18 ideas
| 4187 | 'There is nothing without a reason why it should be rather than not be' (a generalisation of 'Why?') [Schopenhauer] |
| Full Idea: The Principle may be stated as 'There is nothing without a reason why it should be rather than not be', which is a generalisation of the assumption which justifies the question 'Why?', which is the mother of all science. | |
| From: Arthur Schopenhauer (Abstract of 'The Fourfold Root' [1813], Ch.I) | |
| A reaction: This faith is the core of philosophy, to be maintained against all defeatists like Wittgenstein and Colin McGinn. Reality must be rational, or we wouldn't be here to think about it. (Maybe!) |
| 23623 | Predicativism says only predicated sets exist [Hossack] |
| Full Idea: Predicativists doubt the existence of sets with no predicative definition. | |
| From: Keith Hossack (Knowledge and the Philosophy of Number [2020], 02.3) | |
| A reaction: This would imply that sets which encounter paradoxes when they try to be predicative do not therefore exist. Surely you can have a set of random objects which don't fall under a single predicate? |
| 23624 | The iterative conception has to appropriate Replacement, to justify the ordinals [Hossack] |
| Full Idea: The iterative conception justifies Power Set, but cannot justify a satisfactory theory of von Neumann ordinals, so ZFC appropriates Replacement from NBG set theory. | |
| From: Keith Hossack (Knowledge and the Philosophy of Number [2020], 09.9) | |
| A reaction: The modern approach to axioms, where we want to prove something so we just add an axiom that does the job. |
| 23625 | Limitation of Size justifies Replacement, but then has to appropriate Power Set [Hossack] |
| Full Idea: The limitation of size conception of sets justifies the axiom of Replacement, but cannot justify Power Set, so NBG set theory appropriates the Power Set axiom from ZFC. | |
| From: Keith Hossack (Knowledge and the Philosophy of Number [2020], 09.9) | |
| A reaction: Which suggests that the Power Set axiom is not as indispensable as it at first appears to be. |
| 23628 | The connective 'and' can have an order-sensitive meaning, as 'and then' [Hossack] |
| Full Idea: The sentence connective 'and' also has an order-sensitive meaning, when it means something like 'and then'. | |
| From: Keith Hossack (Knowledge and the Philosophy of Number [2020], 10.4) | |
| A reaction: This is support the idea that orders are a feature of reality, just as much as possible concatenation. Relational predicates, he says, refer to series rather than to individuals. Nice point. |
| 23627 | 'Before' and 'after' are not two relations, but one relation with two orders [Hossack] |
| Full Idea: The reason the two predicates 'before' and 'after' are needed is not to express different relations, but to indicate its order. Since there can be difference of order without difference of relation, the nature of relations is not the source of order. | |
| From: Keith Hossack (Knowledge and the Philosophy of Number [2020], 10.3) | |
| A reaction: This point is to refute Russell's 1903 claim that order arises from the nature of relations. Hossack claims that it is ordered series which are basic. I'm inclined to agree with him. |
| 23626 | Transfinite ordinals are needed in proof theory, and for recursive functions and computability [Hossack] |
| Full Idea: The transfinite ordinal numbers are important in the theory of proofs, and essential in the theory of recursive functions and computability. Mathematics would be incomplete without them. | |
| From: Keith Hossack (Knowledge and the Philosophy of Number [2020], 10.1) | |
| A reaction: Hossack offers this as proof that the numbers are not human conceptual creations, but must exist beyond the range of our intellects. Hm. |
| 23621 | Numbers are properties, not sets (because numbers are magnitudes) [Hossack] |
| Full Idea: I propose that numbers are properties, not sets. Magnitudes are a kind of property, and numbers are magnitudes. …Natural numbers are properties of pluralities, positive reals of continua, and ordinals of series. | |
| From: Keith Hossack (Knowledge and the Philosophy of Number [2020], Intro) | |
| A reaction: Interesting! Since time can have a magnitude (three weeks) just as liquids can (three litres), it is not clear that there is a single natural property we can label 'magnitude'. Anything we can manage to measure has a magnitude. |
| 23622 | We can only mentally construct potential infinities, but maths needs actual infinities [Hossack] |
| Full Idea: Numbers cannot be mental objects constructed by our own minds: there exists at most a potential infinity of mental constructions, whereas the axioms of mathematics require an actual infinity of numbers. | |
| From: Keith Hossack (Knowledge and the Philosophy of Number [2020], Intro 2) | |
| A reaction: Doubt this, but don't know enough to refute it. Actual infinities were a fairly late addition to maths, I think. I would think treating fictional complete infinities as real would be sufficient for the job. Like journeys which include imagined roads. |
| 4192 | All necessity arises from causation, which is conditioned; there is no absolute or unconditioned necessity [Schopenhauer] |
