42 ideas
| 7920 | Descriptive metaphysics aims at actual structure, revisionary metaphysics at a better structure [Strawson,P] |
| Full Idea: Descriptive metaphysics (e.g. Aristotle and Kant) is content to describe the actual structure of our thought about the world; revisionary metaphysics (e.g. Descartes, Leibniz, Berkeley) is concerned to produce a better structure. | |
| From: Peter F. Strawson (Individuals:Essay in Descript Metaphysics [1959], Intro) | |
| A reaction: This distinction by Strawson was incredibly helpful in reinstating metaphysics as a feasible activity. I don't want to abandon the revisionary version. We can hammer the current metaphysics into a more efficient shape, or even create new concepts. |
| 7922 | Descriptive metaphysics concerns unchanging core concepts and categories [Strawson,P] |
| Full Idea: Descriptive metaphysics is primarily concerned with categories and concepts which, in their fundamental character, change not at all. They are the commonplaces of the least refined thinking, and the indispensable core for the most sophisticated humans. | |
| From: Peter F. Strawson (Individuals:Essay in Descript Metaphysics [1959], Intro) | |
| A reaction: This seems to be the basic premise for a modern metaphysician such as E.J.Lowe, though such thinkers are not averse to suggesting clarifications of our conceptual scheme. The aim must be good foundations for a successful edifice of knowledge. |
| 7921 | Close examination of actual word usage is the only sure way in philosophy [Strawson,P] |
| Full Idea: Up to a point, the reliance upon a close examination of the actual use of words is the best, and indeed the only sure, way in philosophy. | |
| From: Peter F. Strawson (Individuals:Essay in Descript Metaphysics [1959], Intro) | |
| A reaction: Probably the last bold assertion of ordinary language philosophy, though Strawson goes on the defend his 'deeper' version of the activity, which he says is 'descriptive metaphysics', rather than mere 'analysis'. Mere verbal analysis now looks hopeless. |
| 10842 | The fact which is stated by a true sentence is not something in the world [Strawson,P] |
| Full Idea: The fact which is stated by a true sentence is not something in the world. | |
| From: Peter F. Strawson (Truth [1950], §2) | |
| A reaction: Everything is in the world. This may just be a quibble over how we should use the word 'fact'. At some point the substance of what is stated in a sentence must eventually be out there, or we would never act on what we say. |
| 10843 | Facts aren't exactly true statements, but they are what those statements say [Strawson,P] |
| Full Idea: Facts are what statements (when true) state; they are not what statements are about. ..But it would be wrong to identify 'fact' and 'true statement' for these expressions have different roles in our language. | |
| From: Peter F. Strawson (Truth [1950], §2) | |
| A reaction: Personally I like to reserve the word 'facts' for what is out there, independent of any human thought or speech. As a realist, I believe that the facts are quite independent of our attempts to understand the facts. True statements attempt to state facts. |
| 10844 | The statement that it is raining perfectly fits the fact that it is raining [Strawson,P] |
| Full Idea: What could fit more perfectly the fact that it is raining than the statement that it is raining? | |
| From: Peter F. Strawson (Truth [1950], §2) |
| 10841 | The word 'true' always refers to a possible statement [Strawson,P] |
| Full Idea: It is of prime importance to distinguish the fact that the use of 'true' always glances backwards or forwards to the actual or envisaged making of a statement by someone. | |
| From: Peter F. Strawson (Truth [1950], §1) | |
| A reaction: 'The truth of this matter will never be known'. Strawson is largely right, but it is crazy for any philosopher to use the word 'always' if they can possibly avoid it. |
| 17926 | Rejecting double negation elimination undermines reductio proofs [Colyvan] |
| Full Idea: The intuitionist rejection of double negation elimination undermines the important reductio ad absurdum proof in classical mathematics. | |
| From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 1.1.3) |
| 17925 | Showing a disproof is impossible is not a proof, so don't eliminate double negation [Colyvan] |
| Full Idea: In intuitionist logic double negation elimination fails. After all, proving that there is no proof that there can't be a proof of S is not the same thing as having a proof of S. | |
| From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 1.1.3) | |
| A reaction: I do like people like Colyvan who explain things clearly. All of this difficult stuff is understandable, if only someone makes the effort to explain it properly. |
| 17924 | Excluded middle says P or not-P; bivalence says P is either true or false [Colyvan] |
| Full Idea: The law of excluded middle (for every proposition P, either P or not-P) must be carefully distinguished from its semantic counterpart bivalence, that every proposition is either true or false. | |
| From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 1.1.3) | |
| A reaction: So excluded middle makes no reference to the actual truth or falsity of P. It merely says P excludes not-P, and vice versa. |
