display all the ideas for this combination of texts
26 ideas
| 8078 | Modus ponens is one of five inference rules identified by the Stoics [Chrysippus, by Devlin] |
| Full Idea: Modus ponens is just one of the five different inference rules identified by the Stoics. | |
| From: report of Chrysippus (fragments/reports [c.240 BCE]) by Keith Devlin - Goodbye Descartes Ch.2 | |
| A reaction: Modus ponens strikes me as being more like a definition of implication than a 'rule'. Implication is what gets you from one truth to another. All the implications of a truth must also be true. |
| 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. |
| 10111 | Asserting Excluded Middle is a hallmark of realism about the natural world [George/Velleman] |
| Full Idea: A hallmark of our realist stance towards the natural world is that we are prepared to assert the Law of Excluded Middle for all statements about it. For all statements S, either S is true, or not-S is true. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.4) | |
| A reaction: Personally I firmly subscribe to realism, so I suppose I must subscribe to Excluded Middle. ...Provided the statement is properly formulated. Or does liking excluded middle lead me to realism? |
| 6023 | Every proposition is either true or false [Chrysippus, by Cicero] |
| Full Idea: We hold fast to the position, defended by Chrysippus, that every proposition is either true or false. | |
| From: report of Chrysippus (fragments/reports [c.240 BCE]) by M. Tullius Cicero - On Fate ('De fato') 38 | |
| A reaction: I am intrigued to know exactly how you defend this claim. It may depend what you mean by a proposition. A badly expressed proposition may have indeterminate truth, quite apart from the vague, the undecidable etc. |
| 10129 | A 'model' is a meaning-assignment which makes all the axioms true [George/Velleman] |
| Full Idea: A 'model' of a theory is an assignment of meanings to the symbols of its language which makes all of its axioms come out true. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.7) | |
| A reaction: If the axioms are all true, and the theory is sound, then all of the theorems will also come out true. |
| 10105 | Differences between isomorphic structures seem unimportant [George/Velleman] |
| Full Idea: Mathematicians tend to regard the differences between isomorphic mathematical structures as unimportant. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) | |
| A reaction: This seems to be a pointer towards Structuralism as the underlying story in mathematics. The intrinsic character of so-called 'objects' seems unimportant. How theories map onto one another (and onto the world?) is all that matters? |
| 10119 | Consistency is a purely syntactic property, unlike the semantic property of soundness [George/Velleman] |
| Full Idea: Consistency is a purely syntactic property, unlike the semantic property of soundness. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.6) |
| 10126 | A 'consistent' theory cannot contain both a sentence and its negation [George/Velleman] |
| Full Idea: If there is a sentence such that both the sentence and its negation are theorems of a theory, then the theory is 'inconsistent'. Otherwise it is 'consistent'. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.7) |
| 10120 | Soundness is a semantic property, unlike the purely syntactic property of consistency [George/Velleman] |
| Full Idea: Soundness is a semantic property, unlike the purely syntactic property of consistency. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.6) |
| 10127 | A 'complete' theory contains either any sentence or its negation [George/Velleman] |
| Full Idea: If there is a sentence such that neither the sentence nor its negation are theorems of a theory, then the theory is 'incomplete'. Otherwise it is 'complete'. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.7) | |
| A reaction: Interesting questions are raised about undecidable sentences, irrelevant sentences, unknown sentences.... |
| 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. |
| 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. |