22 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. |
| 23634 | Accepting the existence of anything presupposes the notion of existence [Reid] |
| Full Idea: The belief of the existence of anything seems to suppose a notion of existence - a notion too abstract, perhaps, to enter into the mind of an infant. | |
| From: Thomas Reid (Essays on Intellectual Powers 2: Senses [1785], 05) | |
| A reaction: But even a small infant has to cope with the experience of waking up from a dream. I don't see how existence can be anything other than a primitive concept in any system of ontology. |
| 18431 | Internal relations combine some tropes into a nucleus, which bears the non-essential tropes [Simons, by Edwards] |
| Full Idea: Simons's 'nuclear' option blends features of the substratum and bundle theories. First we have tropes collected by virtue of their internal relations, forming the essential kernel or nucleus. This nucleus then bears the non-essential tropes. | |
| From: report of Peter Simons (Particulars in Particular Clothing [1994], p.567) by Douglas Edwards - Properties 3.5 | |
| A reaction: [compression of Edwards's summary] This strikes me as being a remarkably good theory. I am not sure of the ontological status of properties, such that they can (unaided) combine to make part of an object. What binds the non-essentials? |
| 23635 | Truths are self-evident to sensible persons who understand them clearly without prejudice [Reid] |
| Full Idea: Self-evident propositions are those which appear evident to every man of sound understanding who apprehends the meaning of them distinctly, and attends to them without prejudice. | |
| From: Thomas Reid (Essays on Intellectual Powers 2: Senses [1785], 10) | |
| A reaction: I suspect that there are some truths which are self-evident to dogs. There are also truths which are self-evident to experts, but not to ordinary persons of good understanding. Self-evidence is somewhat contextual. Self-evidence can be empirical. |
| 7631 | Sensation is not committed to any external object, but perception is [Reid] |
| Full Idea: Sensation, by itself, implies neither the conception nor belief of any external object. ...Perception implies a conviction and belief of something external. ...Things so different in their nature ought to be distinguished. | |
| From: Thomas Reid (Essays on Intellectual Powers 2: Senses [1785], II.16), quoted by Barry Maund - Perception | |
| A reaction: Maund sees this as the origin of the two-stage view of perception, followed by Chisholm, Evans, Dretske and Lowe. It implies that 'looks', 'tastes', 'sounds' etc. are ambiguous words, having either phenomenal or realist meanings. I like it. |
| 23637 | Primary qualities are the object of mathematics [Reid] |
| Full Idea: The primary qualities are the object of the mathematical sciences. | |
| From: Thomas Reid (Essays on Intellectual Powers 2: Senses [1785], 17) | |
| A reaction: He spells out this crucial point, which is not so obvious in Locke. The sciences totally rely on the primary qualities, so it is ridiculous to reject the distinction (which Reid accepts). |
| 23638 | Secondary qualities conjure up, and are confused with, the sensations which produce them [Reid] |
| Full Idea: The thought of a secondary quality always carries us back to the sensation which it produces.We give the same name to both, and are apt to confound them. | |
| From: Thomas Reid (Essays on Intellectual Powers 2: Senses [1785], 17) | |
| A reaction: 'Redness', for example. Reid puts the point very nicely. Secondary qualities are not entirely mental; they pick out features of the world, but are much harder to understand than the primary qualities. The qualia question lurks. |
| 23639 | It is unclear whether a toothache is in the mind or in the tooth, but the word has a single meaning [Reid] |
| Full Idea: If it be made a question whether the toothache be in the mind that feels it, or in tooth that is affected, much might be said on both sides, while it is not observed that the word has two meanings. | |
| From: Thomas Reid (Essays on Intellectual Powers 2: Senses [1785], 18) | |
| A reaction: I'm glad Reid was struck by the weird phenomenon of the brain apparently 'projecting' a pain into a tooth. Presumably before the brain's role was known, people were unaware of this puzzle. There certainly are not two distinct experiences. |
| 6492 | Reid is seen as the main direct realist of the eighteenth century [Reid, by Robinson,H] |
| Full Idea: Reid is often represented by modern opponents of the empiricists as the outstanding protagonist of direct or naïve realism and common sense in the eighteenth century. | |
| From: report of Thomas Reid (Essays on Intellectual Powers 2: Senses [1785]) by Howard Robinson - Perception 1.6 | |
| A reaction: Robinson does not deny that this is Reid's view. Keith Lehrer is a great fan of Reid. Personally I think direct realism is quite clearly false, so I find myself losing interest in Reid's so-called 'common sense'. |
| 23641 | People dislike believing without evidence, and try to avoid it [Reid] |
| Full Idea: To believe without evidence is a weakness which every man is concerned to avoid, and which every man wishes to avoid. | |
| From: Thomas Reid (Essays on Intellectual Powers 2: Senses [1785], 20) | |
| A reaction: It seems to be very common, though, for people to believe things on incredibly flimsy evidence, if they find the belief appealing. This is close to Clifford's Principle, but not quite as dogmatic. |
| 23642 | If non-rational evidence reaches us, it is reason which then makes use of it [Reid] |
| Full Idea: If Nature gives us information of things that concern us, by other means that by reasoning, reason itself will direct us to receive that information with thankfulness, and to make the best use of it. | |
| From: Thomas Reid (Essays on Intellectual Powers 2: Senses [1785], 20) | |
| A reaction: This is more of a claim than an argument, but it is hard to see how anything could even be seen as evidence if some sort of rational judgement has not been made. The clever detective sees which facts are evidence. |
| 23640 | Only mature minds can distinguish the qualities of a body [Reid] |
| Full Idea: I think it requires some ripeness of understanding to distinguish the qualities of a body from the body; perhaps this distinction is not made by brutes, or by infants. | |
| From: Thomas Reid (Essays on Intellectual Powers 2: Senses [1785], 19) | |
| A reaction: I'm glad the brutes get a mention in his assessment of these questions. I take such thinking to arise from what can be labelled the faculty of abstraction, which presumably only appears in a mature brain. It is second-level thinking. |