| 8358 | There are no rules for the exact logic of ordinary language, because that doesn't exist [Strawson,P] |
| Full Idea: Neither Aristotelian nor Russellian rules give the exact logic of any expression of ordinary language; for ordinary language has no exact logic. | |
| From: Peter F. Strawson (On Referring [1950], §5) | |
| A reaction: This seems to imply that it is impossible to find precise logical forms, because of the pragmatic element in language, but I don't see why. Even more extreme modern pragmatics (where meaning is shifted) doesn't rule out precise underlying propositions. |
| 6413 | 'The present King of France is bald' presupposes existence, rather than stating it [Strawson,P, by Grayling] |
| Full Idea: Strawson argues that in saying 'the present King of France is bald' one is not stating that a present King of France exists, but presupposing or assuming that it does. | |
| From: report of Peter F. Strawson (On Referring [1950]) by A.C. Grayling - Russell Ch.2 | |
| A reaction: We have the notion of a leading question, such as 'when did you stop beating your wife?' But is a presupposition not simply an implied claim, as Russell said it was? |
| 8354 | Russell asks when 'The King of France is wise' would be a true assertion [Strawson,P] |
| Full Idea: The way in which Russell arrived at his analysis was by asking himself what would be the circumstances in which we would say that anyone who uttered the sentence 'The King of France is wise' had made a true assertion. | |
| From: Peter F. Strawson (On Referring [1950], §1) | |
| A reaction: This seems to connect Russell's theory of definite descriptions with the truth conditions theory of meaning which is associated (initially) with Frege. Truth will require some reference to what actually exists. |
| 17929 | Löwenheim proved his result for a first-order sentence, and Skolem generalised it [Colyvan] |
| Full Idea: Löwenheim proved that if a first-order sentence has a model at all, it has a countable model. ...Skolem generalised this result to systems of first-order sentences. | |
| From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 2.1.2) |
| 17930 | Axioms are 'categorical' if all of their models are isomorphic [Colyvan] |
| Full Idea: A set of axioms is said to be 'categorical' if all models of the axioms in question are isomorphic. | |
| From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 2.1.2) | |
| A reaction: The best example is the Peano Axioms, which are 'true up to isomorphism'. Set theory axioms are only 'quasi-isomorphic'. |
| 17928 | Ordinal numbers represent order relations [Colyvan] |
| Full Idea: Ordinal numbers represent order relations. | |
| From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 1.2.3 n17) |
| 17923 | Intuitionists only accept a few safe infinities [Colyvan] |
| Full Idea: For intuitionists, all but the smallest, most well-behaved infinities are rejected. | |
| From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 1.1.3) | |
| A reaction: The intuitionist idea is to only accept what can be clearly constructed or proved. |
| 17941 | Infinitesimals were sometimes zero, and sometimes close to zero [Colyvan] |
| Full Idea: The problem with infinitesimals is that in some places they behaved like real numbers close to zero but in other places they behaved like zero. | |
| From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 7.1.2) | |
| A reaction: Colyvan gives an example, of differentiating a polynomial. |
| 17922 | Reducing real numbers to rationals suggested arithmetic as the foundation of maths [Colyvan] |
| Full Idea: Given Dedekind's reduction of real numbers to sequences of rational numbers, and other known reductions in mathematics, it was tempting to see basic arithmetic as the foundation of mathematics. | |
| From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 1.1.1) | |
| A reaction: The reduction is the famous Dedekind 'cut'. Nowadays theorists seem to be more abstract (Category Theory, for example) instead of reductionist. |
| 17936 | Transfinite induction moves from all cases, up to the limit ordinal [Colyvan] |
| Full Idea: Transfinite inductions are inductive proofs that include an extra step to show that if the statement holds for all cases less than some limit ordinal, the statement also holds for the limit ordinal. | |
| From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 5.2.1 n11) |
| 17940 | Most mathematical proofs are using set theory, but without saying so [Colyvan] |
| Full Idea: Most mathematical proofs, outside of set theory, do not explicitly state the set theory being employed. | |
| From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 7.1.1) |
| 17931 | Structuralism say only 'up to isomorphism' matters because that is all there is to it [Colyvan] |
| Full Idea: Structuralism is able to explain why mathematicians are typically only interested in describing the objects they study up to isomorphism - for that is all there is to describe. | |
| From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 3.1.2) |
| 17932 | If 'in re' structures relies on the world, does the world contain rich enough structures? [Colyvan] |
