20 ideas
| 21959 | Metaphysics is the most general attempt to make sense of things [Moore,AW] |
| Full Idea: Metaphysics is the most general attempt to make sense of things. | |
| From: A.W. Moore (The Evolution of Modern Metaphysics [2012], Intro) | |
| A reaction: This is the first sentence of Moore's book, and a touchstone idea all the way through. It stands up well, because it says enough without committing to too much. I have to agree with it. It implies explanation as the key. I like generality too. |
| 20744 | Phenomenologists say all experience is about something and is directed [Aho] |
| Full Idea: Phenomenologists agree that all experience has an intentional structure, that is, my experience is always about or of something; it is always directed towards an object. | |
| From: Kevin Aho (Existentialism: an introduction [2014], 2 'Phenomenology') | |
| A reaction: I am just beginning to grasp that the analytic debates about perception are a re-enactment of the Kantian debates about the thing-in-itself. This is the sort of idea you find in McDowell. Presumably the idea denies the Given, and raw sense-data. |
| 12456 | I aim to establish certainty for mathematical methods [Hilbert] |
| Full Idea: The goal of my theory is to establish once and for all the certitude of mathematical methods. | |
| From: David Hilbert (On the Infinite [1925], p.184) | |
| A reaction: This is the clearest statement of the famous Hilbert Programme, which is said to have been brought to an abrupt end by Gödel's Incompleteness Theorems. |
| 12461 | We believe all mathematical problems are solvable [Hilbert] |
| Full Idea: The thesis that every mathematical problem is solvable - we are all convinced that it really is so. | |
| From: David Hilbert (On the Infinite [1925], p.200) | |
| A reaction: This will include, for example, Goldbach's Conjecture (every even is the sum of two primes), which is utterly simple but with no proof anywhere in sight. |
| 9633 | No one shall drive us out of the paradise the Cantor has created for us [Hilbert] |
| Full Idea: No one shall drive us out of the paradise the Cantor has created for us. | |
| From: David Hilbert (On the Infinite [1925], p.191), quoted by James Robert Brown - Philosophy of Mathematics | |
| A reaction: This is Hilbert's famous refusal to accept any account of mathematics, such as Kant's, which excludes actual infinities. Cantor had laid out a whole glorious hierarchy of different infinities. |
| 12460 | We extend finite statements with ideal ones, in order to preserve our logic [Hilbert] |
| Full Idea: To preserve the simple formal rules of ordinary Aristotelian logic, we must supplement the finitary statements with ideal statements. | |
| From: David Hilbert (On the Infinite [1925], p.195) | |
| A reaction: I find very appealing the picture of mathematics as rooted in the physical world, and then gradually extended by a series of 'idealisations', which should perhaps be thought of as fictions. |
| 12462 | Only the finite can bring certainty to the infinite [Hilbert] |
| Full Idea: Operating with the infinite can be made certain only by the finitary. | |
| From: David Hilbert (On the Infinite [1925], p.201) | |
| A reaction: See 'Compactness' for one aspect of this claim. I think Hilbert was fighting a rearguard action, and his idea now has few followers. |
| 12455 | The idea of an infinite totality is an illusion [Hilbert] |
| Full Idea: Just as in the limit processes of the infinitesimal calculus, the infinitely large and small proved to be a mere figure of speech, so too we must realise that the infinite in the sense of an infinite totality, used in deductive methods, is an illusion. | |
| From: David Hilbert (On the Infinite [1925], p.184) | |
| A reaction: This is a very authoritative rearguard action. I no longer think the dispute matters much, it being just a dispute over a proposed new meaning for the word 'number'. |
| 12457 | There is no continuum in reality to realise the infinitely small [Hilbert] |
| Full Idea: A homogeneous continuum which admits of the sort of divisibility needed to realise the infinitely small is nowhere to be found in reality. | |
| From: David Hilbert (On the Infinite [1925], p.186) | |
| A reaction: He makes this remark as a response to Planck's new quantum theory (the year before the big works of Heisenberg and Schrödinger). Personally I don't see why infinities should depend on the physical world, since they are imaginary. |
| 12459 | The subject matter of mathematics is immediate and clear concrete symbols [Hilbert] |
| Full Idea: The subject matter of mathematics is the concrete symbols themselves whose structure is immediately clear and recognisable. | |
| From: David Hilbert (On the Infinite [1925], p.192) | |
| A reaction: I don't think many people will agree with Hilbert here. Does he mean token-symbols or type-symbols? You can do maths in your head, or with different symbols. If type-symbols, you have to explain what a type is. |
| 18112 | Mathematics divides in two: meaningful finitary statements, and empty idealised statements [Hilbert] |
| Full Idea: We can conceive mathematics to be a stock of two kinds of formulas: first, those to which the meaningful communications of finitary statements correspond; and secondly, other formulas which signify nothing and which are ideal structures of our theory. | |
