15 ideas
| 13966 | Analytic philosophy loved the necessary a priori analytic, linguistic modality, and rigour [Soames] |
| Full Idea: The golden age of analytic philosophy (mid 20th c) was when necessary, a priori and analytic were one, all possibility was linguistic possibility, and the linguistic turn gave philosophy a respectable subject matter (language), and precision and rigour. | |
| From: Scott Soames (Significance of the Kripkean Nec A Posteriori [2006], p.166) | |
| A reaction: Gently sarcastic, because Soames is part of the team who have put a bomb under this view, and quite right too. Personally I think the biggest enemy in all of this lot is not 'language' but 'rigour'. A will-o-the-wisp philosophers dream of. |
| 13099 | Analysing right down to primitive concepts seems beyond our powers [Leibniz] |
| Full Idea: An analysis of concepts such that we can reach primitive concepts...does not seem to be within human power. | |
| From: Gottfried Leibniz (Introduction to a Secret Encyclopaedia [1679], C513-14), quoted by Cover,J/O'Leary-Hawthorne,J - Substance and Individuation in Leibniz | |
| A reaction: Leibniz is nevertheless fully committed, I think, to the existence of such primitives, and is in the grip of the rationalist dream that thoughts can become completely clear, and completely well-founded. |
| 13974 | If philosophy is analysis of meaning, available to all competent speakers, what's left for philosophers? [Soames] |
| Full Idea: If all of philosophy is the analysis of meaning, and meaning is fundamentally transparent to competent speakers, there is little room for philosophically significant explanations and theories, since they will be necessary or a priori, or both. | |
| From: Scott Soames (Significance of the Kripkean Nec A Posteriori [2006], p.186) | |
| A reaction: He cites the later Wittgenstein as having fallen into this trap. I suppose any area of life can have its specialists, but I take Shakespeare to be a greater master of English than any philosopher I have ever read. |
| 5022 | We hold a proposition true if we are ready to follow it, and can't see any objections [Leibniz] |
| Full Idea: A proposition is held to be true by us when our mind is ready to follow it and no reason for doubting it can be found. | |
| From: Gottfried Leibniz (Introduction to a Secret Encyclopaedia [1679], p.7) | |
| A reaction: This follows on from Descartes' view, but it now sounds more like psychology than metaphysics. Clearly a false proposition could fit this desciption. Personally I follow propositions to which I can see no objection, without actually holding them true. |
| 17610 | The Axiom of Choice paradoxically allows decomposing a sphere into two identical spheres [Maddy] |
| Full Idea: One feature of the Axiom of Choice that troubled many mathematicians was the so-called Banach-Tarski paradox: using the Axiom, a sphere can be decomposed into finitely many parts and those parts reassembled into two spheres the same size as the original. | |
| From: Penelope Maddy (Defending the Axioms [2011], 1.3) | |
| A reaction: (The key is that the parts are non-measurable). To an outsider it is puzzling that the Axiom has been universally accepted, even though it produces such a result. Someone can explain that, I'm sure. |
| 17620 | Critics of if-thenism say that not all starting points, even consistent ones, are worth studying [Maddy] |
| Full Idea: If-thenism denies that mathematics is in the business of discovering truths about abstracta. ...[their opponents] obviously don't regard any starting point, even a consistent one, as equally worthy of investigation. | |
| From: Penelope Maddy (Defending the Axioms [2011], 3.3) | |
| A reaction: I have some sympathy with if-thenism, in that you can obviously study the implications of any 'if' you like, but deep down I agree with the critics. |
| 17605 | Hilbert's geometry and Dedekind's real numbers were role models for axiomatization [Maddy] |
| Full Idea: At the end of the nineteenth century there was a renewed emphasis on rigor, the central tool of which was axiomatization, along the lines of Hilbert's axioms for geometry and Dedekind's axioms for real numbers. | |
| From: Penelope Maddy (Defending the Axioms [2011], 1.3) |
| 17625 | If two mathematical themes coincide, that suggest a single deep truth [Maddy] |