| Full Idea: In re structuralism does not posit anything other than the kinds of structures that are in fact found in the world. ...The problem is that the world may not provide rich enough structures for the mathematics. | |
| From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 3.1.2) | |
| A reaction: You can perceive a repeating pattern in the world, without any interest in how far the repetitions extend. |
| 16980 | We need a logical use of 'object' as predicate-worthy, and an 'ontological' use [Strawson,P] |
| Full Idea: There is a good case for a conservative reform of the word 'object'. Objects in the 'logical' sense would be all predicate-worthy identifiabilia whatever. Objects in the 'ontological' sense would form one ontological category among many others. | |
| From: Peter F. Strawson (Entity and Identity [1978], I n4) | |
| A reaction: This ambiguity has caused me no end of confusion (and irritation!). I wish philosophers wouldn't hijack perfectly good English words and give them weird meanings. Nice to have a distinguished fellow like Strawson make this suggestion. |
| 16979 | It makes no sense to ask of some individual thing what it is that makes it that individual [Strawson,P] |
| Full Idea: For no object is there a unique character or relation by which it must be identified if it is to be identified at all. This is why it makes no sense to ask, impersonally and in general, of some individual object what makes it the individual object it is. | |
| From: Peter F. Strawson (Entity and Identity [1978], I) | |
| A reaction: He links this remark with the claim that there is no individual essence, but he seems to view an individual essence as indispensable to recognition or individuation of the object, which I don't see. Recognise it first, work out its essence later. |
| 3061 | Anaxarchus said that he was not even sure that he knew nothing [Anaxarchus, by Diog. Laertius] |
| Full Idea: Anaxarchus said that he was not even sure that he knew nothing. | |
| From: report of Anaxarchus (fragments/reports [c.340 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 09.10.1 |
| 17943 | Probability supports Bayesianism better as degrees of belief than as ratios of frequencies [Colyvan] |
| Full Idea: Those who see probabilities as ratios of frequencies can't use Bayes's Theorem if there is no objective prior probability. Those who accept prior probabilities tend to opt for a subjectivist account, where probabilities are degrees of belief. | |
| From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 9.1.8) | |
| A reaction: [compressed] |
| 17939 | Mathematics can reveal structural similarities in diverse systems [Colyvan] |
| Full Idea: Mathematics can demonstrate structural similarities between systems (e.g. missing population periods and the gaps in the rings of Saturn). | |
| From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 6.3.2) | |
| A reaction: [Colyvan expounds the details of his two examples] It is these sorts of results that get people enthusiastic about the mathematics embedded in nature. A misunderstanding, I think. |
| 17938 | Mathematics can show why some surprising events have to occur [Colyvan] |
| Full Idea: Mathematics can show that under a broad range of conditions, something initially surprising must occur (e.g. the hexagonal structure of honeycomb). | |
| From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 6.3.2) |
| 17934 | Proof by cases (by 'exhaustion') is said to be unexplanatory [Colyvan] |
| Full Idea: Another style of proof often cited as unexplanatory are brute-force methods such as proof by cases (or proof by exhaustion). | |
| From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 5.2.1) |
| 17933 | Reductio proofs do not seem to be very explanatory [Colyvan] |
| Full Idea: One kind of proof that is thought to be unexplanatory is the 'reductio' proof. | |
| From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 5.2.1) | |
| A reaction: Presumably you generate a contradiction, but are given no indication of why the contradiction has arisen? Tracking back might reveal the source of the problem? Colyvan thinks reductio can be explanatory. |
| 17935 | If inductive proofs hold because of the structure of natural numbers, they may explain theorems [Colyvan] |
| Full Idea: It might be argued that any proof by induction is revealing the explanation of the theorem, namely, that it holds by virtue of the structure of the natural numbers. | |
| From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 5.2.1) | |
| A reaction: This is because induction characterises the natural numbers, in the Peano Axioms. |
| 17942 | Can a proof that no one understands (of the four-colour theorem) really be a proof? [Colyvan] |
| Full Idea: The proof of the four-colour theorem raises questions about whether a 'proof' that no one understands is a proof. | |
| From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 9.1.6) | |
| A reaction: The point is that the theorem (that you can colour countries on a map with just four colours) was proved with the help of a computer. |
| 9282 | I can only apply consciousness predicates to myself if I can apply them to others [Strawson,P] |
| Full Idea: One can ascribed states of consciousness to oneself only if one can ascribe them to others. One can ascribe them to others only if one can identify other subjects of experience, and they cannot be identified only as subjects of experience. | |
