16 ideas
| 21918 | Sufficient Reason can't be proved, because all proof presupposes it [Schopenhauer, by Lewis,PB] |
| Full Idea: Schopenhauer said the principle of sufficient reason is not susceptible to proof for the simple reason that it is presupposed in any argument or proof. | |
| From: report of Arthur Schopenhauer (Fourfold Root of Princ of Sufficient Reason [1813], §14 p.32-3) by Peter B. Lewis - Schopenhauer 3 | |
| A reaction: I would have thought it might be disproved by a counterexample, such as the Gödel sentence of his incompleteness proof, or quantum effects which seem to elude causation. Personally I believe the principle, which I see as the first axiom of philosophy. |
| 9837 | 0 is not a number, as it answers 'how many?' negatively [Husserl, by Dummett] |
| Full Idea: Husserl contends that 0 is not a number, on the grounds that 'nought' is a negative answer to the question 'how many?'. | |
| From: report of Edmund Husserl (Philosophy of Arithmetic [1894], p.144) by Michael Dummett - Frege philosophy of mathematics Ch.8 | |
| A reaction: I seem to be in a tiny minority in thinking that Husserl may have a good point. One apple is different from one orange, but no apples are the same as no oranges. That makes 0 a very peculiar number. See Idea 9838. |
| 9576 | Multiplicity in general is just one and one and one, etc. [Husserl] |
| Full Idea: Multiplicity in general is no more than something and something and something, etc.; ..or more briefly, one and one and one, etc. | |
| From: Edmund Husserl (Philosophy of Arithmetic [1894], p.85), quoted by Gottlob Frege - Review of Husserl's 'Phil of Arithmetic' | |
| A reaction: Frege goes on to attack this idea fairly convincingly. It seems obvious that it is hard to say that you have seventeen items, if the only numberical concept in your possession is 'one'. How would you distinguish 17 from 16? What makes the ones 'multiple'? |
| 17444 | Husserl said counting is more basic than Frege's one-one correspondence [Husserl, by Heck] |
| Full Idea: Husserl famously argued that one should not explain number in terms of equinumerosity (or one-one correspondence), but should explain equinumerosity in terms of sameness of number, which should be characterised in terms of counting. | |
| From: report of Edmund Husserl (Philosophy of Arithmetic [1894]) by Richard G. Heck - Cardinality, Counting and Equinumerosity 3 | |
| A reaction: [Heck admits he hasn't read the Husserl] I'm very sympathetic to Husserl, though nearly all modern thinking favours Frege. Counting connects numbers to their roots in the world. Mathematicians seem oblivious of such things. |
| 21920 | No need for a priori categories, since sufficient reason shows the interrelations [Schopenhauer, by Lewis,PB] |
| Full Idea: Schopenhauer dispenses with Kant's a priori categories, since all interrelations between representations are given through the principle of sufficient reason. | |
| From: report of Arthur Schopenhauer (Fourfold Root of Princ of Sufficient Reason [1813]) by Peter B. Lewis - Schopenhauer 3 | |
| A reaction: I'm not sure how Schopenhauer manages this move. Is it the stoic idea that reality has a logical structure, which can be inferred? Sounds good to me. Further investigation required. |
| 21362 | Necessity is physical, logical, mathematical or moral [Schopenhauer, by Janaway] |
| Full Idea: For Schopenauer there are physical necessity, logical necessity, mathematical necessity and moral necessity. | |
| From: report of Arthur Schopenhauer (Fourfold Root of Princ of Sufficient Reason [1813]) by Christopher Janaway - Schopenhauer 2 'Fourfold' | |
| A reaction: These derive from four modes of explanation, by causes, by grounding in truths or facts, by mathematical reality, and by motives. Not clear why mathematics gets its own necessity. I like metaphysics derived from explanations, though. Necessity makers. |
| 21361 | For Schopenhauer, material things would not exist without the mind [Schopenhauer, by Janaway] |
| Full Idea: Schopenhauer is not a realist about material things, but an idealist: that is, material things would not exist, for him, without the mind. | |
| From: report of Arthur Schopenhauer (Fourfold Root of Princ of Sufficient Reason [1813]) by Christopher Janaway - Schopenhauer 2 'Fourfold' | |
| A reaction: Janaway places his views as close to Kant's, but it is not clear that Kant would agree that no mind means no world. Did Schopenhauer believe in the noumenon? |
| 21919 | Object for a subject and representation are the same thing [Schopenhauer] |
| Full Idea: To be object for a subject and to be representation is to be one and the same thing. All representations are objects for a subject, all objects for a subject are representations. | |
| From: Arthur Schopenhauer (Fourfold Root of Princ of Sufficient Reason [1813], §16 p.41-2), quoted by Peter B. Lewis - Schopenhauer 3 | |
| A reaction: This is pure idealism in early Schopenhauer, derived from Kant. Are being 'an object for a subject' and being an object 'in itself' two different things? Compare Idea 21914, written later. I think Nietzsche's 'perspective' representations helps here. |
