23 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. |
| 21793 | Genuine truth is the resolution of the highest contradiction [Hegel] |
| Full Idea: The highest truth, truth as such, is the resolution of the highest opposition and contradiction. | |
| From: Georg W.F.Hegel (Lectures on Aesthetics [1826], I: 99), quoted by Stephen Houlgate - An Introduction to Hegel 09 'Art' | |
| A reaction: Uneasy about the word 'highest', and the general Hegelian dream of 'resolving' contradictions, rather than just eliminating at least one component of them. No one else uses the word 'truth' like this. I suppose this Truth has a capital 'T'. |
| 21795 | What I hold true must also be part of my feelings and character [Hegel] |
| Full Idea: Whatever I hold as true, whatever ought to be valid for me, must also be in my feeling, must belong to my being and character. | |
| From: Georg W.F.Hegel (Lectures on Aesthetics [1826], I: 97), quoted by Stephen Houlgate - An Introduction to Hegel 09 'Philosophy' | |
| A reaction: I can see that truths do tend to become part of our character, but not that they ought to do so. I suppose I try to live my life enmeshed in the many truths which I have personally selected from the maelstrom of possibilities that engulf us. |
| 12129 | 'Truth' may only apply within a theory [Kuhn] |
| Full Idea: 'Truth' may, like 'proof', be a term with only intra-theoretic applications. | |
| From: Thomas S. Kuhn (Reflections on my Critics [1970], §5) | |
| A reaction: I think we can blame Tarski (via Quine, Kuhn's teacher) for this one. I take it to be an utter failure to grasp the meaning of the word 'truth' (and sneakily substituting 'satisfaction' for it). For a start, we have to compare theories on some basis. |
| 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. |
| 6809 | Kuhn came to accept that all scientists agree on a particular set of values [Kuhn, by Bird] |
| Full Idea: Kuhn later came to accept that there are five values to which scientists in all paradigms adhere: accuracy; consistency with accepted theories; broad scope; simplicity; and fruitfulness. | |
| From: report of Thomas S. Kuhn (Reflections on my Critics [1970]) by Alexander Bird - Philosophy of Science Ch.8 | |
| A reaction: To shake off the relativism for which Kuhn is notorious, we should begin by asking the question WHY scientists favoured these particular values, rather than (say) bizarreness, consistency with Lewis Carroll, or alliteration. (They are epistemic virtues). |
| 12128 | In theory change, words shift their natural reference, so the theories are incommensurable [Kuhn] |
| Full Idea: In transitions between theories words change their meanings or applicability. Though most of the signs are used before and after a revolution - force, mass, cell - the ways they attach to nature has changed. Successive theories are thus incommensurable. | |
| From: Thomas S. Kuhn (Reflections on my Critics [1970], §6) | |
| A reaction: A very nice statement of the view, from the horse's mouth. A great deal of recent philosophy has been implicitly concerned with meeting Kuhn's challenge, by providing an account of reference that doesn't have such problems. |
| 18549 | Nineteenth century aesthetics focused on art rather than nature (thanks to Hegel) [Hegel, by Scruton] |
| Full Idea: Only In the course of the nineteenth century, and in the wake of Hegel's posthumously published lectures on aesthetics, did the topic of art come to replace that of natural beauty as the core subject-matter of aesthetics. | |
| From: report of Georg W.F.Hegel (Lectures on Aesthetics [1826], 5) by Roger Scruton - Beauty: a very short introduction |
| 22043 | Hegel largely ignores aesthetic pleasure, taste and beauty, and focuses on the meaning of artworks [Hegel, by Pinkard] |
| Full Idea: Unlike his predecessors (including Kant), Hegel does not focus on aesthetic pleasure, nor on good taste, nor even on the nature and criteria for beauty. Instead he focuses on the meaning of artworks and their role in forming mankind's self-consciousness. | |
| From: report of Georg W.F.Hegel (Lectures on Aesthetics [1826]) by Terry Pinkard - German Philosophy 1760-1860 11 | |
| A reaction: Personally I dislike over-intellectualising art. The aim of a work of art is to give a certain experience, not to generate an ensuing sequence of theorising. I doubt whether Vermeer had any 'meaning' in mind in his obsessive work. |
| 22042 | Natural beauty is unimportant, because it doesn't show human freedom [Hegel, by Pinkard] |
| Full Idea: Hegel thinks that natural beauty is of no real significance since it cannot display our freedom to us; nature per se is meaningless. | |
| From: report of Georg W.F.Hegel (Lectures on Aesthetics [1826]) by Terry Pinkard - German Philosophy 1760-1860 11 | |
| A reaction: Presumably freedom is in the creation, and so creativity is what matters in aesthetics. But what are the criteria of good creativity? |
| 20413 | For Hegel the importance of art concerns the culture, not the individual [Hegel, by Eldridge] |
| Full Idea: Hegel locates the significance of art in its role in cultural life in general, not in relation to the psychological needs of individuals. | |
| From: report of Georg W.F.Hegel (Lectures on Aesthetics [1826]) by Richard Eldridge - G.W.F. Hegel (aesthetics) 1 | |
| A reaction: I'm beginning to see that art is a wonderful focus and test case for political attitudes. Roughly, liberalism focuses on individual responses, but more societal views (from right and left) see it in terms of role in the community. Which are you? |
| 20394 | The purpose of art is to reveal to Spirit its own nature [Hegel, by Davies,S] |
| Full Idea: According to Hegel, the goal of art was to serve as a phase in a process by which Spirit would come to understand its own nature. | |
| From: report of Georg W.F.Hegel (Lectures on Aesthetics [1826]) by Stephen Davies - The Philosophy of Art (2nd ed) 2.7 | |
| A reaction: I try very hard to understand ideas like this. Really really hard. However, since I see little sign of 'Spirit' really understanding its own nature, I'm guessing that the project is not going well. |
| 21794 | The main purpose of art is to express the unity of human life [Hegel] |
| Full Idea: Art's primary function, for Hegel, is to give expression to the unity and wholeness of life - especially human life - that the contingencies of everyday existence frequently conceal. | |
| From: Georg W.F.Hegel (Lectures on Aesthetics [1826]), quoted by Stephen Houlgate - An Introduction to Hegel 09 'Beauty' | |
| A reaction: I don't find the view that human life is 'unified' and 'whole' vary illuminating, and I have no objection to art which reflects the fragmentary and unstable aspects of life. I suspect Hegel would just prefer it if life were a unity. |
| 20415 | Art forms a bridge between the sensuous world and the world of pure thought [Hegel] |
| Full Idea: Spirit generates out of itself works of fine art as the first reconciling middle term between pure thought and what is merely external, sensuous and transient - between finite natural reality and the infinite freedom of conceptual thinking. | |
| From: Georg W.F.Hegel (Lectures on Aesthetics [1826], p.8), quoted by Richard Eldridge - G.W.F. Hegel (aesthetics) | |
| A reaction: This apparently says that there is necessarily an intellectual and conceptual component in art. This means little to me. Does he include portraits? Dutch domestic scenes? Would photography qualify? |