| From: Peter F. Strawson (Individuals:Essay in Descript Metaphysics [1959], 3.4) | |
| A reaction: A neat linguistic twist on the analogy argument, but rather dubious, if it is actually meant to prove that other minds exist. It is based on his view of predicates - see Idea 9281. If the rest of humanity are zombies, why would I not apply them? |
| 17937 | Mathematical generalisation is by extending a system, or by abstracting away from it [Colyvan] |
| Full Idea: One type of generalisation in mathematics extends a system to go beyond what is was originally set up for; another kind involves abstracting away from some details in order to capture similarities between different systems. | |
| From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 5.2.2) |
| 9263 | A person is an entity to which we can ascribe predicates of consciousness and corporeality [Strawson,P] |
| Full Idea: What I mean by the concept of a person is the concept of a type of entity such that both predicates ascribing states of consciousness and predicates ascribing corporeal characteristics are equally applicable to a single individual of that single type. | |
| From: Peter F. Strawson (Individuals:Essay in Descript Metaphysics [1959], 3.4) | |
| A reaction: As Frankfurt points out, merely requiring the entity to be 'conscious' is a grossly inadequate definition of what we mean by a person, which is typically a being that is self-aware and capable of rational decisions between alternatives. |
| 8356 | The meaning of an expression or sentence is general directions for its use, to refer or to assert [Strawson,P] |
| Full Idea: To give the meaning of an expression is to give general directions for its use to refer to or mention particular objects or persons; in like manner, sentences are for use to make true or false assertions. | |
| From: Peter F. Strawson (On Referring [1950], §2) | |
| A reaction: The influence of Wittgenstein? I don't like it. The general idea that you can say what something is by giving directions for its use is what I think of as the Functional Fallacy: confusing the role of x with its inherent nature. Shirt as goalpost. |
| 10430 | Reference is mainly a social phenomenon [Strawson,P, by Sainsbury] |
| Full Idea: Strawson's early work gave a new direction to the study of reference by stressing that it is a social phenomenon. | |
| From: report of Peter F. Strawson (On Referring [1950]) by Mark Sainsbury - The Essence of Reference 18.2 | |
| A reaction: The question is whether speakers refer, or sentences, or expressions, or propositions. The modern consensus seems to be that some parts of language are inherently referring, but speakers combine such tools with context. Sounds right. |
| 10448 | If an expression can refer to anything, it may still instrinsically refer, but relative to a context [Bach on Strawson,P] |
| Full Idea: Strawson claimed that virtually any expression that can be used to refer to one thing in one context can be used to refer to something else in another context. Maybe expressions still refer, but only relative to a context. | |
| From: comment on Peter F. Strawson (On Referring [1950]) by Kent Bach - What Does It Take to Refer? 22.2 | |
| A reaction: If there is complete freedom, then Bach's criticism doesn't sound plausible. If something is semantically referential, that should impose pretty tight restrictions on speakers. Why distinguish names as intrinsically referential, and descriptions as not? |
| 8355 | Expressions don't refer; people use expressions to refer [Strawson,P] |
| Full Idea: 'Mentioning', or 'referring', is not something an expression does; it is something that someone can use an expression to do. | |
| From: Peter F. Strawson (On Referring [1950], §2) | |
| A reaction: That can't be whole story, because I might make a mistake when referring, so that I used the expression to refer to x, but unfortunately the words themselves referred to y. The power of language exceeds the intentions of speakers. |
| 8357 | If an utterance fails to refer then it is a pseudo-use, though a speaker may think they assert something [Strawson,P] |
| Full Idea: If an utterance is not talking about anything, then the speaker's use is not a genuine one, but a spurious or pseudo-use; he is not making either a true or a false assertion, though he may think he is. | |
| From: Peter F. Strawson (On Referring [1950], §2) | |
| A reaction: This is Strawson's verdict on 'The present King of France is bald'. His view puts speculative statements in no man's land. What do we make of 'Elvis lives' or 'phlogiston explains fire'? |
| 9281 | The idea of a predicate matches a range of things to which it can be applied [Strawson,P] |
| Full Idea: The idea of a predicate is correlative with a range of distinguishable individuals of which the predicate can be significantly, though not necessarily truly, affirmed. | |
| From: Peter F. Strawson (Individuals:Essay in Descript Metaphysics [1959], 3.4 n1) | |
| A reaction: Said to be one of Strawson's most important ideas. The idea is that you understand a predicate if you understand its range, not just a one-off application. So you must understand the implied universal, whatever that is. |