| 2279 | A triangle has a separate non-invented nature, shown by my ability to prove facts about it [Descartes] |
| Full Idea: A triangle has a determinate nature, which I did not fabricate, and which does not depend on my mind. This is evident from the fact that various properties can be demonstrated regarding it, such as that its three angles are equal to two right angles. | |
| From: René Descartes (Meditations [1641], §5.64) |
| 2602 | What experience could prove 'If a=c and b=c then a=b'? [Descartes] |
| Full Idea: Please tell me what the corporeal motion is that is capable of forming some common notion to the effect that 'things which are equal to a third thing are equal to each other'. | |
| From: René Descartes (Comments on a Certain Broadsheet [1644], p.366) |
| 5012 | 'Nothing comes from nothing' is an eternal truth found within the mind [Descartes] |
| Full Idea: The proposition 'nothing comes from nothing' is not to be considered as an existing thing, or the mode of a thing, but as a certain eternal truth which has its seat in our mind and is a common notion or axiom. | |
| From: René Descartes (Principles of Philosophy [1646], I.49) | |
| A reaction: There is a tension here, in his assertion that it is 'eternal', but 'not existing'. How does one distinguish an innate idea from an innate truth? 'Eternal' sounds like an external guarantee of truth, but being 'in our mind' sounds less reliable. |
| 9344 | Mathematical analysis ends in primitive principles, which cannot be and need not be demonstrated [Leibniz] |
| Full Idea: At the end of the analytical method in mathematics there are simple ideas of which no definition can be given. Moreover there are axioms and postulates, in short, primitive principles, which cannot be demonstrated and do not need demonstration. | |
| From: Gottfried Leibniz (Monadology [1716], §35) | |
| A reaction: My view is that we do not know such principles when we apprehend them in isolation. I would call them 'intuitions'. They only ascend to the status of knowledge when the mathematics is extended and derived from them, and found to work. |
| 9155 | An a priori proof is independent of experience [Leibniz] |
| Full Idea: An a priori proof is a proof independent of experience. | |
| From: Gottfried Leibniz (Primary Truths [1686]) | |
| A reaction: Burge says Leibniz gave the first modern account of a priori knowledge. There may be no explicit reference to experience involved, but it would beg many questions to deny that implicit experience may be at the root of the proof. |
| 5404 | Two plus two objects make four objects even if experience is impossible, so Kant is wrong [Russell on Kant] |
| Full Idea: Two physical objects and two other physical objects must make four physical objects, even if physical objects cannot be experienced, so Kant's solution unduly limits the scope of a priori propositions. | |
| From: comment on Immanuel Kant (Critique of Pure Reason [1781]) by Bertrand Russell - Problems of Philosophy Ch.8 | |
| A reaction: The point seems good, though it is doubtful whether Russell is entitled to be so confident. If the basis of a priori certainty is pushed outside the mind, our ontology becomes dramatically more complicated. |
| 9345 | Propositions involving necessity are a priori, and pure a priori if they only derive from other necessities [Kant] |
| Full Idea: If a proposition is thought along with its necessity, it is an a priori judgement; if it is, moreover, also not derived from any proposition except one that in turn is valid as a necessary proposition, then it is absolutely a priori. | |
| From: Immanuel Kant (Critique of Pure Reason [1781], B003) | |
| A reaction: The misunderstanding behind this is that we can obtain certainty in this way. I presume that consistency with empirical experience would increase our certainty of (say) maths or logic. There is no 'pure' a priori, delivering 'pure' necessity. |
| 16893 | The apriori is independent of its sources, and marked by necessity and generality [Kant, by Burge] |
| Full Idea: Kant defines apriority in terms of independence from genesis and from sense experience, and it is indicated by its necessity and by it generality or universality. | |
| From: report of Immanuel Kant (Critique of Pure Reason [1781], B003-4) by Tyler Burge - Frege on Apriority (with ps) 2 |
| 9347 | A priori knowledge is indispensable for the possibility and certainty of experience [Kant] |
| Full Idea: One could establish the indispensability of the reality of pure a priori principles for the possibility of experience itself, and thus establish it a priori. Where would experience gets its certainty if it was based on empirical, contingent rules? | |
| From: Immanuel Kant (Critique of Pure Reason [1781], B005) | |
| A reaction: [compressed] There seems a touch of circularity here, apart from the transcendental argument. Proving the a priori by a priori means? All very odd. And experience is certain because it is based on a priori rules, which are necessary? |
| 9352 | An a priori truth is one derived from general laws which do not require proof [Frege] |
| Full Idea: If the proof of a truth can be derived exclusively from general laws, which themselves neither need nor admit of proof, then the truth is a priori. | |
| From: Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §03) | |
| A reaction: Presumably the unproved general laws from which the derivation comes are more securely a priori, as are the principles used to make the derivation. As Frege says, he is trying to spell out Kant's view; see Idea 9345. |
