display all the ideas for this combination of philosophers
34 ideas
| 12376 | Demonstrations by reductio assume excluded middle [Aristotle] |
| Full Idea: Demonstrations by reduction to the impossible assume that everything is asserted or denied. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 77a23) | |
| A reaction: This sounds like the lynchpin of classical logic. |
| 11033 | Predications of predicates are predications of their subjects [Aristotle] |
| Full Idea: Whenever one thing is predicated of another as of a subject, all things said of what is predicated will be said of the subject also. | |
| From: Aristotle (Categories [c.331 BCE], 01b10) |
| 11026 | Classical logic is deliberately extensional, in order to model mathematics [Fitting] |
| Full Idea: Mathematics is typically extensional throughout (we write 3+2=2+3 despite the two terms having different meanings). ..Classical first-order logic is extensional by design since it primarily evolved to model the reasoning of mathematics. | |
| From: Melvin Fitting (Intensional Logic [2007], §1) |
| 12373 | Something holds universally when it is proved of an arbitrary and primitive case [Aristotle] |
| Full Idea: Something holds universally when it is proved of an arbitrary and primitive case. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 73b33) | |
| A reaction: A key idea in mathematical logic, but it always puzzles me. If you snatch a random person in London, and they are extremely tall, does that prove that people of London are extremely tall? How do we know the arbitrary is representative? |
| 11148 | Deduction is when we suppose one thing, and another necessarily follows [Aristotle] |
| Full Idea: A deduction is a discourse in which, certain things having been supposed, something different from the things supposed results of necessity because these things are so. | |
| From: Aristotle (Prior Analytics [c.328 BCE], 24b18) | |
| A reaction: Notice that it is modal ('suppose', rather than 'know'), that necessity is involved, which is presumably metaphysical necessity, and that there are assumptions about what would be true, and not just what follows from what. |
| 21593 | In talking of future sea-fights, Aristotle rejects bivalence [Aristotle, by Williamson] |
| Full Idea: Unlike Aristotle, Stoics did not reject Bivalence for future contingencies; it is true or false that there will be a sea-fight tomorrow. | |
| From: report of Aristotle (On Interpretation [c.330 BCE], 19a31) by Timothy Williamson - Vagueness 1.2 | |
| A reaction: I'd never quite registered this simple account of the sea-fight. As Williamson emphasises, one should not lightly reject the principle of bivalence. Has Aristotle entered a slippery slope? Stoics disagreed with Aristotle. |
| 22154 | For Aristotle bivalence is a feature of reality [Aristotle, by Boulter] |
| Full Idea: For Aristotle the principle of bivalence is primarily a principle of metaphysics, not logic. It applies to entities in the real order first, and to propositions in the rational order second. | |
| From: report of Aristotle (Metaphysics [c.324 BCE]) by Stephen Boulter - Why Medieval Philosophy Matters 5 | |
| A reaction: This is because nothing is vague. Boulter says this is also the case with non-contradiction. I like this idea very much. I reject the Fregean picture of the autonomy of the rational order. Logic is powerful because it reflects reality. |
| 1701 | A prayer is a sentence which is neither true nor false [Aristotle] |
| Full Idea: A prayer is a sentence which is neither true nor false. | |
| From: Aristotle (On Interpretation [c.330 BCE], 17a01) |
| 12363 | Everything is either asserted or denied truly [Aristotle] |
| Full Idea: Of the fact that everything is either asserted or denied truly, we must believe that it is the case. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 71a14) | |
| A reaction: Presumably this means that every assertion which could possibly be asserted must come out as either true or false. This will have to include any assertions with vague objects or predicates, and any universal assertions, and negative assertions. |
| 18896 | Aristotle places terms at opposite ends, joined by a quantified copula [Aristotle, by Sommers] |
| Full Idea: Aristotle often preferred to formulate predications by placing the terms at opposite ends of the sentence and joining them by predicating expressions like 'belongs-to-some' or 'belongs-to-every'. | |
| From: report of Aristotle (Prior Analytics [c.328 BCE]) by Fred Sommers - Intellectual Autobiography 'Conceptions' | |
| A reaction: This is Sommers's picture of Aristotle, which led Sommers to develop his modern Term Logic. |
| 4730 | For Aristotle, the subject-predicate structure of Greek reflected a substance-accident structure of reality [Aristotle, by O'Grady] |
