20 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. |
| 8228 | Being is revealed at the point between waking and sleep [Anon (Cent)] |
| Full Idea: At the point of sleep when sleep has not yet come and external wakefulness vanishes, at this point being is revealed. | |
| From: Anon (Cent) (Centring [c.500 BCE], 50) | |
| A reaction: One for Heidegger. The problem with eastern philosophy is that no one expects that this revelation could be put into words, so we cannot compare our revelations of being, or pass them on to others. Which means they can't be criticised. |
| 14381 | A statue is essentially the statue, but its lump is not essentially a statue, so statue isn't lump [Yablo, by Rocca] |
| Full Idea: Yablo proposes the argument that Statue A is essentially a statue, and Lump 1 is not essentially a statue, so Statue A is not identical with Lump 1. | |
| From: report of Stephen Yablo (Identity, Essence and Indiscernibility [1987]) by Michael della Rocca - Essentialists and Essentialism I | |
| A reaction: Della Rocca and Yablo unashamedly elide necessary properties with essential properties, so this argument doesn't bother me too much. It concerns the statue and the clay having different modal properties. |
| 8232 | Neglect your self, and feel the consciousness of each other being [Anon (Cent)] |
| Full Idea: Feel the consciousness of each person as your own consciousness. So, leaving aside concern for self, become each being. | |
| From: Anon (Cent) (Centring [c.500 BCE], 83) | |
| A reaction: Good. The western scepticism about other minds puts up a barrier to this sort of thought. The best of Zen is when it encourages the use of imagination to explore what is real. But imagination struggles to distinguish what is true. |
| 8230 | Just as you have the impulse to do something, stop [Anon (Cent)] |
| Full Idea: Just as you have the impulse to do something, stop. | |
| From: Anon (Cent) (Centring [c.500 BCE], 64) | |
| A reaction: Nice. You might train your own will like a dog in this way. It is a counterexample to the simplistic idea that all you need is a belief and a desire, and you have got an action. But (pace Searle, Ideas 3817 + 3818) this does not prove free will. |
| 8234 | Bondage and liberation are relative terms, which only frighten those already terrified of the universe [Anon (Cent)] |
| Full Idea: Since in truth, bondage and freedom are relative, these words are only for those terrified with the universe. The universe is a reflection of minds. As you see many suns in water from one sun, so see bondage and liberation. | |
| From: Anon (Cent) (Centring [c.500 BCE], 110) | |
| A reaction: Since most easterners have experienced permanent social repression, their philosophies all encourage them not to worry about it. No wonder marxism, proved popular, when it suggested you could actually change things. |
| 8227 | Feel your whole body saturated with cosmic essence [Anon (Cent)] |
| Full Idea: Feel your substance, bones, flesh, blood, saturated with cosmic essence. | |
| From: Anon (Cent) (Centring [c.500 BCE], 23) | |
| A reaction: I find this unsatisfactory. Being a sad victim of materialistic western scientific culture, I don't think 'cosmic essence' exists. I could imagine myself full of the stuff, and that might feel good, but I could also imagine I had won the lottery. |
| 8231 | Abandon attachment to body, and feel the joy of being everywhere [Anon (Cent)] |
| Full Idea: Toss attachment for body aside, realising I am everywhere. One who is everywhere is joyous. | |
| From: Anon (Cent) (Centring [c.500 BCE], 79) | |
| A reaction: I really don't think it is wisdom to spend your time imagining things which are not true. I might imagine that some gorgeous film star is in love with me, but I don't recommend it. Live according to nature. We are physical beings. |
| 8229 | The serenity in blue sky beyond clouds [Anon (Cent)] |
| Full Idea: Simply by looking into blue sky beyond clouds - the serenity. | |
| From: Anon (Cent) (Centring [c.500 BCE], 59) | |
| A reaction: Philip Larkin finds the same experience looking through high windows. If we articulate the experience, it seems to combine humility and detachment. The sky makes us insignificant, but the mind can project into the sky. |
| 8233 | Imagine fire burning up your whole body, but not you [Anon (Cent)] |
| Full Idea: Focus on fire rising through your form from the toes up until the body burns to ashes, but not you. | |
| From: Anon (Cent) (Centring [c.500 BCE], 28) | |
| A reaction: Try very hard to persuade yourself that you are immortal, even if you are not. Hm. Zen Buddhism actually contains very little commitment to what is true or false. It explores interesting beliefs like children playing with toys. Very post-modern. |