| Full Idea: The fact that two apparently fruitful mathematical themes turn out to coincide makes it all the more likely that they're tracking a genuine strain of mathematical depth. | |
| From: Penelope Maddy (Defending the Axioms [2011], 5.3ii) |
| 17615 | Every infinite set of reals is either countable or of the same size as the full set of reals [Maddy] |
| Full Idea: One form of the Continuum Hypothesis is the claim that every infinite set of reals is either countable or of the same size as the full set of reals. | |
| From: Penelope Maddy (Defending the Axioms [2011], 2.4 n40) |
| 17618 | Set-theory tracks the contours of mathematical depth and fruitfulness [Maddy] |
| Full Idea: Our set-theoretic methods track the underlying contours of mathematical depth. ...What sets are, most fundamentally, is markers for these contours ...they are maximally effective trackers of certain trains of mathematical fruitfulness. | |
| From: Penelope Maddy (Defending the Axioms [2011], 3.4) | |
| A reaction: This seems to make it more like a map of mathematics than the actual essence of mathematics. |
| 17614 | The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy] |
| Full Idea: Ordinary perceptual cognition is most likely involved in our grasp of elementary arithmetic, but ...this connection to the physical world has long since been idealized away in the infinitary structures of contemporary pure mathematics. | |
| From: Penelope Maddy (Defending the Axioms [2011], 2.3) | |
| A reaction: Despite this, Maddy's quest is for a 'naturalistic' account of mathematics. She ends up defending 'objectivity' (and invoking Tyler Burge), rather than even modest realism. You can't 'idealise away' the counting of objects. I blame Cantor. |
| 13969 | Kripkean essential properties and relations are necessary, in all genuinely possible worlds [Soames] |
| Full Idea: By (Kripkean) 'essential' properties and relations I mean simply properties and relations that hold necessarily of objects (in all genuinely possible world-states in which the objects exist). | |
| From: Scott Soames (Significance of the Kripkean Nec A Posteriori [2006], p.168 n5) | |
| A reaction: This is the standard modern view of essences which I find so unsatisfactory. Kit Fine has helped to take us back to the proper Aristotelian view, where 'necessary' and 'essential' actually have different meanings. Note the inclusion of relations. |
| 13973 | A key achievement of Kripke is showing that important modalities are not linguistic in source [Soames] |
| Full Idea: None of Kripke's many achievements is more important than his breaking the spell of the linguistic as the source of philosophically important modalities. | |
| From: Scott Soames (Significance of the Kripkean Nec A Posteriori [2006], p.186) | |
| A reaction: Put like that, Kripke may have had the single most important thought of modern times. I take good philosophy to be exactly the same as good scientific theorising, in that it all arises out of the nature of reality (and I include logic in that). |
| 13968 | Kripkean possible worlds are abstract maximal states in which the real world could have been [Soames] |
| Full Idea: For the Kripkean possible states of the world are not alternate concrete universes, but abstract objects. Metaphysically possible world-states are maximally complete ways the real concrete universe could have been. | |
| From: Scott Soames (Significance of the Kripkean Nec A Posteriori [2006], p.167) | |
| A reaction: This is probably clearer about the Kripkean view than Kripke ever is, but then that is part of Soames's mission. It sounds like the right way to conceive possible worlds. At least there is some commitment there, rather than instrumentalism about them. |
| 13972 | Two-dimensionalism reinstates descriptivism, and reconnects necessity and apriority to analyticity [Soames] |
| Full Idea: Two-dimensionalism is a fundamentally anti-Kripkean attempt to reinstate descriptivism about names and natural kind terms, to reconnect necessity and apriority to analyticity, and return philosophy to analytic paradigms of its golden age. | |
| From: Scott Soames (Significance of the Kripkean Nec A Posteriori [2006], p.183) | |
| A reaction: I presume this is right, and it is so frustrating that you need Soames to spell it out, when Chalmers is much more low-key. Philosophers hate telling you what their real game is. Why is that? |