28 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? |
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. |
16039 | Supervenience: No A-difference without a B-difference [Bennett,K] |
Full Idea: The slogan for supervenience might be 'there cannot be an A-difference without a B-difference'. …(qualifying as a 'perfect forgery' would be an example). | |
From: Karen Bennett (Supervenience [2011], Intro) | |
A reaction: The key point about supervenience is that it is one-way. Presumably 'tracking' would be a better single word for it than 'dependence', which implies some sort of causal power. Supervenience describes, but doesn't attempt to explain. |
16043 | Supervenience is non-symmetric - sometimes it's symmetric, and sometimes it's one-way [Bennett,K] |
Full Idea: Supervenience is neither symmetric nor asymmetric; it is non-symmetric. Sometimes it holds symmetrically. …And sometimes it holds asymmetrically. | |
From: Karen Bennett (Supervenience [2011], §3.2) | |
A reaction: I think of supervenience as 'tracking'. Stalkers track victims; married couples track one another. Beauty tracks statues, but statues don't seem to track beauty. I take so-called mind-brain supervenience to be two-way, not one-way. |
16047 | Weak supervenience is in one world, strong supervenience in all possible worlds [Bennett,K] |
Full Idea: Weak supervenience says there is no possible world that contains individuals that are B-indiscernible but A-discernible. Strong supervenience entails the same even if they are in different possible worlds. | |
From: Karen Bennett (Supervenience [2011], §4.1) | |
A reaction: In other words (I presume), in simple language, the weak version says they happen supervene, the strong version says they have to supervene. |
16040 | Aesthetics, morality and mind supervene on the physical? Modal on non-modal? General on particular? [Bennett,K] |
Full Idea: It has been claimed that aesthetic, moral and mental properties supervene upon physical properties, …and that modal truths supervene on non-modal ones, and that general truths supervene on particular ones. | |
From: Karen Bennett (Supervenience [2011], Intro) | |
A reaction: I am attracted to the last bit. I am bewildered by people who try to derive particular truths from general ones, such as deriving physical behaviour from laws, or the nature of some creature simply from its species. Only some tigers are man-eaters. |
16044 | Some entailments do not involve supervenience, as when brotherhood entails siblinghood [Bennett,K] |
Full Idea: Some entailments do not suffice for supervenience. Being a brother entails being a sibling, but being a sibling does not supervene on being a brother. Sarah has a sister and Jack in an only child. Sarah, unlike Jack, is a sibling; neither is a brother. | |
From: Karen Bennett (Supervenience [2011], §3.2) | |
A reaction: The whole point of supervenience, I take it, is to label a relation of tracking, while offering no explanation of the tracking. Entailment would be a rather powerful explanation, as would a dog's being tied to a cart. |
16046 | Reduction requires supervenience, but does supervenience suffice for reduction? [Bennett,K] |
Full Idea: Everyone agrees that reduction requires supervenience, …but the more interesting issue is whether supervenience suffices for reduction. | |
From: Karen Bennett (Supervenience [2011], §3.3) | |
A reaction: I think we should assume that there is a reason for every genuine case of supervenience (i.e. there are no cases of eternal or ubiquitious coincidence). One-way causation seems to give supervenience without reduction. |
16049 | Definitions of physicalism are compatible with a necessary God [Bennett,K] |
Full Idea: All definitions of physicalism are compatible with the existence of a necessarily existing God. | |
From: Karen Bennett (Supervenience [2011], 5.4) | |
A reaction: All the definitions seem to depend on all the facts covarying with the physical facts, so anything which is invariant (such as divine or platonic entities) will stand outside the definition. Physicalism is more like a credo about all facts whatever. |
16042 | The metaphysically and logically possible worlds are the same, so they are the same strength [Bennett,K] |
Full Idea: Metaphysical necessity is just as strong as logical necessity in that the space of metaphysical possibility is exactly the same as the space of logical possibility: the logically possible worlds = the metaphysically possible worlds. | |
From: Karen Bennett (Supervenience [2011], §3.1) | |
A reaction: I think this is wrong. To be the 'same strength' there would also have to be the same number of logical as metaphysical truths, and I presume that is not the case. There are far more logical than metaphysical possibilities. |
8337 | Some says mental causation is distinct because we can recognise single occurrences [Mackie] |
Full Idea: It is sometimes suggested that our ability to recognise a single occurrence as an instance of mental causation is a feature which distinguishes mental causation from physical or 'Humean' causation. | |
From: J.L. Mackie (Causes and Conditions [1965], §9) | |
A reaction: Hume says regularities are needed for mental causation too. Concentrate hard on causing a lightning flash - 'did I do that?' Gradually recovering from paralysis; you wouldn't just move your leg once, and know it was all right! |
