28 ideas
| 13913 | The four 'perfect syllogisms' are called Barbara, Celarent, Darii and Ferio [Engelbretsen/Sayward] |
| Full Idea: There are four 'perfect syllogisms': Barbara (every M is P, every S is M, so every S is P); Celarent (no M is P, every S is M, so no S is P); Darii (every M is P, some S is M, so some S is P); Ferio (no M is P, some S is M, so some S is not P). | |
| From: Engelbretsen,G/Sayward,C (Philosophical Logic: Intro to Advanced Topics [2011], 8) | |
| A reaction: The four names are mnemonics from medieval universities. |
| 13914 | Syllogistic logic has one rule: what is affirmed/denied of wholes is affirmed/denied of their parts [Engelbretsen/Sayward] |
| Full Idea: It has often been claimed (e.g. by Leibniz) that a single rule governs all syllogistic validity, called 'dictum de omni et null', which says that what is affirmed or denied of any whole is affirmed or denied of any part of that whole. | |
| From: Engelbretsen,G/Sayward,C (Philosophical Logic: Intro to Advanced Topics [2011], 8) | |
| A reaction: This seems to be the rule which is captured by Venn Diagrams. |
| 13915 | Syllogistic can't handle sentences with singular terms, or relational terms, or compound sentences [Engelbretsen/Sayward] |
| Full Idea: Three common kinds of sentence cannot be put into syllogistic ('categorical') form: ones using singular terms ('Mars is red'), ones using relational terms ('every painter owns some brushes'), and compound sentences. | |
| From: Engelbretsen,G/Sayward,C (Philosophical Logic: Intro to Advanced Topics [2011], 8) |
| 13916 | Term logic uses expression letters and brackets, and '-' for negative terms, and '+' for compound terms [Engelbretsen/Sayward] |
| Full Idea: Term logic begins with expressions and two 'term functors'. Any simple letter is a 'term', any term prefixed by a minus ('-') is a 'negative term', and any pair of terms flanking a plus ('+') is a 'compound term'. Parenthese are used for grouping. | |
| From: Engelbretsen,G/Sayward,C (Philosophical Logic: Intro to Advanced Topics [2011], 8) | |
| A reaction: [see Engelbretsen and Sayward for the full formal system] |
| 13850 | In modern logic all formal validity can be characterised syntactically [Engelbretsen/Sayward] |
| Full Idea: One of the key ideas of modern formal logic is that all formally valid inferences can be specified in strictly syntactic terms. | |
| From: Engelbretsen,G/Sayward,C (Philosophical Logic: Intro to Advanced Topics [2011], Ch.2) |
| 13849 | Classical logic rests on truth and models, where constructivist logic rests on defence and refutation [Engelbretsen/Sayward] |
| Full Idea: Classical logic rests on the concepts of truth and falsity (and usually makes use of a semantic theory based on models), whereas constructivist logic accounts for inference in terms of defense and refutation. | |
| From: Engelbretsen,G/Sayward,C (Philosophical Logic: Intro to Advanced Topics [2011], Intro) | |
| A reaction: My instincts go with the classical view, which is that inferences do not depend on the human capacity to defend them, but sit there awaiting revelation. My view isn't platonist, because I take the inferences to be rooted in the physical world. |
| 13851 | Unlike most other signs, = cannot be eliminated [Engelbretsen/Sayward] |
| Full Idea: Unlike ∨, →, ↔, and ∀, the sign = is not eliminable from a logic. | |
| From: Engelbretsen,G/Sayward,C (Philosophical Logic: Intro to Advanced Topics [2011], Ch.3) |
| 13852 | Axioms are ω-incomplete if the instances are all derivable, but the universal quantification isn't [Engelbretsen/Sayward] |
| Full Idea: A set of axioms is said to be ω-incomplete if, for some universal quantification, each of its instances is derivable from those axioms but the quantification is not thus derivable. | |
| From: Engelbretsen,G/Sayward,C (Philosophical Logic: Intro to Advanced Topics [2011], 7) |
| 1553 | No perceptible object is truly straight or curved [Protagoras] |
| Full Idea: No perceptible object is geometrically straight or curved; after all, a circle does not touch a ruler at a point, as Protagoras used to say, in arguing against the geometers. | |
| From: Protagoras (fragments/reports [c.441 BCE], B07), quoted by Aristotle - Metaphysics 998a1 |
| 18933 | Not-Being obviously doesn't exist, and the five modes of Being are all impossible [Gorgias, by Diog. Laertius] |
