30 ideas
20962 | Habermas seems to make philosophy more democratic [Habermas, by Bowie] |
Full Idea: Habermas is concerned to avoid the traumas of modern German history by making democracy an integral part of philosophy. | |
From: report of Jürgen Habermas (The Theory of Communicative Action [1981]) by Andrew Bowie - Introduction to German Philosophy Conc 'Habermas' | |
A reaction: Hence Habermas's emphasis on communication as central to language, which is central to philosophy. Modern philosophy departments are amazingly hierarchical. |
15670 | The aim of 'post-metaphysical' philosophy is to interpret the sciences [Habermas, by Finlayson] |
Full Idea: For Habermas, the task of what he calls 'post-metaphysical' philosophy is to be a stand-in and interpreter for the specialized sciences. | |
From: report of Jürgen Habermas (The Theory of Communicative Action [1981]) by James Gordon Finlayson - Habermas Ch.5:65 |
15665 | We can do social philosophy by studying coordinated action through language use [Habermas, by Finlayson] |
Full Idea: Habermas claims to have embarked upon a new way of doing social philosophy, one that begins from an analysis of language use and that locates the rational basis of the coordination of action in speech. | |
From: report of Jürgen Habermas (The Theory of Communicative Action [1981]) by James Gordon Finlayson - Habermas Ch.3:28 |
20573 | Rather than instrumental reason, Habermas emphasises its communicative role [Habermas, by Oksala] |
Full Idea: Instead of Enlightenment instrumental rationality (criticised by Adorno and Horkheimer), Habermas emphasizes 'communicative rationality', which makes critical discussion and mutual understanding possible. | |
From: report of Jürgen Habermas (The Theory of Communicative Action [1981]) by Johanna Oksala - Political Philosophy: all that matters Ch.6 | |
A reaction: There was a good reason not to smoke cigarettes, before we found out what it is. In one sense, reasons are in the world. This is interesting, but I feel analytic vertigo, as the lovely concept of 'rationality' becomes blurred and diffused. |
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. |
12456 | I aim to establish certainty for mathematical methods [Hilbert] |
Full Idea: The goal of my theory is to establish once and for all the certitude of mathematical methods. | |
From: David Hilbert (On the Infinite [1925], p.184) | |
A reaction: This is the clearest statement of the famous Hilbert Programme, which is said to have been brought to an abrupt end by Gödel's Incompleteness Theorems. |
12461 | We believe all mathematical problems are solvable [Hilbert] |
Full Idea: The thesis that every mathematical problem is solvable - we are all convinced that it really is so. | |
From: David Hilbert (On the Infinite [1925], p.200) | |
A reaction: This will include, for example, Goldbach's Conjecture (every even is the sum of two primes), which is utterly simple but with no proof anywhere in sight. |
9633 | No one shall drive us out of the paradise the Cantor has created for us [Hilbert] |
Full Idea: No one shall drive us out of the paradise the Cantor has created for us. | |
From: David Hilbert (On the Infinite [1925], p.191), quoted by James Robert Brown - Philosophy of Mathematics | |
A reaction: This is Hilbert's famous refusal to accept any account of mathematics, such as Kant's, which excludes actual infinities. Cantor had laid out a whole glorious hierarchy of different infinities. |
12460 | We extend finite statements with ideal ones, in order to preserve our logic [Hilbert] |
Full Idea: To preserve the simple formal rules of ordinary Aristotelian logic, we must supplement the finitary statements with ideal statements. | |
From: David Hilbert (On the Infinite [1925], p.195) | |
A reaction: I find very appealing the picture of mathematics as rooted in the physical world, and then gradually extended by a series of 'idealisations', which should perhaps be thought of as fictions. |
12462 | Only the finite can bring certainty to the infinite [Hilbert] |
Full Idea: Operating with the infinite can be made certain only by the finitary. | |
From: David Hilbert (On the Infinite [1925], p.201) | |
A reaction: See 'Compactness' for one aspect of this claim. I think Hilbert was fighting a rearguard action, and his idea now has few followers. |
12455 | The idea of an infinite totality is an illusion [Hilbert] |
Full Idea: Just as in the limit processes of the infinitesimal calculus, the infinitely large and small proved to be a mere figure of speech, so too we must realise that the infinite in the sense of an infinite totality, used in deductive methods, is an illusion. | |
From: David Hilbert (On the Infinite [1925], p.184) | |
A reaction: This is a very authoritative rearguard action. I no longer think the dispute matters much, it being just a dispute over a proposed new meaning for the word 'number'. |
12457 | There is no continuum in reality to realise the infinitely small [Hilbert] |
