, and an even greater person can teach it [Plato] |
| Full Idea: Only a man of very great natural gifts will be able to understand that everything has a class and absolute essence, and an even more wonderful man can teach this. | |
| From: Plato (Parmenides [c.364 BCE], 135a) |
| 225 | The unlimited has no shape and is endless [Plato] |
| Full Idea: The unlimited partakes neither of the round nor of the straight, because it has no ends nor edges. | |
| From: Plato (Parmenides [c.364 BCE], 137e) |
| 233 | Some things do not partake of the One [Plato] |
| Full Idea: The others cannot partake of the one in any way; they can neither partake of it nor of the whole. | |
| From: Plato (Parmenides [c.364 BCE], 159d) | |
| A reaction: Compare Idea 231 |
| 2062 | The only movement possible for the One is in space or in alteration [Plato] |
| Full Idea: If the One moves it either moves spatially or it is altered, since these are the only motions. | |
| From: Plato (Parmenides [c.364 BCE], 138b) |
| 231 | Everything partakes of the One in some way [Plato] |
| Full Idea: The others are not altogether deprived of the one, for they partake of it in some way. | |
| From: Plato (Parmenides [c.364 BCE], 157c) | |
| A reaction: Compare Idea 233. |
| 234 | We couldn't discuss the non-existence of the One without knowledge of it [Plato] |
| Full Idea: There must be knowledge of the one, or else not even the meaning of the words 'if the one does not exist' would be known. | |
| From: Plato (Parmenides [c.364 BCE], 160d) |