| Full Idea: Aristotle apparently believed that the subject-predicate structure of Greek reflected the substance-accident nature of reality. | |
| From: report of Aristotle (works [c.330 BCE]) by Paul O'Grady - Relativism Ch.4 | |
| A reaction: We need not assume that Aristotle is wrong. It is a chicken-and-egg. There is something obvious about subject-predicate language, if one assumes that unified objects are part of nature, and not just conventional. |
| 16967 | 'Are Coriscus and Callias at home?' sounds like a single question, but it isn't [Aristotle] |
| Full Idea: If you ask 'Are Coriscus and Callias at home or not at home?', whether they are both at home or not there, the number of propositions is more than one. For if the answer is true, it does not follow that the question is a single one. | |
| From: Aristotle (Sophistical Refutations [c.331 BCE], 176a08) | |
| A reaction: [compressed] Aristotle is saying that some questions should not receive a 'yes' or 'no' answer, because they are equivocal. Arthur Prior cites this passage, on 'and'. Ordinary use of 'and' need not be the logical use of 'and'. |
| 3300 | Aristotle's logic is based on the subject/predicate distinction, which leads him to substances and properties [Aristotle, by Benardete,JA] |
| Full Idea: Basic to Aristotle's logic is the grammatical distinction between subject and predicate, which he glosses in terms of the contrast between a substance and its properties. | |
| From: report of Aristotle (Prior Analytics [c.328 BCE]) by José A. Benardete - Metaphysics: the logical approach Intro | |
| A reaction: The introduction of quantifiers and 'logical form' can't disguise the fact that we still talk about (and with) objects and predicates, because no one can think of any other way to talk. |
| 11028 | λ-abstraction disambiguates the scope of modal operators [Fitting] |
| Full Idea: λ-abstraction can be used to abstract and disambiguate a predicate. De re is [λx◊P(x)](f) - f has the possible-P property - and de dicto is ◊[λxP(x)](f) - possibly f has the P-property. Also applies to □. | |
| From: Melvin Fitting (Intensional Logic [2007], §3.3) | |
| A reaction: Compare the Barcan formula. Originated with Church in the 1930s, and Carnap 1947, but revived by Stalnaker and Thomason 1968. Because it refers to the predicate, it has a role in intensional versions of logic, especially modal logic. |
| 11149 | Affirming/denying sentences are universal, particular, or indeterminate [Aristotle] |
| Full Idea: Affirming/denying sentences are universal, particular, or indeterminate. Belonging 'to every/to none' is universal; belonging 'to some/not to some/not to every' is particular; belonging or not belonging (without universal/particular) is indeterminate. | |
| From: Aristotle (Prior Analytics [c.328 BCE], 24a16) |
| 8079 | Aristotelian logic has two quantifiers of the subject ('all' and 'some') [Aristotle, by Devlin] |
| Full Idea: Aristotelian logic has two quantifiers of the subject ('all' and 'some'), and two ways to combine the subject with the predicate ('have', and 'have not'), giving four propositions: all-s-have-p, all-s-have-not-p, some-s-have-p, and some-s-have-not-p. | |
| From: report of Aristotle (Prior Analytics [c.328 BCE]) by Keith Devlin - Goodbye Descartes Ch.2 | |
| A reaction: Frege seems to have switched from 'some' to 'at-least-one'. Since then other quantifiers have been proposed. See, for example, Ideas 7806 and 6068. |
| 13004 | Aristotle's axioms (unlike Euclid's) are assumptions awaiting proof [Aristotle, by Leibniz] |
| Full Idea: Aristotle's way with axioms, rather than Euclid's, is as assumptions which we are willing to agree on while awaiting an opportunity to prove them | |
| From: report of Aristotle (Posterior Analytics [c.327 BCE], 76b23-) by Gottfried Leibniz - New Essays on Human Understanding 4.07 | |
| A reaction: Euclid's are understood as basic self-evident truths which will be accepted by everyone, though the famous parallel line postulate undermined that. The modern view of axioms is a set of minimum theorems that imply the others. I like Aristotle. |
| 11264 | Aporia 3: Does one science investigate all being, or does each kind of being have a science? [Aristotle, by Politis] |
| Full Idea: Aporia 3: Is it the task of a single science to investigate all beings, or is it the task of fundamentally different sciences to investigate different kinds of being? | |
| From: report of Aristotle (Metaphysics [c.324 BCE], 0997a15-25) by Vassilis Politis - Aristotle and the Metaphysics 3.4 | |
| A reaction: One might ask whether neuroscience is entirely distinct from psychology, or partical physics from biology. |
| 11261 | Puzzles arise when reasoning seems equal on both sides [Aristotle] |