Full Idea: A homogeneous continuum which admits of the sort of divisibility needed to realise the infinitely small is nowhere to be found in reality. | |
From: David Hilbert (On the Infinite [1925], p.186) | |
A reaction: He makes this remark as a response to Planck's new quantum theory (the year before the big works of Heisenberg and Schrödinger). Personally I don't see why infinities should depend on the physical world, since they are imaginary. |
12459 | The subject matter of mathematics is immediate and clear concrete symbols [Hilbert] |
Full Idea: The subject matter of mathematics is the concrete symbols themselves whose structure is immediately clear and recognisable. | |
From: David Hilbert (On the Infinite [1925], p.192) | |
A reaction: I don't think many people will agree with Hilbert here. Does he mean token-symbols or type-symbols? You can do maths in your head, or with different symbols. If type-symbols, you have to explain what a type is. |
18112 | Mathematics divides in two: meaningful finitary statements, and empty idealised statements [Hilbert] |
Full Idea: We can conceive mathematics to be a stock of two kinds of formulas: first, those to which the meaningful communications of finitary statements correspond; and secondly, other formulas which signify nothing and which are ideal structures of our theory. | |
From: David Hilbert (On the Infinite [1925], p.196), quoted by David Bostock - Philosophy of Mathematics 6.1 |
9636 | My theory aims at the certitude of mathematical methods [Hilbert] |
Full Idea: The goal of my theory is to establish once and for all the certitude of mathematical methods. | |
From: David Hilbert (On the Infinite [1925], p.184), quoted by James Robert Brown - Philosophy of Mathematics Ch.5 | |
A reaction: This dream is famous for being shattered by Gödel's Incompleteness Theorem a mere six years later. Neverless there seem to be more limited certainties which are accepted in mathematics. The certainty of the whole of arithmetic is beyond us. |
20961 | What is considered a priori changes as language changes [Habermas, by Bowie] |
Full Idea: Habermas claims that what is regarded as a priori changes with history. This is because the linguistic structures on which judgements depend are themselves part of history, not prior to it. | |
From: report of Jürgen Habermas (The Theory of Communicative Action [1981]) by Andrew Bowie - Introduction to German Philosophy Conc 'Habermas' | |
A reaction: This is an interesting style of argument generally only found in continental philosophers, because they see the problem as historical rather than timeless. Compare Idea 20595, which sees analyticity historically. |
15667 | To understand a statement is to know what would make it acceptable [Habermas] |
Full Idea: We understand the meaning of a speech act when we know what would make it acceptable. | |
From: Jürgen Habermas (The Theory of Communicative Action [1981], I:297), quoted by James Gordon Finlayson - Habermas Ch.3:37 | |
A reaction: Finlayson glosses this as requiring the reasons which would justify the speech act. |
15668 | Meaning is not fixed by a relation to the external world, but a relation to other speakers [Habermas, by Finlayson] |
Full Idea: On Habermas's view, meanings are not determined by the speaker's relation to the external world, but by his relation to his interlocutors; meaning is essentially intersubjective. | |
From: report of Jürgen Habermas (The Theory of Communicative Action [1981]) by James Gordon Finlayson - Habermas Ch.3:38 | |
A reaction: This view is not the same as Grice's, but it is clearly much closer to Grice than to (say) the Frege/Davidson emphasis on truth-conditions. I'm not sure if I would know how to begin arbitrating between the two views! |
15669 | People endorse equality, universality and inclusiveness, just by their communicative practices [Habermas, by Finlayson] |
Full Idea: The ideal of equality, universality, and inclusiveness are inscribed in the communicative practices of the lifeworld, and agents, merely by virtue of communicating, conform to them. | |
From: report of Jürgen Habermas (The Theory of Communicative Action [1981]) by James Gordon Finlayson - Habermas Ch.4:60 | |
A reaction: This summary of Habermas's social views strikes me as thoroughly Kantian. It is something like the ideals of the Kingdom of Ends, necessarily implemented in a liberal society. Habermas emphasises the social, where Kant starts from the liberal. |
23416 | Political involvement is needed, to challenge existing practices [Habermas, by Kymlicka] |
Full Idea: Habermas thinks political deliberation is required precisely because in its absence people will tend to accept existing practices as given, and thereby perpetuate false needs. | |
From: report of Jürgen Habermas (The Theory of Communicative Action [1981]) by Will Kymlicka - Community 'need' | |
A reaction: If the dream is healthy and intelligent progress, it is not clear where that should come from. The problem with state involvement in the authority and power of the state. Locals are often prejudiced, so the intermediate level may be best. |