23 ideas
| 2666 | Carneades' pinnacles of philosophy are the basis of knowledge (the criterion of truth) and the end of appetite (good) [Carneades, by Cicero] |
| Full Idea: Carneades said the two greatest things in philosophy were the criterion of truth and the end of goods, and no man could be a sage who was ignorant of the existence of either a beginning of the process of knowledge or an end of appetition. | |
| From: report of Carneades (fragments/reports [c.174 BCE]) by M. Tullius Cicero - Academica II.09.29 | |
| A reaction: Nice, but I would want to emphasise the distinction between truth and its criterion. Admittedly we would have no truth without a good criterion, but the truth itself should be held in higher esteem than our miserable human means of grasping it. |
| 21390 | Future events are true if one day we will say 'this event is happening now' [Carneades] |
| Full Idea: We call those past events true of which at an earlier time this proposition was true: 'They are present now'; similarly, we shall call those future events true of which at some future time this proposition will be true: 'They are present now'. | |
| From: Carneades (fragments/reports [c.174 BCE]), quoted by M. Tullius Cicero - On Fate ('De fato') 9.23-8 | |
| A reaction: This is a very nice way of paraphrasing statements about the necessity of true future contingent events. It still relies, of course, on the veracity of a tensed assertion |
| 21672 | We say future things are true that will possess actuality at some following time [Carneades, by Cicero] |
| Full Idea: Just as we speak of past things as true that possessed true actuality at some former time, so we speak of future things as true that will possess true actuality at some following time. | |
| From: report of Carneades (fragments/reports [c.174 BCE]) by M. Tullius Cicero - On Fate ('De fato') 11.27 | |
| A reaction: This ducks the Aristotle problem of where it is true NOW when you say there will be a sea-fight tomorrow, and it turns out to be true. Carneades seems to be affirming a truth when it does not yet have a truthmaker. |
| 12452 | Our dislike of contradiction in logic is a matter of psychology, not mathematics [Brouwer] |
| Full Idea: Not to the mathematician, but to the psychologist, belongs the task of explaining why ...we are averse to so-called contradictory systems in which the negative as well as the positive of certain propositions are valid. | |
| From: Luitzen E.J. Brouwer (Intuitionism and Formalism [1912], p.79) | |
| A reaction: Was the turning point of Graham Priest's life the day he read this sentence? I don't agree. I take the principle of non-contradiction to be a highly generalised observation of how the world works (and Russell agrees with me). |
| 15941 | For intuitionists excluded middle is an outdated historical convention [Brouwer] |
| Full Idea: From the intuitionist standpoint the dogma of the universal validity of the principle of excluded third in mathematics can only be considered as a phenomenon of history of civilization, like the rationality of pi or rotation of the sky about the earth. | |
| From: Luitzen E.J. Brouwer (works [1930]), quoted by Shaughan Lavine - Understanding the Infinite VI.2 | |
| A reaction: [Brouwer 1952:510-11] |
| 18119 | Mathematics is a mental activity which does not use language [Brouwer, by Bostock] |
| Full Idea: Brouwer made the rather extraordinary claim that mathematics is a mental activity which uses no language. | |
| From: report of Luitzen E.J. Brouwer (Mathematics, Science and Language [1928]) by David Bostock - Philosophy of Mathematics 7.1 | |
| A reaction: Since I take language to have far less of a role in thought than is commonly believed, I don't think this idea is absurd. I would say that we don't use language much when we are talking! |
| 18247 | Brouwer saw reals as potential, not actual, and produced by a rule, or a choice [Brouwer, by Shapiro] |
| Full Idea: In his early writing, Brouwer took a real number to be a Cauchy sequence determined by a rule. Later he augmented rule-governed sequences with free-choice sequences, but even then the attitude is that Cauchy sequences are potential, not actual infinities. | |
| From: report of Luitzen E.J. Brouwer (works [1930]) by Stewart Shapiro - Philosophy of Mathematics 6.6 | |
| A reaction: This is the 'constructivist' view of numbers, as espoused by intuitionists like Brouwer. |
| 12451 | Scientific laws largely rest on the results of counting and measuring [Brouwer] |
| Full Idea: A large part of the natural laws introduced by science treat only of the mutual relations between the results of counting and measuring. | |
| From: Luitzen E.J. Brouwer (Intuitionism and Formalism [1912], p.77) | |