| Full Idea: Necessity has no meaning other than the irresistible sequence of the effect where the cause is given. All necessity is thus conditioned, and absolute or unconditioned necessity is a contradiction in terms. | |
| From: Arthur Schopenhauer (Abstract of 'The Fourfold Root' [1813], Ch.VIII) | |
| A reaction: I.e. there is only natural necessity, and no such thing as metaphysical necessity. But what about logical necessity(e.g. 2+3=5)? I think there may be metaphysical necessity, but we can't know much about it, and we are over-confident in assessing it. |
| 4190 | All understanding is an immediate apprehension of the causal relation [Schopenhauer] |
| Full Idea: All understanding is an immediate apprehension of the causal relation. | |
| From: Arthur Schopenhauer (Abstract of 'The Fourfold Root' [1813], Ch.IV) | |
| A reaction: Based, I take it, on Hume. Presumably he means a posteriori understanding, as it hardly fits an understanding of arithmetic. Understanding needs more than just causation. What aspects of causation? |
| 3488 | Freud treats the unconscious as intentional and hence mental [Freud, by Searle] |
| Full Idea: Freud thinks that our unconscious mental states exist as occurrent intrinsic intentional states even when unconscious. Their ontology is that of the mental, even when they are unconscious. | |
| From: report of Sigmund Freud (works [1900]) by John Searle - The Rediscovery of the Mind Ch. 7.V | |
| A reaction: Searle states this view in order to attack it. Whether such states are labelled as 'mental' seems uninteresting. Whether unconscious states can be intentional is crucial, and modern scientific understanding of the brain strongly suggest they can. |
| 4191 | What we know in ourselves is not a knower but a will [Schopenhauer] |
| Full Idea: What we know in ourselves is never what knows, but what wills, the will. | |
| From: Arthur Schopenhauer (Abstract of 'The Fourfold Root' [1813], Ch.VII) | |
| A reaction: An interesting slant on Hume's scepticism about personal identity. Hume was hunting for a thing-which-experiences. If he had sought his will, he might have spotted it. |
| 5689 | Freud and others have shown that we don't know our own beliefs, feelings, motive and attitudes [Freud, by Shoemaker] |
| Full Idea: Freud persuaded many that beliefs, wishes and feelings are sometimes unconscious, and even sceptics about Freud acknowledge that there is self-deception about motive and attitudes. | |
| From: report of Sigmund Freud (works [1900]) by Sydney Shoemaker - Introspection p.396 | |
| A reaction: This seems to me obviously correct. The traditional notion is that the consciousness is the mind, but now it seems obvious that consciousness is only one part of the mind, and maybe even a peripheral (epiphenomenal) part of it. |
| 21368 | The knot of the world is the use of 'I' to refer to both willing and knowing [Schopenhauer] |
| Full Idea: The identity of the subject of willing with that of knowing by virtue whereof ...the word 'I' includes and indicates both, is the knot of the world, and hence inexplicable. | |
| From: Arthur Schopenhauer (Abstract of 'The Fourfold Root' [1813], p.211-2), quoted by Christopher Janaway - Schopenhauer 4 'Self' | |
| A reaction: I'm struggling to see this as a deep mystery. If we look objectively at animals and ask 'what is their brain for?' the answer seems obvious. This may be a case of everything looking mysterious after a philosopher has stared at it for a while. |
| 23950 | Freud said passions are pressures of some flowing hydraulic quantity [Freud, by Solomon] |
| Full Idea: Freud argued that the passions in general …were the pressures of a yet unknown 'quantity' (which he simply designated 'Q'). He first thought this flowed through neurones, …and always couched the idea in the language of hydraulics. | |
| From: report of Sigmund Freud (works [1900]) by Robert C. Solomon - The Passions 3.4 | |
| A reaction: This is the main target of Solomon's criticism, because its imagery has become so widespread. It leads to talk of suppressing emotions, or sublimating them. However, it is not too different from Nietzsche's 'drives' or 'will to power'. |
| 22344 | Freud is pessimistic about human nature; it is ambivalent motive and fantasy, rather than reason [Freud, by Murdoch] |
| Full Idea: Freud takes a thoroughly pessimistic view of human nature. ...Introspection reveals only the deep tissue of ambivalent motive, and fantasy is a stronger force than reason. Objectivity and unselfishness are not natural to human beings. | |
| From: report of Sigmund Freud (works [1900], II) by Iris Murdoch - The Sovereignty of Good II | |
| A reaction: Interesting. His view seems to have coloured the whole of modern culture, reinforced by the hideous irrationality of the Nazis. Adorno and Horkheimer attacking the Enlightenment was the last step in that process. |
| 4189 | Time may be defined as the possibility of mutually exclusive conditions of the same thing [Schopenhauer] |
| Full Idea: Time may be defined as the possibility of mutually exclusive conditions of the same thing. | |
| From: Arthur Schopenhauer (Abstract of 'The Fourfold Root' [1813], Ch.IV) | |
| A reaction: An off-beat philosophical view of the question. Sounds more like a consequence of time than its essential nature. |