10 ideas
21900 | Deleuze relies on Spinoza (immanence), Bergson (duration), and difference (Nietzsche) [May] |
Full Idea: The three tripods on which the philosophy of Deleuze stands are immanence (Spinoza), duration (Bergson), and the affirmation of difference (Nietzsche). | |
From: Todd May (Gilles Deleuze [2006], 2.12) | |
A reaction: [Just to begin sketching how continental philosophy sees its tradition]. |
17963 | The facts of geometry, arithmetic or statics order themselves into theories [Hilbert] |
Full Idea: The facts of geometry order themselves into a geometry, the facts of arithmetic into a theory of numbers, the facts of statics, electrodynamics into a theory of statics, electrodynamics, or the facts of the physics of gases into a theory of gases. | |
From: David Hilbert (Axiomatic Thought [1918], [03]) | |
A reaction: This is the confident (I would say 'essentialist') view of axioms, which received a bit of a setback with Gödel's Theorems. I certainly agree that the world proposes an order to us - we don't just randomly invent one that suits us. |
17966 | Axioms must reveal their dependence (or not), and must be consistent [Hilbert] |
Full Idea: If a theory is to serve its purpose of orienting and ordering, it must first give us an overview of the independence and dependence of its propositions, and second give a guarantee of the consistency of all of the propositions. | |
From: David Hilbert (Axiomatic Thought [1918], [09]) | |
A reaction: Gödel's Second theorem showed that the theory can never prove its own consistency, which made the second Hilbert requirement more difficult. It is generally assumed that each of the axioms must be independent of the others. |
17967 | To decide some questions, we must study the essence of mathematical proof itself [Hilbert] |
Full Idea: It is necessary to study the essence of mathematical proof itself if one wishes to answer such questions as the one about decidability in a finite number of operations. | |
From: David Hilbert (Axiomatic Thought [1918], [53]) |
17965 | The whole of Euclidean geometry derives from a basic equation and transformations [Hilbert] |
Full Idea: The linearity of the equation of the plane and of the orthogonal transformation of point-coordinates is completely adequate to produce the whole broad science of spatial Euclidean geometry purely by means of analysis. | |
From: David Hilbert (Axiomatic Thought [1918], [05]) | |
A reaction: This remark comes from the man who succeeded in producing modern axioms for geometry (in 1897), so he knows what he is talking about. We should not be wholly pessimistic about Hilbert's ambitious projects. He had to dig deeper than this idea... |
17964 | Number theory just needs calculation laws and rules for integers [Hilbert] |
Full Idea: The laws of calculation and the rules of integers suffice for the construction of number theory. | |
From: David Hilbert (Axiomatic Thought [1918], [05]) | |
A reaction: This is the confident Hilbert view that the whole system can be fully spelled out. Gödel made this optimism more difficult. |
21898 | For existentialists the present is empty without the pull of the future and weight of the past [May] |
Full Idea: For the existential view of lived time, the present would be empty if it were not for the pull of the future and the weight of the past that give it its character. | |
From: Todd May (Gilles Deleuze [2006], 2.05) | |
A reaction: Bergson seems to be important in developing this idea, though I suspect that Kierkegaard is a source. |
21905 | Liberal theory starts from the governed, not from the governor [May] |
Full Idea: For liberal theory, it is the individual to be governed, not the governor, who is the starting point. | |
From: Todd May (Gilles Deleuze [2006], 4.02) | |
A reaction: I'm inclined to see this as the single-handed achievement of Thomas Hobbes, who starts from the need of citizens to secure their contracts. Plato's society starts from entrepreneurs, but their need for a ruler seems a priori. |
7825 | The politics of Leibniz was the reunification of Christianity [Stewart,M] |
Full Idea: The politics of Leibniz may be summed up in one word: theocracy. The specific agenda motivating much of his work was to reunite the Protestant and Catholic churches | |
From: Matthew Stewart (The Courtier and the Heretic [2007], Ch. 5) | |
A reaction: This would be a typical project for a rationalist philosopher, who thinks that good reasoning will gradually converge on the one truth. |
17968 | By digging deeper into the axioms we approach the essence of sciences, and unity of knowedge [Hilbert] |
Full Idea: By pushing ahead to ever deeper layers of axioms ...we also win ever-deeper insights into the essence of scientific thought itself, and become ever more conscious of the unity of our knowledge. | |
From: David Hilbert (Axiomatic Thought [1918], [56]) | |
A reaction: This is the less fashionable idea that scientific essentialism can also be applicable in the mathematic sciences, centring on the project of axiomatisation for logic, arithmetic, sets etc. |