15 ideas
| 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? |
| 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. |
| 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) |
| 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. |
| 19729 | 'Modal epistemology' demands a connection between the belief and facts in possible worlds [Black,T] |
| Full Idea: In 'modal epistemologies' a belief counts as knowledge only if there is a modal connection - a connection not only to the actual world, but also to other non-actual possible worlds - between the belief and the facts of the matter. | |
| From: Tim Black (Modal and Anti-Luck Epistemology [2011], 1) | |
| A reaction: [Pritchard 2005 seems to be a source for this] This sounds to me a bit like Nozick's tracking or sensitivity theory. Nozick is, I suppose, diachronic (time must pass, for the tracking), where this theory is synchronic. |
| 19728 | Gettier and lottery cases seem to involve luck, meaning bad connection of beliefs to facts [Black,T] |
| Full Idea: The protagonists in Gettier cases and in lottery cases fail to have knowledge because their beliefs are true simply as a matter of luck, where this means that their beliefs themselves are not appropriately connected to the facts. | |
| From: Tim Black (Modal and Anti-Luck Epistemology [2011], 1) | |
| A reaction: The lottery problem is you correctly believe 'my ticket won't win the lottery' even though you don't seem to actually know it won't. Is the Gettier problem simply the problem of lucky knowledge? 'Luck' is a rather vague concept. |
| 21798 | To universalise 'give everything to the poor' leads to absurdity [Hegel] |
| Full Idea: If everyone gave everything to the poor, then soon there would be no more poor to give anything to, or no more persons who would have anything to give. | |
| From: Georg W.F.Hegel (Lectures on the Philosophy of Religion [1827], III: 152), quoted by Stephen Houlgate - An Introduction to Hegel 10 'Faith' | |
| A reaction: Matthew 5:8, 19:21. Beautifully clear. [I always believed that I had thought of this idea - but not so]. If the logic is that it is better to be poor than to be rich, then the implication is that all excess wealth should be thrown into the sea. |
| 21797 | Immortality does not come at a later time, but when pure knowing Spirit fully grasps the universal [Hegel] |
| Full Idea: The immortality of the soul must not be imagined as though it first emerges into actuality at some later time; rather it is a present quality. ...As pure knowing or as thinking, Spirit has the universal for its object - this is eternity. | |
| From: Georg W.F.Hegel (Lectures on the Philosophy of Religion [1827], III: 208), quoted by Stephen Houlgate - An Introduction to Hegel 10 'Death' | |
| A reaction: An unusual view of immortality, which challenges orthodoxy. The idea seems to be that 'pure knowing' is a grasping of the pure reason which embodies nature, which in turn is the nature of God. You enter eternity, rather than reside in it? |