10 ideas
| 21463 | Hamann, Herder and Jacobi were key opponents of the Enlightenment [Gardner] |
| Full Idea: Hamann, Herder and Jacobi are central figues in the reaction against Enlightenment. | |
| From: Sebastian Gardner (Kant and the Critique of Pure Reason [1999], 10 'immediate') | |
| A reaction: From a British perspective I would see Hume as the leading such figure. Hamann emphasised the neglect of the role of language. Jacobi was a Christian. |
| 21459 | Kant halted rationalism, and forced empiricists to worry about foundations [Gardner] |
| Full Idea: Kant's Critique swiftly brought rationalism to a halt, and after Kant empiricism has displayed a nervousness regarding its foundations, and been forced to assume more sophisticated forms. | |
| From: Sebastian Gardner (Kant and the Critique of Pure Reason [1999], 10 Intro) | |
| A reaction: See the ideas of Laurence Bonjour for a modern revival of rationalism. After Kant philosophers either went existential, or stared gloomily into the obscure depths. Formal logic was seen as a possible rope ladder down. |
| 21460 | Only Kant and Hegel have united nature, morals, politics, aesthetics and religion [Gardner] |
| Full Idea: Apart from Hegel, no later philosophical system equals in stature Kant's attempt to weld together the diverse fields of natural science, morality, politics, aesthetics and religion into a systematic overarching epistemological and metaphysical unity. | |
| From: Sebastian Gardner (Kant and the Critique of Pure Reason [1999], 10) | |
| A reaction: Earlier candidate are Plato and Aristotle. Earlier Enlightenment figures say little about morality or aesthetics. Hobbes ranges widely. Aquinas covered most things. |
| 21443 | Transcendental proofs derive necessities from possibilities (e.g. possibility of experiencing objects) [Gardner] |
| Full Idea: A transcendental proof converts a possibility into a necessity: by saying under what conditions experience of objects is possible, transcendental proofs show those conditions to be necessary for us to the extent that we have any experience of objects. | |
| From: Sebastian Gardner (Kant and the Critique of Pure Reason [1999], 02 'Transc') | |
| A reaction: They appear to be hypothetical necessities, rather than true metaphysical necessities. Gardner is discussing Kant, but seems to be generalising. Hypothetical necessities are easy: if it is flying, it is necessarily above the ground. |
| 17962 | The truth-maker principle is that every truth has a sufficient truth-maker [Forrest] |
| Full Idea: Item x is said to be a sufficient truth-maker for truth-bearer p just in case necessarily if x exists then p is true. ...Every truth has a sufficient truth-maker. Hence, I take it, the sum of all sufficient truth-makers is a universal truth-maker. | |
| From: Peter Forrest (General Facts,Phys Necessity, and Metaph of Time [2006], 1) | |
| A reaction: Note that it is not 'necessary', because something else might make p true instead. |
| 21444 | Modern geoemtry is either 'pure' (and formal), or 'applied' (and a posteriori) [Gardner] |
| Full Idea: There is now 'pure' geometry, consisting of formal systems based on axioms for which truth is not claimed, and which are consequently not synthetic; and 'applied', a branch of physics, the truth of which is empirical, and therefore not a priori. | |
| From: Sebastian Gardner (Kant and the Critique of Pure Reason [1999], 03 'Maths') | |
| A reaction: His point is that there is no longer any room for a priori geometry. Might the same division be asserted of arithmetic, or analysis, or set theory? |
| 8698 | Modal structuralism says mathematics studies possible structures, which may or may not be actualised [Hellman, by Friend] |
| Full Idea: The modal structuralist thinks of mathematical structures as possibilities. The application of mathematics is just the realisation that a possible structure is actualised. As structures are possibilities, realist ontological problems are avoided. | |
| From: report of Geoffrey Hellman (Mathematics without Numbers [1989]) by Michèle Friend - Introducing the Philosophy of Mathematics 4.3 | |
| A reaction: Friend criticises this and rejects it, but it is appealing. Mathematics should aim to be applicable to any possible world, and not just the actual one. However, does the actual world 'actualise a mathematical structure'? |
| 9557 | Statements of pure mathematics are elliptical for a sort of modal conditional [Hellman, by Chihara] |
| Full Idea: Hellman represents statements of pure mathematics as elliptical for modal conditionals of a certain sort. | |
| From: report of Geoffrey Hellman (Mathematics without Numbers [1989]) by Charles Chihara - A Structural Account of Mathematics 5.3 | |
| A reaction: It's a pity there is such difficulty in understanding conditionals (see Graham Priest on the subject). I intuit a grain of truth in this, though I take maths to reflect the structure of the actual world (with possibilities being part of that world). |
| 10263 | Modal structuralism can only judge possibility by 'possible' models [Shapiro on Hellman] |
| Full Idea: The usual way to show that a sentence is possible is to show that it has a model, but for Hellman presumably a sentence is possible if it might have a model (or if, possibly, it has a model). It is not clear what this move brings us. | |
| From: comment on Geoffrey Hellman (Mathematics without Numbers [1989]) by Stewart Shapiro - Philosophy of Mathematics 7.3 | |
| A reaction: I can't assess this, but presumably the possibility of the model must be demonstrated in some way. Aren't all models merely possible, because they are based on axioms, which seem to be no more than possibilities? |
| 21453 | Leibnizian monads qualify as Kantian noumena [Gardner] |
| Full Idea: Leibnizian monads clearly satisfy Kant's definition of noumena. | |
| From: Sebastian Gardner (Kant and the Critique of Pure Reason [1999], 06 'Noumena') | |
| A reaction: This needs qualifying, because Leibniz clearly specifies the main attributes of monads, where Kant is adamant that we can saying virtually nothing about noumena. |