| Full Idea: The equality of opposite reasonings is the cause of aporia; for it is when we reason on both [sides of a question] and it appears to us that everything can come about either way, that we are in a state of aporia about which of the two ways to take up. | |
| From: Aristotle (Topics [c.331 BCE], 145b17), quoted by Vassilis Politis - Aristotle and the Metaphysics 3.1 | |
| A reaction: Other philosophers give up on the subject in this situation, but I love Aristotle because he takes this to be the place where philosophy begins. |
| 11258 | We must start with our puzzles, and progress by solving them, as they reveal the real difficulty [Aristotle] |
| Full Idea: We should first address those puzzles ('aporiai') that first arise. ..Subsequent progress depends on the resolution of the first puzzles, and one cannot solve these without knowing the difficulty, and our confusion shows this to be the case. | |
| From: Aristotle (Metaphysics [c.324 BCE], 0995a27-) | |
| A reaction: This stands in nice opposition to the Wittgenstein view, that confusion is largely a self-inflicted wound arising from our language, having little to do with reality. For Aristotle it is reality which is the source of our mental confusion. He's right. |
| 11265 | Aporia 4: Does metaphysics just investigate pure being, or also the characteristics of being? [Aristotle, by Politis] |
| Full Idea: Aporia 4: Is the task of metaphysics only to investigate the (primary) beings or also to investigate the common characteristics of the (primary) beings? | |
| From: report of Aristotle (Metaphysics [c.324 BCE], 0997a25-34) by Vassilis Politis - Aristotle and the Metaphysics 3.4 | |
| A reaction: Politis points out that metaphysics would then be in danger of collapsing into all sorts of special sciences. |
| 11262 | Aporia 1: is there one science of explanation, or many? [Aristotle, by Politis] |
| Full Idea: Aporia 1: Is it the task of a single science to investigate all the different causes and explanations of things, or is this the task of fundamentally different sciences? | |
| From: report of Aristotle (Metaphysics [c.324 BCE], 0996a18-b26) by Vassilis Politis - Aristotle and the Metaphysics 3.4 | |
| A reaction: [This is the 10,000th idea to be entered into this database - 1st February 2010, at 7:21pm] I think there are two sorts of philosopher - those, like myself, who cling on to the idea of one science, and the pluralists, perfectly happy with many. |
| 11263 | Aporia 2: Does one science investigate both ultimate and basic principles of being? [Aristotle, by Politis] |
| Full Idea: Aporia 2: Is it the task of a single science to investigate both the ultimate principles of being and the basic principles of reasoning (e.g. non-contradiction)? Or is this the task of fundamentally different sciences? | |
| From: report of Aristotle (Metaphysics [c.324 BCE], 0996b26-997a15) by Vassilis Politis - Aristotle and the Metaphysics 3.4 | |
| A reaction: Although I favour the dream of one science dealing with everything, I hesitate over this aporia. I like the unity of modern science and metaphysics, but maybe logic precedes them both and has a different basis. Nice question! |
| 11266 | Aporia 5: Do other things exist besides what is perceptible by the senses? [Aristotle, by Politis] |
| Full Idea: Aporia 5: Do only sense-perceptible things exist or do non-sense-perceptible things exist, too, in addition to or besides (para) sense-perceptible ones? | |
| From: report of Aristotle (Metaphysics [c.324 BCE], 0997a34-998a19) by Vassilis Politis - Aristotle and the Metaphysics 3.4 | |
| A reaction: Nowadays we have discovered so much that is beyond our natural perceptions that it is obvious that there may be stuff we can never detect. ...And yet if 'to exist is to have causal powers' then everything would be detectable in principle. Hm. |
| 11270 | Aporia 9: Is there one principle, or one kind of principle? [Aristotle, by Politis] |
| Full Idea: Aporia 9: Are principles one in kind, or one in number? | |
| From: report of Aristotle (Metaphysics [c.324 BCE], 0999b24-1000a04) by Vassilis Politis - Aristotle and the Metaphysics 3.4 | |
| A reaction: A key aporia, which can be answered in both directions. In what respects are the essences of two different human beings identical? It is a key question for any essentialist. |
| 11267 | Aporia 6: Are the basic principles of a thing the kinds to which it belongs, or its components? [Aristotle, by Politis] |
| Full Idea: Aporia 6: Are the principles of a thing the kinds to which the thing belongs or are they rather the ultimate elements that are present in the thing and compose the thing? | |
| From: report of Aristotle (Metaphysics [c.324 BCE], 0998a20-b13) by Vassilis Politis - Aristotle and the Metaphysics 3.4 | |