| From: David Hilbert (On the Infinite [1925], p.196), quoted by David Bostock - Philosophy of Mathematics 6.1 |
| 9636 | My theory aims at the certitude of mathematical methods [Hilbert] |
| Full Idea: The goal of my theory is to establish once and for all the certitude of mathematical methods. | |
| From: David Hilbert (On the Infinite [1925], p.184), quoted by James Robert Brown - Philosophy of Mathematics Ch.5 | |
| A reaction: This dream is famous for being shattered by Gödel's Incompleteness Theorem a mere six years later. Neverless there seem to be more limited certainties which are accepted in mathematics. The certainty of the whole of arithmetic is beyond us. |
| 21958 | Appearances are nothing beyond representations, which is transcendental ideality [Moore,AW] |
| Full Idea: Appearances in general are nothing outside our representations, which is just what we mean by transcendental ideality. | |
| From: A.W. Moore (The Evolution of Modern Metaphysics [2012], B535/A507) |
| 20736 | Science has to abstract out the subjective attributes of things, focusing on what is objective [Aho] |
| Full Idea: Crucial to the scientific method is the ability to abstract out the subjective qualities that we give to things - such as beauty, meaning, purpose, and value - and focus only on the objective qualities of things, which can be measured and quantified. | |
| From: Kevin Aho (Existentialism: an introduction [2014], 1 'Emergence') | |
| A reaction: This seems to me exactly right. People who deny the primary/secondary distinction, like Hume, are usually correspondingly pessimistic about science. And Hume was wrong about that. |
| 20734 | Anxiety, nausea, guilt and absurdity shake us up, revealing our freedom and limits [Aho] |
| Full Idea: Some moods, such as 'anxiety' (Heidegger), 'nausea' (Sartre), 'guilt' (Kierkegaard), and 'absurdity' (Camus) are important because they have the capacity to shake us out of complacency and self-deception, disclosing our freedom and finitude. | |
| From: Kevin Aho (Existentialism: an introduction [2014], Pref 'What?) | |
| A reaction: [bit compressed] Problem: if I fail to feel such things, and deliberately induce them in myself, am I being inauthentic? Making a huge and unnatural effort to be an existentialist seems all wrong. And who wants the permanent grip of such feelings? |
| 20733 | Our 'existence' is how we create ourselves, unconstrained by any prior 'essence' [Aho] |
| Full Idea: 'Existence precedes essence' means there is no pre-given 'essence' that determines who and what we are. We are self-making beings. | |
| From: Kevin Aho (Existentialism: an introduction [2014], Pref 'What?) | |
| A reaction: This not a yes/no dilemma. Personally I believe (with Aristotle, and Steven Pinker) that there is a fairly comprehensive 'human nature' which we all share, and is the basis of ethics. On top of that, though, a fair bit of 'self-making' can go on. |
| 20753 | The self is constituted by its choices made within a social context [Aho] |
| Full Idea: The [existential] self is constituted by the continuous, open-ended process of choosing and pulling together the social interpretations that we care about and that are made available by the situation we grow into. | |
| From: Kevin Aho (Existentialism: an introduction [2014], 4 'Self') | |
| A reaction: These kind of explanations always seem wrong. That the self is influenced and moulded strongly by the choices it makes sounds right. But that the choices 'constitute' the chooser sounds like a bit of a muddle. |
| 20738 | Social contracts and markets have made society seem disconnected and artificial [Aho] |
| Full Idea: Modern society has come to be viewed as something artificial, an aggregate of disconnected individuals that is held together by instrumental social contracts and monetary exchanges. | |
| From: Kevin Aho (Existentialism: an introduction [2014], 1 'Emergence') | |
| A reaction: This is all long of you, Thomas Hobbes! Aho is explaining the rebellion of existentialists against this - though existentialism strikes me as another variant of liberal individualism. |
| 20737 | Protestantism brought the modern emphasis on inner states of the soul [Aho] |
| Full Idea: An important development in the formation of the modern worldview was the emergence of Protestantism, that reconfigured the self by privileging the inner states of the soul. Salvation concerns inner feelings, thoughts and desires, which can be genuine. | |
| From: Kevin Aho (Existentialism: an introduction [2014], 1 'Emergence') | |
| A reaction: [bit compressed] He is preparing the historical background for the existentialist concept of authenticity. We can link this Protestant idea with Descartes's Cogito, which grounds knowledge in the inner self. |
| 20766 | Four Noble Truths: life is suffering, caused by attachment, it is avoidable, there is a path [Aho] |
| Full Idea: The teachings of the Buddha are summarised in 'four noble truths': 1) life means suffering, 2) the origin of suffering is attachment, 3) the end of suffering is attainable, and 4) the path to the end of suffering. | |
| From: Kevin Aho (Existentialism: an introduction [2014], 9 'dukkha') | |
| A reaction: 1) and 2) summarise everything I dislike about most eastern philosophy. In the modern world life does not have to be suffering. To break off attachments in order to avoid suffering is a hideous injunction. |