8342 | Mackie tries to analyse singular causal statements, but his entities are too vague for events [Kim on Mackie] |
Full Idea: In spite of Mackie's announced aim of analysing singular causal statements, it is doubtful that the entities that he is concerned with can be consistently interpreted as spatio-temporally bounded individual events. | |
From: comment on J.L. Mackie (Causes and Conditions [1965]) by Jaegwon Kim - Causes and Events: Mackie on causation §3 | |
A reaction: This is because Mackie mainly talks about 'conditions'. Nearly every theory I encounter in modern philosophy gets accused of either circular definitions, or inadequate individuation conditions for key components. A tough world for theory-makers. |
8343 | Necessity and sufficiency are best suited to properties and generic events, not individual events [Kim on Mackie] |
Full Idea: Relations of necessity and sufficiency seem best suited for properties and for property-like entities such as generic states and events; their application to individual events and states is best explained as derivative from properties and generic events. | |
From: comment on J.L. Mackie (Causes and Conditions [1965]) by Jaegwon Kim - Causes and Events: Mackie on causation §4 | |
A reaction: This seems to suggest that necessity must either derive from laws, or from powers. It is certainly hard to see how you could do Mackie's assessment of necessary and sufficient components, without comparing similar events. |
8385 | A cause is part of a wider set of conditions which suffices for its effect [Mackie, by Crane] |
Full Idea: The details of Mackie's analysis are complex, but the general idea is that the cause is part of a wider set of conditions which suffices for its effect. | |
From: report of J.L. Mackie (Causes and Conditions [1965]) by Tim Crane - Causation 1.3.3 | |
A reaction: Helpful. Why does something have to be 'the' cause? Immediacy is a vital part of it. A house could be a 'fire waiting to happen'. Oxygen is an INUS condition for a fire. |
8335 | Necessary conditions are like counterfactuals, and sufficient conditions are like factual conditionals [Mackie] |
Full Idea: A necessary causal condition is closely related to a counterfactual conditional: if no-cause then no-effect, and a sufficient causal condition is closely related to a factual conditional (Goodman's phrase): since cause-here then effect. | |
From: J.L. Mackie (Causes and Conditions [1965], §4) | |
A reaction: The 'factual conditional' just seems to be an assertion that causation occurred (dressed up with the logical-sounding 'since'). An important distinction for Lewis. Sufficiency doesn't seem to need possible-worlds talk. |
8336 | The INUS account interprets single events, and sequences, causally, without laws being known [Mackie] |
Full Idea: My account shows how a singular causal statement can be interpreted, and how the corresponding sequence can be shown to be causal, even if the corresponding complete laws are not known. | |
From: J.L. Mackie (Causes and Conditions [1965], §9) | |
A reaction: Since the 'complete' laws are virtually never known, it would be a bit much to require that to assert causation. His theory is the 'INUS' account of causal conditions - see Idea 8333. |
8333 | A cause is an Insufficient but Necessary part of an Unnecessary but Sufficient condition [Mackie] |
Full Idea: If a short-circuit causes a fire, the so-called cause is, and is known to be, an Insufficient but Necessary part of a condition which is itself Unnecessary but Sufficient for the result. Let us call this an INUS condition. | |
From: J.L. Mackie (Causes and Conditions [1965], §1) | |
A reaction: I'm not clear why it is necessary, given that the fire could have started without the short-circuit. The final situation must certainly be sufficient. If only one situation can cause an effect, then the whole situation is necessary. |
8395 | Mackie has a nomological account of general causes, and a subjunctive conditional account of single ones [Mackie, by Tooley] |
Full Idea: For general causal statements Mackie favours a nomological account, but for singular causal statements he argued for an analysis in terms of subjunctive conditionals. | |
From: report of J.L. Mackie (Causes and Conditions [1965]) by Michael Tooley - Causation and Supervenience 5.2 | |
A reaction: These seem to be consistent, by explaining each by placing it within a broader account of reality. Personally I think Ducasse gives the best account of how you get from the particular to the general (via similarity and utility). |
8334 | The virus causes yellow fever, and is 'the' cause; sweets cause tooth decay, but they are not 'the' cause [Mackie] |
Full Idea: We may say not merely that this virus causes yellow fever, but also that it is 'the' cause of yellow fever; but we could only say that sweet-eating causes dental decay, not that it is the cause of dental decay (except in an individual case). | |
From: J.L. Mackie (Causes and Conditions [1965], §3) | |
A reaction: A bit confusing, but there seems to be something important here, concerning the relation between singular causation and law-governed causation. 'The' cause may not be sufficient (I'm immune to yellow fever). So 'the' cause is the only necessary one? |