12 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) |
| 6455 | Maybe 'sense-data' just help us to talk about unusual perceptual situations [Lacey] |
| Full Idea: One possibility is that talk of sense-data is a mere linguistic convenience, providing a noun for talking about appearances, as when seeing a red object in sodium light (when it looks grey). | |
| From: A.R. Lacey (A Dictionary of Philosophy [1976], p.196) | |
| A reaction: The term seems to have been coined to deal with situations where there is a gap between appearance and presumed reality, as in illusions. Maybe illusions prove the existence of sense-data, rather than it being a 'convenient' term. |
| 6454 | Where do sense-data begin or end? Can they change? What sort of thing are they? [Lacey] |
| Full Idea: It is hard to individuate sense-data, saying where one ends and the next begins, and hard to say whether they can change; are they substances, qualities, events, or what? | |
| From: A.R. Lacey (A Dictionary of Philosophy [1976], p.196) | |
| A reaction: The problem is not that these questions are unanswerable. The answer seems to be either that they are physical and external, or that they are mental and internal, and that there is no ontological space for them between the two. |
| 6453 | Some claim sense-data are public, and are parts of objects [Lacey] |
| Full Idea: Sometimes it is said that sense-data are public, and parts either of objects or of the surfaces of objects. | |
| From: A.R. Lacey (A Dictionary of Philosophy [1976], p.196) | |
| A reaction: This suggests two drastically different theories, one making sense-data into mental events, the other placing them in the 'external' world. The latter theory can dovetail them with the physics, but then why would we need them? |
| 9591 | The human intellect has not been, and cannot be, fully formalized [Nagel/Newman] |
| Full Idea: The resources of the human intellect have not been, and cannot be, fully formalized. | |
| From: E Nagel / JR Newman (Gödel's Proof [1958], VIII) | |
| A reaction: This conclusion derives from Gödel's Theorem. Some people (e.g. Penrose) get over-excited by this discovery, and conclude that the human mind is supernatural. Imagination is the key - it is a feature of rationality that escapes mechanization. |