15 ideas
| 18241 | Sufficient reason is implied by contradiction, of an insufficient possible which exists [Wolff, by Korsgaard] |
| Full Idea: Wolff believed that the principle of sufficient reason could be derived from the principle of contradiction, for there would be a contradiction in the insufficiently determined existence of a merely possible thing. | |
| From: report of Christian Wolff (works [1730]) by Christine M. Korsgaard - Intro to Ethics, Politics, Religion in Kant 'A child' | |
| A reaction: Sounds as if he might be begging to question. You would only protest against the insufficient determination of something if you already believed in the principle of sufficient reason. Nice try. |
| 13838 | A decent modern definition should always imply a semantics [Hacking] |
| Full Idea: Today we expect that anything worth calling a definition should imply a semantics. | |
| From: Ian Hacking (What is Logic? [1979], §10) | |
| A reaction: He compares this with Gentzen 1935, who was attempting purely syntactic definitions of the logical connectives. |
| 13833 | 'Thinning' ('dilution') is the key difference between deduction (which allows it) and induction [Hacking] |
| Full Idea: 'Dilution' (or 'Thinning') provides an essential contrast between deductive and inductive reasoning; for the introduction of new premises may spoil an inductive inference. | |
| From: Ian Hacking (What is Logic? [1979], §06.2) | |
| A reaction: That is, inductive logic (if there is such a thing) is clearly non-monotonic, whereas classical inductive logic is monotonic. |
| 13834 | Gentzen's Cut Rule (or transitivity of deduction) is 'If A |- B and B |- C, then A |- C' [Hacking] |
| Full Idea: If A |- B and B |- C, then A |- C. This generalises to: If Γ|-A,Θ and Γ,A |- Θ, then Γ |- Θ. Gentzen called this 'cut'. It is the transitivity of a deduction. | |
| From: Ian Hacking (What is Logic? [1979], §06.3) | |
| A reaction: I read the generalisation as 'If A can be either a premise or a conclusion, you can bypass it'. The first version is just transitivity (which by-passes the middle step). |
| 13835 | Only Cut reduces complexity, so logic is constructive without it, and it can be dispensed with [Hacking] |
| Full Idea: Only the cut rule can have a conclusion that is less complex than its premises. Hence when cut is not used, a derivation is quite literally constructive, building up from components. Any theorem obtained by cut can be obtained without it. | |
| From: Ian Hacking (What is Logic? [1979], §08) |
| 13845 | The various logics are abstractions made from terms like 'if...then' in English [Hacking] |
| Full Idea: I don't believe English is by nature classical or intuitionistic etc. These are abstractions made by logicians. Logicians attend to numerous different objects that might be served by 'If...then', like material conditional, strict or relevant implication. | |
| From: Ian Hacking (What is Logic? [1979], §15) | |
| A reaction: The idea that they are 'abstractions' is close to my heart. Abstractions from what? Surely 'if...then' has a standard character when employed in normal conversation? |
| 13840 | First-order logic is the strongest complete compact theory with Löwenheim-Skolem [Hacking] |
| Full Idea: First-order logic is the strongest complete compact theory with a Löwenheim-Skolem theorem. | |
| From: Ian Hacking (What is Logic? [1979], §13) |
| 13844 | A limitation of first-order logic is that it cannot handle branching quantifiers [Hacking] |
| Full Idea: Henkin proved that there is no first-order treatment of branching quantifiers, which do not seem to involve any idea that is fundamentally different from ordinary quantification. | |
| From: Ian Hacking (What is Logic? [1979], §13) | |
| A reaction: See Hacking for an example of branching quantifiers. Hacking is impressed by this as a real limitation of the first-order logic which he generally favours. |
| 13842 | Second-order completeness seems to need intensional entities and possible worlds [Hacking] |
| Full Idea: Second-order logic has no chance of a completeness theorem unless one ventures into intensional entities and possible worlds. | |
| From: Ian Hacking (What is Logic? [1979], §13) |
| 13837 | With a pure notion of truth and consequence, the meanings of connectives are fixed syntactically [Hacking] |
| Full Idea: My doctrine is that the peculiarity of the logical constants resides precisely in that given a certain pure notion of truth and consequence, all the desirable semantic properties of the constants are determined by their syntactic properties. | |
| From: Ian Hacking (What is Logic? [1979], §09) | |
| A reaction: He opposes this to Peacocke 1976, who claims that the logical connectives are essentially semantic in character, concerned with the preservation of truth. |
| 13839 | Perhaps variables could be dispensed with, by arrows joining places in the scope of quantifiers [Hacking] |
| Full Idea: For some purposes the variables of first-order logic can be regarded as prepositions and place-holders that could in principle be dispensed with, say by a system of arrows indicating what places fall in the scope of which quantifier. | |
| From: Ian Hacking (What is Logic? [1979], §11) | |
| A reaction: I tend to think of variables as either pronouns, or as definite descriptions, or as temporary names, but not as prepositions. Must address this new idea... |
| 13843 | If it is a logic, the Löwenheim-Skolem theorem holds for it [Hacking] |
| Full Idea: A Löwenheim-Skolem theorem holds for anything which, on my delineation, is a logic. | |
| From: Ian Hacking (What is Logic? [1979], §13) | |
| A reaction: I take this to be an unusually conservative view. Shapiro is the chap who can give you an alternative view of these things, or Boolos. |
| 22040 | Freedom is produced by the activity of the mind, and is not intrinsically given [Hegel] |
| Full Idea: Actual freedom is not something immediately existent in mindedness, but is something to be produced by the mind's own activity. It is thus as the producer of its freedom that we have to consider mindedness in philosophy. | |
| From: Georg W.F.Hegel (Philosophy of Mind (Encylopedia III) [1817], §382, Zusatz), quoted by Terry Pinkard - German Philosophy 1760-1860 11 | |
| A reaction: Pinkard glosses this as an agent being free by being the centre of a group of social responsibilities. Hence I presume small children have no freedom. Presumably we could deprive citizens of all responsibility, and hence of metaphysical freedom. |
| 22039 | Geist is distinct from nature, not as a substance, but because of its normativity [Hegel, by Pinkard] |
| Full Idea: Hegel argued that it was the impossibility of a naturalistic account of normativity that distinguished Geist from nature, not Geist's being any kind of metaphysical substance. | |
| From: report of Georg W.F.Hegel (Philosophy of Mind (Encylopedia III) [1817]) by Terry Pinkard - German Philosophy 1760-1860 11 | |
| A reaction: Hegel always seems to want to have his cake and eat it. Without a mental substance, how can Geist not be part of nature? What is Geist made of? Is his view functionalist? But that is usually naturalistic. Is normativity magic? |
| 18242 | Confucius shows that ethics can rest on reason, rather than on revelation [Wolff, by Korsgaard] |
| Full Idea: Wolff claimed that the moral philosophy of Confucius shows that ethics is accessible to natural reason and independent of revelation. | |
| From: report of Christian Wolff (works [1730]) by Christine M. Korsgaard - Intro to Ethics, Politics, Religion in Kant 'A child' | |
| A reaction: Wolff was banished for proposing this idea. |