| Full Idea: I. Nothing exists. a) Not-Being does not exist. b) Being does not exist as everlasting, as created, as both, as One, or as Many. II. If anything does exist, it is incomprehensible. III. If existence is comprehensible, it is incommunicable. | |
| From: report of Gorgias (fragments/reports [c.443 BCE], B03) by Diogenes Laertius - Lives of Eminent Philosophers 09 | |
| A reaction: [Also Sextus Empiricus, Against Logicians I.65-] For Part I he works through all the possible modes of being he can think of, and explains why none of them are possible. It is worth remembering that Gorgias loved rhetoric, not philosophy! |
| 1549 | Everything that exists consists in being perceived [Protagoras] |
| Full Idea: Everything that exists consists in being perceived. | |
| From: Protagoras (fragments/reports [c.441 BCE]), quoted by Didymus the Blind - Commentary on the Psalms (frags) | |
| A reaction: A striking anticipation of Berkeley's "esse est percipi" (to be is to be perceived). |
| 1545 | Protagoras was the first to claim that there are two contradictory arguments about everything [Protagoras, by Diog. Laertius] |
| Full Idea: Protagoras was the first to claim that there are two contradictory arguments about everything. | |
| From: report of Protagoras (fragments/reports [c.441 BCE], A01) by Diogenes Laertius - Lives of Eminent Philosophers 09.51 |
| 1547 | Man is the measure of all things - of things that are, and of things that are not [Protagoras] |
| Full Idea: He began one of his books as follows: 'Man is the measure of all things - of the things that are, that they are, and of the things that are not, that they are not'. | |
| From: Protagoras (fragments/reports [c.441 BCE], B01), quoted by Diogenes Laertius - Lives of Eminent Philosophers 09.51 |
| 3305 | There is no more purely metaphysical doctrine than Protagorean relativism [Benardete,JA on Protagoras] |
| Full Idea: No purer metaphysical doctrine can possibly be found than the Protagorean thesis that to be (anything at all) is to be relative ( to something or other). | |
| From: comment on Protagoras (fragments/reports [c.441 BCE]) by José A. Benardete - Metaphysics: the logical approach Ch.3 |
| 3313 | If my hot wind is your cold wind, then wind is neither hot nor cold, and so not as cold as itself [Benardete,JA on Protagoras] |
| Full Idea: Because the wind is cold to me but not you, Protagoras takes it to in itself neither cold nor not-cold. Accordingly, I very much doubt that he can allow the wind to be exactly as cold as itself. | |
| From: comment on Protagoras (fragments/reports [c.441 BCE]) by José A. Benardete - Metaphysics: the logical approach Ch.8 |
| 3317 | You can only state the problem of the relative warmth of an object by agreeing on the underlying object [Benardete,JA on Protagoras] |
| Full Idea: Only if the thing that is cold to me is precisely identical with the thing that is not cold to you can Protagoras launch his argument, but then it is seen to be the thing in itself that exists absolutely speaking. | |
| From: comment on Protagoras (fragments/reports [c.441 BCE]) by José A. Benardete - Metaphysics: the logical approach Ch.8 |
| 247 | God is "the measure of all things", more than any man [Plato on Protagoras] |
| Full Idea: In our view it is God who is pre-eminently the "measure of all things", much more so than any "man", as they say. | |
| From: comment on Protagoras (fragments/reports [c.441 BCE]) by Plato - The Laws 716c |
| 606 | Protagoras absurdly thought that the knowing or perceiving man is 'the measure of all things' [Aristotle on Protagoras] |
| Full Idea: When Protagoras quipped that man is the measure of all things, he had in mind, of course, the knowing or perceiving man. The grounds are that they have perception/knowledge, and these are said to be the measures of objects. Utter nonsense! | |
| From: comment on Protagoras (fragments/reports [c.441 BCE]) by Aristotle - Metaphysics 1053b |
| 612 | Relativists think if you poke your eye and see double, there must be two things [Aristotle on Protagoras] |
| Full Idea: In fact there is no difference between Protagoreanism and saying this: if you stick your finger under your eyes and make single things seem two, then they are two, just because they seem to be two. | |
| From: comment on Protagoras (fragments/reports [c.441 BCE]) by Aristotle - Metaphysics 1063a06 |
