| 13819 | Aristotle's said some Fs are G or some Fs are not G, forgetting that there might be no Fs [Bostock on Aristotle] |
| Full Idea: Aristotle's system accepted as correct some laws which nowadays we reject, for example |= (Some Fs are G) or (some Fs are not G). He failed to take into account the possibility of there being no Fs at all. | |
| From: comment on Aristotle (Prior Analytics [c.328 BCE]) by David Bostock - Intermediate Logic 8.4 |
| 20778 | Stoics like syllogisms, for showing what is demonstrative, which corrects opinions [Stoic school, by Diog. Laertius] |
| Full Idea: Stoics say the study of syllogisms is extremely useful; for it indicates what is demonstrative, and this makes a big contribution toward correcting one's opinions; and orderliness and good memory indicate attentive comprehension. | |
| From: report of Stoic school (fragments/reports [c.200 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 07.45 | |
| A reaction: The stoics also developed propositional logic. The main point is that they liked formal logic, which is not true of all the ancient schools. |
| 8084 | Syllogisms are verbal fencing, not discovery [Locke] |
| Full Idea: Syllogisms are useless for discovery, and serve only for verbal fencing. | |
| From: John Locke (Essay Conc Human Understanding (2nd Ed) [1694]), quoted by Keith Devlin - Goodbye Descartes Ch.3 | |
| A reaction: This illustrates the low status of logic, and the new high status of experimental science, in Locke's time. Locke's seems to miss the point that you can infer new discoveries from old ones. |
| 12572 | Many people can reason well, yet can't make a syllogism [Locke] |
| Full Idea: There are many men that reason exceeding clear and rightly, who know not how to make a syllogism | |
| From: John Locke (Essay Conc Human Understanding (2nd Ed) [1694], 4.17.04) | |
| A reaction: On the one hand this is just Locke's scepticism about the whole business of Aristotelian logic, but on the other hand it may be a perspicuous observation that logical thought extends far beyond what was catalogued by Aristotle. |
| 18806 | Frege thought traditional categories had psychological and linguistic impurities [Frege, by Rumfitt] |
| Full Idea: Frege rejected the traditional categories as importing psychological and linguistic impurities into logic. | |
| From: report of Gottlob Frege (Function and Concept [1891]) by Ian Rumfitt - The Boundary Stones of Thought 1.2 | |
| A reaction: Resisting such impurities is the main motivation for making logic entirely symbolic, but it doesn't follow that the traditional categories have to be dropped. |
| 14453 | The Darapti syllogism is fallacious: All M is S, all M is P, so some S is P' - but if there is no M? [Russell] |
| Full Idea: Some moods of the syllogism are fallacious, e.g. 'Darapti': 'All M is S, all M is P, therefore some S is P', which fails if there is no M. | |
| From: Bertrand Russell (Introduction to Mathematical Philosophy [1919], XV) | |
| A reaction: This critique rests on the fact that the existential quantifier entails some existence, but the universal quantifier does not. |
| 5401 | The mortality of Socrates is more certain from induction than it is from deduction [Russell] |
| Full Idea: We would do better to go straight from the evidence that some men have died to the mortality of Socrates, than to go via 'all men are mortal', for the probability that Socrates is mortal is greater than the probability that all men are mortal. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 7) | |
| A reaction: Russell claims that deduction should stick to a priori truth, and induction is best for the real world. Interesting. To show that something is a member of a set (e.g. planets) you need an awful lot of knowledge of the set. |
| 18949 | The universal syllogism is now expressed as the transitivity of subclasses [Putnam] |
| Full Idea: On its modern interpretation, the validity of the inference 'All S are M; All M are P; so All S are P' just expresses the transitivity of the relation 'subclass of'. | |
| From: Hilary Putnam (Philosophy of Logic [1971], Ch.1) | |
| A reaction: A simple point I've never quite grasped. Since lots of syllogisms can be expressed as Venn Diagrams, in which the circles are just sets, it's kind of obvious really. So why does Sommers go back to 'terms'? See 'Term Logic'. |
| 15879 | The Square of Opposition has two contradictory pairs, one contrary pair, and one sub-contrary pair [Harré] |
| Full Idea: Square of Opposition: 'all A are B' and 'no A are B' are contraries; 'some A are B' and 'some A are not B' are sub-contraries; the pairs 'all A are B'/'some A are B' and 'no A are B'/'some A are B' are contradictories. | |
| From: Rom Harré (Laws of Nature [1993], 3) | |
| A reaction: [the reader may construct his own diagram from this description!] The contraries are at the extremes of contradiction, but the sub-contraries are actual compatible. You could add possible worlds to this picture. |
| 13439 | Venn Diagrams map three predicates into eight compartments, then look for the conclusion [Bostock] |
| Full Idea: Venn Diagrams are a traditional method to test validity of syllogisms. There are three interlocking circles, one for each predicate, thus dividing the universe into eight possible basic elementary quantifications. Is the conclusion in a compartment? | |
| From: David Bostock (Intermediate Logic [1997], 3.8) |
| 19006 | An 'enthymeme' is an argument with an indispensable unstated assumption [Yablo] |
| Full Idea: An 'enthymeme' is a deductive argument with an unstated assumption that must be true for the premises to lead to the conclusion. | |
| From: Stephen Yablo (Aboutness [2014], 11.1) |
| 8081 | 'No councillors are bankers' and 'All bankers are athletes' implies 'Some athletes are not councillors' [Devlin] |
| Full Idea: Most people find it hard to find any conclusion that fits the following premises: 'No councillors are bankers', and 'All bankers are athletes'. There is a valid conclusion ('Some athletes are not councillors') but it takes quite an effort to find it. | |
| From: Keith Devlin (Goodbye Descartes [1997], Ch. 2) | |
| A reaction: A nice illustration of the fact that syllogistic logic is by no means automatic and straightforward. There is a mechanical procedure, but a lot of intuition and common sense is also needed. |
| 10688 | 'Equivocation' is when terms do not mean the same thing in premises and conclusion [Beall/Restall] |
| Full Idea: 'Equivocation' is when the terms do not mean the same thing in the premises and in the conclusion. | |
| From: JC Beall / G Restall (Logical Consequence [2005], Intro) |
| 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) |