| 16889 | A truth is a priori if it can be proved entirely from general unproven laws [Frege] |
| Full Idea: If it is possible to derive a proof purely from general laws, which themselves neither need nor admit of proof, then the truth is a priori. | |
| From: Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §03), quoted by Tyler Burge - Frege on Apriority (with ps) 1 | |
| A reaction: Burge brings out the contrast with Kant, for whom a priori truths are derived from particular facts, not general ones. |
| 16894 | An apriori truth is grounded in generality, which is universal quantification [Frege, by Burge] |
| Full Idea: Generality for Frege is simply universal quantification; what makes a truth apriori is that its ultimate grounds are universally quantified. | |
| From: report of Gottlob Frege (works [1890]) by Tyler Burge - Frege on Apriority (with ps) 2 |
| 5397 | The rationalists were right, because we know logical principles without experience [Russell] |
| Full Idea: In the most important point of the controversy between empiricists and rationalist, the rationalists were right, since logical principles are known to us, but cannot be proved by experience, since all proof presupposes them | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 7) | |
| A reaction: Russell initially presents this as the answer to 'innate ideas'. I would prefer to say, in the style of Descartes, that logic is self-evident to the natural light of reason. The debate isn't over. A Turing machine may be able to do logic. |
| 5198 | We could verify 'a thing can't be in two places at once' by destroying one of the things [Ierubino on Ayer] |
| Full Idea: It is possible to challenge the proposition 'a material thing cannot be in two places at once' empirically; if you destroy one object, the other should also instantly be destroyed if they are a single thing. | |
| From: comment on A.J. Ayer (Language,Truth and Logic [1936], Ch.2) by Virgil Ierubino - works | |
| A reaction: This leaves us having to decide whether the proposition is metaphysically necessary, or is empirical, or is tautological. This idea inclines me towards the view that it is empirical. Imagine two 'separate' objects which responded identically to stimuli. |
| 9354 | Why should necessities only be knowable a priori? That Hesperus is Phosporus is known empirically [Devitt] |
| Full Idea: Why should we accept that necessities can only be known a priori? Prima facie, some necessities are known empirically; for example, that water is necessarily H2O, and that Hesperus is necessarily Phosphorus. | |
| From: Michael Devitt (There is no a Priori [2005], §2) | |
| A reaction: An important question, whatever your view. If the only thing we can know a priori is necessities, it doesn't follow that necessities can only be known a priori. It gets interesting if we say that some necessities can never be known a priori. |
| 19565 | How could the mind have a link to the necessary character of reality? [Devitt] |
| Full Idea: What non-experiential link to reality could support insights into its necessary character? | |
| From: Michael Devitt (There is No A Priori (and reply) [2005], 4) | |
| A reaction: The key to it, I think, is your theory of mind. If you are a substance dualist, then connecting to such deep things looks fine, but if you are a reductive physicalist then it looks absurdly hopeful. |
| 20472 | Analysis of the a priori by necessity or analyticity addresses the proposition, not the justification [Casullo] |
| Full Idea: There is reason to view non-epistemic analyses of a priori knowledge (in terms of necessity or analyticity) with suspicion. The a priori concerns justification. Analysis by necessity or analyticity concerns the proposition rather than the justification. | |
| From: Albert Casullo (A Priori Knowledge [2002], 2.1) | |
| A reaction: [compressed] The fact that the a priori is entirely a mode of justification, rather than a type of truth, is the modern view, influenced by Kripke. Given that assumption, this is a good objection. |
| 14712 | A sentence is a priori if no possible way the world might actually be could make it false [Chalmers] |
| Full Idea: The Core Thesis for rationalist 2D semantics is that for any sentence S, S is apriori iff S has a necessary 1-intension. (That is, there is no possible way the world might be that, if it actually obtained, would make S false). | |
| From: David J.Chalmers (Epistemic Two-Dimensional Semantics [2004], p.165), quoted by Laura Schroeter - Two-Dimensional Semantics 2.3.2 | |
| A reaction: [The parenthesis is by Schroeter] A '1-intension' is defined by a diagonal on a 2D semantic matrix. Chalmers defends conceivability as the guide to possibility. This is a very traditional view of the a priori, expressed in modern terms. |
| 9369 | 'Snow is white or it isn't' is just true, not made true by stipulation [Boghossian] |
| Full Idea: Isn't it overwhelmingly obvious that 'Either snow is white or it isn't' was true before anyone stipulated a meaning for it, and that it would have been true even if no one had thought about it, or chosen it to be expressed by one of our sentences? | |
| From: Paul Boghossian (Analyticity Reconsidered [1996], §I) | |
| A reaction: Boghossian would have to believe in propositions (unexpressed truths) to hold this - which he does. I take the notion of truth to only have relevance when there are minds around. Otherwise the so-called 'truths' are just the facts. |