| 5864 | Destroy seriousness with laughter, and laughter with seriousness [Gorgias] |
| Full Idea: Destroy the seriousness of others with laughter, and their laughter with seriousness. | |
| From: Gorgias (fragments/reports [c.443 BCE]), quoted by Aristotle - The Art of Rhetoric 1419b | |
| A reaction: This sounds like brilliant tactical advice, which should be on the wall of every barrister's chambers. This is a case of rhetoric having something to teach us which is nothing at all to do with truth. It is more like learning karate. |
| 9866 | Gorgias says rhetoric is the best of arts, because it enslaves without using force [Gorgias, by Plato] |
| Full Idea: Gorgias insists that the art of persuasion is superior to all others because it enslaves all the rest, with their own consent, not by force, and is therefore by far the best of all the arts. | |
| From: report of Gorgias (fragments/reports [c.443 BCE]) by Plato - Philebus 58a | |
| A reaction: A nice point, and it is not unreasonable to rank the arts in order of their power. To enchant, without achieving agreement, and to speak truth without persuading, are both very fine, but there is something about success that cannot be gainsaid. |
| 6016 | Early sophists thought convention improved nature; later they said nature was diminished by it [Protagoras, by Miller,FD] |
| Full Idea: Protagoras and Hippias evidently believed that convention was an improvement on nature, whereas later sophists such as Antiphon, Thrasymachus and Callicles seemed to contend that conventional morality was undermined because it was 'against nature'. | |
| From: report of Protagoras (fragments/reports [c.441 BCE]) by Fred D. Miller jr - Classical Political Thought | |
| A reaction: This gets to the heart of a much more interesting aspect of the nomos-physis (convention-nature) debate, rather than just a slanging match between relativists and the rest. The debate still goes on, over issues about the free market and intervention. |
| 1580 | For Protagoras the only bad behaviour is that which interferes with social harmony [Protagoras, by Roochnik] |
| Full Idea: For Protagoras the only constraint on human behaviour is that it not interfere with social harmony, the essential condition for human survival. | |
| From: report of Protagoras (fragments/reports [c.441 BCE]) by David Roochnik - The Tragedy of Reason p.63 |
| 205 | Protagoras contradicts himself by saying virtue is teachable, but then that it is not knowledge [Plato on Protagoras] |
| Full Idea: Protagoras claimed that virtue was teachable, but now tries to show it is not knowledge, which makes it less likely to be teachable. | |
| From: comment on Protagoras (fragments/reports [c.441 BCE]) by Plato - Protagoras 361b |
| 1659 | Protagoras seems to have made the huge move of separating punishment from revenge [Protagoras, by Vlastos] |
| Full Idea: The distinction of punishment from revenge must be regarded as one of the most momentous of the conceptual discoveries ever made by humanity in the course of its slow, tortuous, precarious, emergence from barbaric tribalism. Protagoras originated it. | |
| From: report of Protagoras (fragments/reports [c.441 BCE]) by Gregory Vlastos - Socrates: Ironist and Moral Philosopher p.187 |
| 532 | Successful education must go deep into the soul [Protagoras] |
| Full Idea: Education does not take root in the soul unless one goes deep. | |
| From: Protagoras (fragments/reports [c.441 BCE], B11), quoted by Plutarch - On Practice 178.25 |
| 1552 | He spent public money on education, as it benefits the individual and the state [Protagoras, by Diodorus of Sicily] |
| Full Idea: He used legislation to improve the condition of illiterate people, on the grounds that they lack one of life's great goods, and thought literacy should be a matter of public concern and expense. | |
| From: report of Protagoras (fragments/reports [c.441 BCE]) by Diodorus of Sicily - Universal History 12.13.3.3 |
| 1551 | He said he didn't know whether there are gods - but this is the same as atheism [Diogenes of Oen. on Protagoras] |
| Full Idea: He said that he did not know whether there were gods - but this is the same as saying that he knew there were no gods. | |
| From: comment on Protagoras (fragments/reports [c.441 BCE], A23) by Diogenes (Oen) - Wall inscription 11 Chil 2 |