19 ideas
| 8349 | The best way to do ontology is to make sense of our normal talk [Davidson] |
| Full Idea: I do not know any better way of showing what there is than looking at the assumptions needed to make sense of our normal talk. | |
| From: Donald Davidson (Causal Relations [1967], §4) | |
| A reaction: Davidson was a pupil of Quine. This I take to be the last flowering of twentieth century linguistic philosophy. The ontology we deduce from talk in a children's playground might be very bizarre, but we are unlikely to endorse it. 'Honest, it's true!' |
| 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. |
| 8348 | If we don't assume that events exist, we cannot make sense of our common talk [Davidson] |
| Full Idea: The assumption, ontological and metaphysical, that there are events, is one without which we cannot make sense of much of our most common talk. | |
| From: Donald Davidson (Causal Relations [1967], §4) | |
| A reaction: He considers events to be unanalysable basics. Explanation of normal talk also needs ghosts, premonitions, telepathy and Father Christmas. It is extremely hard to individuate events, unless they are subatomic, and rather numerous. |
| 8347 | Explanations typically relate statements, not events [Davidson] |
| Full Idea: Explanations typically relate statements, not events. | |
| From: Donald Davidson (Causal Relations [1967], §4) | |
| A reaction: An oddly linguistic way of putting our attempts to understand the world. Presumably the statements are supposed to be about the events (or whatever), and they are supposed to be true, so we are trying to relate features of the world. |
| 18555 | The beautiful is that from which nothing can be subtracted and to which nothing can be added [Alberti] |
| Full Idea: The beautiful is that from which nothing can be taken away and to which nothing can be added but for the worse. | |
| From: Leon Battista Alberti (De Re Aedificatoria [1485]), quoted by Roger Scruton - Beauty: a very short introduction 9 | |
| A reaction: Scruton rejects this Platonic tradition of beauty as organic wholeness, because you can't say how it would be 'worse' without invoking beauty, which makes it circular. Scruton appears to be correct. |
| 10371 | Distinguish causation, which is in the world, from explanations, which depend on descriptions [Davidson, by Schaffer,J] |
| Full Idea: Davidson distinguishes between causation, an extensional relation that holds between coarse events, and explanation, which is an intensional relation that holds between the coarse events under a description. | |
| From: report of Donald Davidson (Causal Relations [1967]) by Jonathan Schaffer - The Metaphysics of Causation 1.2 | |
| A reaction: I'm unclear why everything has to be so coarse, when reality and causal events seem to fine-grained, but the distinction strikes me as good. Explanations relate to human understanding and human interests. Cf. Anscombe's view. |
| 8403 | Either facts, or highly unspecific events, serve better as causes than concrete events [Field,H on Davidson] |
| Full Idea: It is best to avoid Davidson's view that only quite concrete events can serve as causes; we should either say that facts as well as events can serve as causes; or that the events can be highly unspecific, including 'omissions'. | |
| From: comment on Donald Davidson (Causal Relations [1967]) by Hartry Field - Causation in a Physical World 1 | |
| A reaction: Something NOT happening might be the main cause of an effect (drought), or an effect may mainly result from a situation rather than an event (famine). |
| 8346 | Full descriptions can demonstrate sufficiency of cause, but not necessity [Davidson] |
| Full Idea: The fuller we make the description of a cause, the better our chances of demonstrating that it was sufficient (as described) to produce the effect, and the worse our chances of demonstrating that it was necessary. (For the effect, it is the opposite). | |
| From: Donald Davidson (Causal Relations [1967], §3) | |
| A reaction: If the fullness of description is relevant, this suggests that Davidson is focusing on human explanations, rather than on the ontology of causation. If the cause IS necessary, why wouldn't a better description make that clearer? |
| 4778 | A singular causal statement is true if it is held to fall under a law [Davidson, by Psillos] |
| Full Idea: For Davidson, what makes singular causal statements true is the existence of some regularities or laws. All causal is nomological: c causes e iff there is a law that connects events like c with events like e. | |
| From: report of Donald Davidson (Causal Relations [1967]) by Stathis Psillos - Causation and Explanation §2.6 | |
| A reaction: I wonder if the cart is before the horse here. Scriven says this is just a claim that there are "phantom laws". It is the Humean view of causation, but surely the laws come after the causation, so can't be used to explain it? |