| A reaction: This is the heart of the modern debate on essentialism, between sortal essentialists (Brody and Wiggins) and those basing essences on powers and basic stuff (Ellis, Fine). I say the sortal bunch are wrong, wrong, wrong. |
| 11268 | Aporia 7: Is a thing's kind the most general one, or the most specific one? [Aristotle, by Politis] |
| Full Idea: Aporia 7: If a thing's principle is its general kind, is that the most general kind to which it belongs, or the least general kind to which it belongs? | |
| From: report of Aristotle (Metaphysics [c.324 BCE], 0998b13-999a23) by Vassilis Politis - Aristotle and the Metaphysics 3.4 | |
| A reaction: This is a question for the sortal essentialists. I think it amounts to an argument against sortal essentialism, because there are nested kinds, and nothing to decide which one of them matters, |
| 11269 | Aporia 8: Are there general kinds, or merely particulars? [Aristotle, by Politis] |
| Full Idea: Aporia 8: Do general kinds exist at all, in addition to the sense-perceptible particulars? | |
| From: report of Aristotle (Metaphysics [c.324 BCE], 0999a24-b24) by Vassilis Politis - Aristotle and the Metaphysics 3.4 | |
| A reaction: Aristotle is beginning to confront the whole issue of natural kinds. It seems OK to say that the elements are natural kinds, but things get more difficult when you talk about 'planets' or 'tigers'. Aristotle decides there are natural kinds. |
| 11271 | Aporia 10: Do perishables and imperishables have the same principle? [Aristotle, by Politis] |
| Full Idea: Aporia 10: Are the principles of perishable and imperishable things the same, or different? | |
| From: report of Aristotle (Metaphysics [c.324 BCE], 1000a05-1001a03) by Vassilis Politis - Aristotle and the Metaphysics 3.4 | |
| A reaction: Locke proposed that having a 'life' was an essential distinction between these two, but this has been rather undermined by modern biochemistry. Aristotle wants to know if nature is a unity. |
| 11272 | Aporia 11: Are primary being and unity distinct, or only in the things that are? [Aristotle, by Politis] |
| Full Idea: Aporia 11: Is primary being simply being itself and unity itself, or is primary being rather things that are and are one? | |
| From: report of Aristotle (Metaphysics [c.324 BCE], 1001a04--b25) by Vassilis Politis - Aristotle and the Metaphysics 3.4 | |
| A reaction: I can't make sense of 'being' in itself, though Heidegger seems to have devoted his life to the idea. It appears that Aristotle agrees with me. |
| 11273 | Aporia 12: Do mathematical entities exist independently, or only in objects? [Aristotle, by Politis] |
| Full Idea: Aporia 12: Are numbers, solids, surfaces and points themselves the primary beings or are they primary beings only because other things (e.g. this horse) have such geometrical and in general mathematical properties? | |
| From: report of Aristotle (Metaphysics [c.324 BCE], 1001b26-1002b11) by Vassilis Politis - Aristotle and the Metaphysics 3.4 | |
| A reaction: The thinking of Pythagoras and Plato hovers behind this question. Aristotle seems to be groping for a compromise view. |
| 11274 | Aporia 13: Are there kinds, as well as particulars and mathematical entities? [Aristotle, by Politis] |
| Full Idea: Aporia 13: Are there kinds ('eidé') in addition to or besides both sense-perceptible things and the entities postulated by mathematics? | |
| From: report of Aristotle (Metaphysics [c.324 BCE], 1002b12-32) by Vassilis Politis - Aristotle and the Metaphysics 3.4 | |
| A reaction: This seems close to Aporia 8 (Idea 11269). I can't make sense of a kind which has no particulars, except as a fond memory, like the dodo, and a fictional entity like the gryphon. ...Or perhaps something we aim to bio-engineer. |
| 11276 | Aporia 15: Are the causes of things universals or particulars? [Aristotle, by Politis] |
| Full Idea: Aporia 15: Are the principles of things universals or particulars? | |
| From: report of Aristotle (Metaphysics [c.324 BCE], 1003a05-17) by Vassilis Politis - Aristotle and the Metaphysics 3.4 | |
| A reaction: Aristotle seems to be groping for a compromise answer. Explanations must be universal, but primary being seems to reside in the particulars. The modern idea of Aristotelianism is universals-only-in-particulars. |
| 11275 | Aporia 14: Are ultimate causes of things potentialities, or must they be actual? [Aristotle, by Politis] |
| Full Idea: Aporia 14: Are the elements of things potentialities and capacities for causing and generating those things or are they what actually causes and generates those things? | |
| From: report of Aristotle (Metaphysics [c.324 BCE], 1002b32-1003a05) by Vassilis Politis - Aristotle and the Metaphysics 3.4 | |
| A reaction: We would now call this a question about 'dispositions', and the consensus seems to be that they are potential rather than actual, since a vase may be fragile without having to actually break. |