| A reaction: His point, I take it, is that the higher reaches of numbers have lost touch with the original point of the system. I now see the whole issue as just depending on conventions about the agreed extension of the word 'number'. |
| 18118 | Brouwer regards the application of mathematics to the world as somehow 'wicked' [Brouwer, by Bostock] |
| Full Idea: Brouwer regards as somehow 'wicked' the idea that mathematics can be applied to a non-mental subject matter, the physical world, and that it might develop in response to the needs which that application reveals. | |
| From: report of Luitzen E.J. Brouwer (Mathematics, Science and Language [1928]) by David Bostock - Philosophy of Mathematics 7.1 | |
| A reaction: The idea is that mathematics only concerns creations of the human mind. It presumably has no more application than, say, noughts-and-crosses. |
| 12454 | Intuitionists only accept denumerable sets [Brouwer] |
| Full Idea: The intuitionist recognises only the existence of denumerable sets. | |
| From: Luitzen E.J. Brouwer (Intuitionism and Formalism [1912], p.80) | |
| A reaction: That takes you up to omega, but not beyond, presumably because it then loses sight of the original intuition of 'bare two-oneness' (Idea 12453). I sympathise, but the word 'number' has shifted its meaning a lot these days. |
| 12453 | Neo-intuitionism abstracts from the reuniting of moments, to intuit bare two-oneness [Brouwer] |
| Full Idea: Neo-intuitionism sees the falling apart of moments, reunited while remaining separated in time, as the fundamental phenomenon of human intellect, passing by abstracting to mathematical thinking, the intuition of bare two-oneness. | |
| From: Luitzen E.J. Brouwer (Intuitionism and Formalism [1912], p.80) | |
| A reaction: [compressed] A famous and somewhat obscure idea. He goes on to say that this creates one and two, and all the finite ordinals. |
| 8728 | Intuitionist mathematics deduces by introspective construction, and rejects unknown truths [Brouwer] |
| Full Idea: Mathematics rigorously treated from the point of view of deducing theorems exclusively by means of introspective construction, is called intuitionistic mathematics. It deviates from classical mathematics, which believes in unknown truths. | |
| From: Luitzen E.J. Brouwer (Consciousness, Philosophy and Mathematics [1948]), quoted by Stewart Shapiro - Thinking About Mathematics 1.2 | |
| A reaction: Clearly intuitionist mathematics is a close cousin of logical positivism and the verification principle. This view would be anathema to Frege, because it is psychological. Personally I believe in the existence of unknown truths, big time! |
| 14596 | Call 'nominalism' the denial of numbers, properties, relations and sets [Dorr] |
| Full Idea: Just as there are no numbers or properties, there are no relations (like 'being heavier than' or 'betweenness'), or sets. I will provisionally use 'nominalism' for the conjunction of these four claims. | |
| From: Cian Dorr (There Are No Abstract Objects [2008], 1) | |
| A reaction: If you are going to be a nominalist, do it properly! My starting point in metaphysics is strong sympathy with this view. Right now [Tues 22nd Nov 2011, 10:57 am GMT] I think it is correct. |
| 14597 | Natural Class Nominalism says there are primitive classes of things resembling in one respect [Dorr] |
| Full Idea: Natural Class Nominalists take as primitive the notion of a 'natural' class - a class of things that all resemble one another in some one respect and resemble nothing else in that respect. | |
| From: Cian Dorr (There Are No Abstract Objects [2008], 4) | |
| A reaction: Dorr rejects this view because he doesn't believe in 'classes'. How committed to classes do you have to be before you are permitted to talk about them? All vocabulary (such as 'resemble') seems metaphysically tainted in this area. |
| 15825 | Carneades denied the transitivity of identity [Carneades, by Chisholm] |
| Full Idea: Carneades denied the principle of the transitivity of identity. | |
| From: report of Carneades (fragments/reports [c.174 BCE], fr 41-42) by Roderick Chisholm - Person and Object 3.1 | |
| A reaction: Chisholm calls this 'extreme', but I assume Carneades wouldn't deny the principle in mathematics. I'm guessing that he just means that nothing ever stays quite the same. |
| 21389 | Carneades distinguished logical from causal necessity, when talking of future events [Long on Carneades] |
| Full Idea: From 'E will take place is true' it follows that E must take place. But 'must' here is logical not causal necessity. It is a considerable achievement of Carneades to have distinguished these two senses of necessity. | |
| From: comment on Carneades (fragments/reports [c.174 BCE]) by A.A. Long - Hellenistic Philosophy 3 | |
