display all the ideas for this combination of philosophers
8 ideas
| 5637 | Nowadays logic is seen as the science of extensions, not intensions [Scruton] |
| Full Idea: Logicians have come increasingly to realise that logic is the science not of the intension, but of the extension of terms. | |
| From: Roger Scruton (Short History of Modern Philosophy [1981], Ch.4) | |
| A reaction: I take this to be because the notion of a 'set' is basic, which is defined strictly in terms of its members. This move is probably because we can be clear about extensions, but not intensions. Tidiness is no substitute for complex truth. |
| 11026 | Classical logic is deliberately extensional, in order to model mathematics [Fitting] |
| Full Idea: Mathematics is typically extensional throughout (we write 3+2=2+3 despite the two terms having different meanings). ..Classical first-order logic is extensional by design since it primarily evolved to model the reasoning of mathematics. | |
| From: Melvin Fitting (Intensional Logic [2007], §1) |
| 21595 | Excluded middle is the maxim of definite understanding, but just produces contradictions [Hegel] |
| Full Idea: The law of excluded middle is ...the maxim of the definite understanding, which would fain avoid contradiction, but in doing so falls into it. | |
| From: Georg W.F.Hegel (Logic (Encyclopedia I) [1817], p.172), quoted by Timothy Williamson - Vagueness 1.5 | |
| A reaction: Not sure how this works, but he would say this, wouldn't he? |
| 21777 | Negation of negation doubles back into a self-relationship [Hegel, by Houlgate] |
| Full Idea: For Hegel, the 'negation of negation' is negation that, as it were, doubles back on itself and 'relates itself to itself'. | |
| From: report of Georg W.F.Hegel (works [1812]) by Stephen Houlgate - An Introduction to Hegel 6 'Space' | |
| A reaction: [ref VNP 1823 p.108] Glad we've cleared that one up. |
| 11028 | λ-abstraction disambiguates the scope of modal operators [Fitting] |
| Full Idea: λ-abstraction can be used to abstract and disambiguate a predicate. De re is [λx◊P(x)](f) - f has the possible-P property - and de dicto is ◊[λxP(x)](f) - possibly f has the P-property. Also applies to □. | |
| From: Melvin Fitting (Intensional Logic [2007], §3.3) | |
| A reaction: Compare the Barcan formula. Originated with Church in the 1930s, and Carnap 1947, but revived by Stalnaker and Thomason 1968. Because it refers to the predicate, it has a role in intensional versions of logic, especially modal logic. |
| 15628 | The idea that contradiction is essential to rational understanding is a key modern idea [Hegel] |
| Full Idea: The thought that the contradiction which is posited by the determinations of the understanding in what is rational is essential and necessary, has to be considered one of the most important and profound advances of the philosophy of modern times. | |
| From: Georg W.F.Hegel (Logic (Encyclopedia I) [1817], §48) | |
| A reaction: This is the aspect of Kant's philosophy which launched the whole career of Hegel. Hegel is the philosopher of the antinomies. Graham Priest is his current representative on earth. |
| 15629 | Tenderness for the world solves the antinomies; contradiction is in our reason, not in the essence of the world [Hegel] |
| Full Idea: The solution to the antinomies is as trivial as they are profound; it consists merely in a tenderness for the things of this world. The stain of contradiction ought not to be in the essence of what is in the world; it must belong only to thinking reason. | |
| From: Georg W.F.Hegel (Logic (Encyclopedia I) [1817], §48 Rem) | |
| A reaction: A rather Wittgensteinian remark. I love his 'tenderness for the things of this world'! I'm not clear why our thinking should be considered to be inescapably riddled with basic contradictions, as Hegel seems to imply. Just make more effort. |
| 15630 | Antinomies are not just in four objects, but in all objects, all representations, all objects and all ideas [Hegel] |
| Full Idea: The main point that has to be made is that antinomy is found not only in Kant's four particular objects taken from cosmology, but rather in all objects of all kinds, in all representations, concepts and ideas. | |
| From: Georg W.F.Hegel (Logic (Encyclopedia I) [1817], §48 Rem) | |
| A reaction: I suppose Heraclitus and Empedocles, with their oppositional accounts of reality, are the ancestors of this worldview. I just don't feel that sudden flood of insight from this idea of Hegel that comes from some of the other great philsophical theories. |