| 21917 | The four explanations: objects by causes, concepts by ground, maths by spacetime, ethics by motive [Schopenhauer, by Lewis,PB] |
| Full Idea: There are four forms of explanation, depending on their topic. Causes explain objects. Grounding explains concepts, Points and moments explain mathematics. Motives explain ethics. | |
| From: report of Arthur Schopenhauer (Fourfold Root of Princ of Sufficient Reason [1813], §43 p.214) by Peter B. Lewis - Schopenhauer 3 | |
| A reaction: [My compression of Lewis's summary. I'm particularly pleased with this. I have done Schopenhauer a huge favour, should anyone ever visit this website]. The quirky account of mathematics derives from Kant. I greatly admire this whole idea. |
| 9575 | Husserl identifies a positive mental act of unification, and a negative mental act for differences [Husserl, by Frege] |
| Full Idea: Husserl identifies a 'unitary mental act' where several contents are connected or related to one another, and also a difference-relation where two contents are related to one another by a negative judgement. | |
| From: report of Edmund Husserl (Philosophy of Arithmetic [1894], p.73-74) by Gottlob Frege - Review of Husserl's 'Phil of Arithmetic' p.322 | |
| A reaction: Frege is setting this up ready for a fairly vicious attack. Where Hume has a faculty for spotting resemblances, it is not implausible that we should also be hard-wired to spot differences. 'You look different; have you changed your hair style?' |
| 21921 | Concepts are abstracted from perceptions [Schopenhauer, by Lewis,PB] |
| Full Idea: For Schopenhauer concepts are abstractions from perception, what he calls 'representations of representations', and are linked to the creation of language. | |
| From: report of Arthur Schopenhauer (Fourfold Root of Princ of Sufficient Reason [1813]) by Peter B. Lewis - Schopenhauer 3 | |
| A reaction: This is a traditional view which dates back to Aristotle, and which I personally think is entirely correct. These days I am in minority on that. This idea means that (contrary to Kant) perception is not conceptual. |
| 21214 | We clarify concepts (e.g. numbers) by determining their psychological origin [Husserl, by Velarde-Mayol] |
| Full Idea: Husserl said that the clarification of any concept is made by determining its psychological origin. He is concerned with the psychological origins of the operation of calculating cardinal numbers. | |
| From: report of Edmund Husserl (Philosophy of Arithmetic [1894]) by Victor Velarde-Mayol - On Husserl 2.2 | |
| A reaction: This may not be the same as the 'psychologism' that Frege so despised, because Husserl is offering a clarification, rather than the intrinsic nature of number concepts. It is not a theory of the origin of numbers. |
| 9819 | Psychologism blunders in focusing on concept-formation instead of delineating the concepts [Dummett on Husserl] |
| Full Idea: Husserl substitutes his account of the process of concept-formation for a delineation of the concept. It is above all in making this substitution that psychologism is objectionable (and Frege opposed it so vehemently). | |
| From: comment on Edmund Husserl (Philosophy of Arithmetic [1894]) by Michael Dummett - Frege philosophy of mathematics Ch.2 | |
| A reaction: While this is a powerful point which is a modern orthodoxy, it hardly excludes a study of concept-formation from being of great interest for other reasons. It may not appeal to logicians, but it is crucial part of the metaphysics of nature. |
| 9851 | Husserl wanted to keep a shadowy remnant of abstracted objects, to correlate them [Dummett on Husserl] |
| Full Idea: Husserl saw that abstracted units, though featureless, must in some way retain their distinctness, some shadowy remnant of their objects. So he wanted to correlate like-numbered sets, not just register their identity, but then abstractionism fails. | |
| From: comment on Edmund Husserl (Philosophy of Arithmetic [1894]) by Michael Dummett - Frege philosophy of mathematics Ch.12 | |
| A reaction: Abstractionism is held to be between the devil and the deep blue sea, of depending on units which are identifiable, when they are defined as devoid of all individuality. We seem forced to say that the only distinction between them is countability. |
| 21363 | Motivation is causality seen from within [Schopenhauer] |
| Full Idea: Motivation is causality seen from within. | |
| From: Arthur Schopenhauer (Fourfold Root of Princ of Sufficient Reason [1813], p.214), quoted by Christopher Janaway - Schopenhauer 2 'Fourfold' | |
| A reaction: This is more illuminating about causation than about motivation, since we can be motivated without actually doing anything. |
| 468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
| Full Idea: In singing and playing the lyre, a boy will be likely to reveal not only courage and moderation, but also justice. | |
| From: Damon (fragments/reports [c.460 BCE], B4), quoted by (who?) - where? |