| A reaction: Personally I am inclined to think 'necessity' is univocal, and does not have two senses. What Carneades has nicely done is distinguish the two different grounds for the necessities. |
| 14598 | Abstracta imply non-logical brute necessities, so only nominalists can deny such things [Dorr] |
| Full Idea: If there are abstract objects, there are necessary truths about these things that cannot be reduced to truths of logic. So only the nominalist, who denies that there are any such things, can adequately respect the idea that there are no brute necessities. | |
| From: Cian Dorr (There Are No Abstract Objects [2008], 4) | |
| A reaction: This is where two plates of my personal philosophy grind horribly against one another. I love nominalism, and I love natural necessities. They meet like a ring-species in evolution. I'll just call it a 'paradox', and move on (swiftly). |
| 21671 | Voluntary motion is intrinsically within our power, and this power is its cause [Carneades, by Cicero] |
| Full Idea: Voluntary motion possesses the intrinsic property of being in our power and of obeying us, and its obedience is not uncaused, for its nature is itself the cause of this. | |
| From: report of Carneades (fragments/reports [c.174 BCE]) by M. Tullius Cicero - On Fate ('De fato') 11.25 | |
| A reaction: To say that actions arise from our 'intrinsic power' is not much of an explanation, but it is still informative - that you should study the intrinsic powers of humans if you want to explain it. |
| 21391 | Some actions are within our power; determinism needs prior causes for everything - so it is false [Carneades, by Cicero] |
| Full Idea: Now something is in our power; but if everything happens as a result of destiny all things happen as a result of antecedent causes; therefore what happens does not happen as a result of destiny. | |
| From: report of Carneades (fragments/reports [c.174 BCE]) by M. Tullius Cicero - On Fate ('De fato') 14.31 | |
| A reaction: This invites the question of whether some things really are 'in our power'. Carneades (as expressed by Cicero) takes that for granted. Our 'power' may be antecedent causes in disguise. |
| 21674 | Even Apollo can only foretell the future when it is naturally necessary [Carneades, by Cicero] |
| Full Idea: Carneades used to say that not even Apollo could tell any future events except those whose causes were so held together that they must necessarily happen. | |
| From: report of Carneades (fragments/reports [c.174 BCE]) by M. Tullius Cicero - On Fate ('De fato') 14.32 | |
| A reaction: Carneades is opposing the usual belief in divination, where even priests can foretell contingent future events to some extent. Careneades, of course, was defending free will. |
| 10117 | Intuitonists in mathematics worried about unjustified assertion, as well as contradiction [Brouwer, by George/Velleman] |
| Full Idea: The concern of mathematical intuitionists was that the use of certain forms of inference generates, not contradiction, but unjustified assertions. | |
| From: report of Luitzen E.J. Brouwer (Intuitionism and Formalism [1912]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.6 | |
| A reaction: This seems to be the real origin of the verificationist idea in the theory of meaning. It is a hugely revolutionary idea - that ideas are not only ruled out of court by contradiction, but that there are other criteria which should also be met. |
| 7398 | Carneades said that after a shipwreck a wise man would seize the only plank by force [Carneades, by Tuck] |
| Full Idea: Carneades argued forcefully that in the event of a shipwreck, the wise man would be prepared to seize the only plank capable of bearing him to shore, even if that meant pushing another person off it. | |
| From: report of Carneades (fragments/reports [c.174 BCE]) by Richard Tuck - Hobbes Ch.1 | |
| A reaction: [source for this?] This thought seems to have provoked great discussion in the sixteenth century (mostly sympathetic). I can't help thinking the right answer depends on assessing your rival. Die for a hero, drown a nasty fool. |
| 21392 | People change laws for advantage; either there is no justice, or it is a form of self-injury [Carneades, by Lactantius] |
| Full Idea: The same people often changed laws according to circumstances; there is no natural law. There is no such thing as justice or, if there is, it is the height of folly, since a man injures himself in taking thought for the advantage of others. | |
| From: report of Carneades (fragments/reports [c.174 BCE]) by Lactantius - Institutiones Divinae 5.16.4 | |
| A reaction: [An argument used by Carneades on his notorious 156BCE visit to Rome, where he argued both for and against justice] This is probably the right wing view of justice. Why give other people what they want, if it is at our expense? |