17 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. |
| 3286 | An organism is conscious if and only if there is something it is like to be that organism [Nagel] |
| Full Idea: An organism only has conscious mental states if and only if there is something that it is like to be that organism. | |
| From: Thomas Nagel (What is it like to be a bat? [1974], p.166) | |
| A reaction: It is hard to argue with this, but one should push on and ask what features of its consciousness make it such that there is a 'what it is like'. What is it like to have a subconscious mind, or be deeply asleep, or drive while daydreaming? |
| 3288 | Can we describe our experiences to zombies? [Nagel] |
| Full Idea: The goal of an objective phenomenology would be to describe, at least in part, the subjective character of experiences in a form comprehensible to beings incapable of having those experiences. | |
| From: Thomas Nagel (What is it like to be a bat? [1974], p.179) | |
| A reaction: This seems a bizarre expectation. We can already explain visual experience to the blind up to a point, but no one is dreaming of an "objective phenomenology" which will give blind people total understanding, just by reading about it in braille. |
| 4883 | Nagel's title creates an impenetrable mystery, by ignoring a bat's ways that may not be "like" anything [Dennett on Nagel] |
| Full Idea: Nagel's title invites us to ignore all the different ways in which bats might accomplish their cunning feats without its "being like" anything for them. We create an impenetrable mystery for ourselves if we assume that Nagel's title makes sense. | |
| From: comment on Thomas Nagel (What is it like to be a bat? [1974]) by Daniel C. Dennett - Kinds of Minds Ch.6 | |
| A reaction: This could well be correct about bats, but the question applies to humans as well, and we can't deny that "what it is like" is a feature of some creatures' realities. On the fringes of our own consciousness there are mental events that are "like" nothing. |
| 3287 | We can't be objective about experience [Nagel] |
| Full Idea: If the subjective character of experience is fully comprehensible only from one point of view, then any shift to greater objectivity does not take us nearer to the real nature of the phenomenon: it takes us further away from it. | |
| From: Thomas Nagel (What is it like to be a bat? [1974], p.174) | |
| A reaction: We can, however, talk to one another about our subjectivity, and compare notes, and such 'inter-subjectivity' may be one approach to objectivity. We must concede Nagel's point, but we also miss something about a stone if we must remain outside of it. |
| 4989 | Physicalism should explain how subjective experience is possible, but not 'what it is like' [Kirk,R on Nagel] |
| Full Idea: A physicalist account of conscious experience must explain how it is possible for a physical system to be a conscious subject, but not 'what it is like' for some organism. | |
| From: comment on Thomas Nagel (What is it like to be a bat? [1974]) by Robert Kirk - Mind and Body §4.2 | |
| A reaction: You can't entirely evade Nagel's challenge. We are trying to discover the 'neural correlate of consciousness', which will explain why we are conscious, but we also want to know why we experience green for one wavelength, and red for another. |
| 468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
| Full Idea: In singing and playing the lyre, a boy will be likely to reveal not only courage and moderation, but also justice. | |
| From: Damon (fragments/reports [c.460 BCE], B4), quoted by (who?) - where? |