| 3342 | Seeing that only one parallel can be drawn to a line through a given point is clearly synthetic a priori [Kant, by Benardete,JA] |
| Full Idea: Kant took Euclidean geometry to be an obvious source of synthetic a prior truths, as one can just see that through a point outside a straight line one and only one parallel to it can be drawn. | |
| From: report of Immanuel Kant (Critique of Pure Reason [1781]) by José A. Benardete - Metaphysics: the logical approach Ch.18 |
| 20943 | Kant bases the synthetic a priori on the categories of oneness and manyness [Kant, by Bowie] |
| Full Idea: The categories of oneness and manyness are the basis of what Kant terms 'synthetic judgements a priori'. | |
| From: report of Immanuel Kant (Critique of Pure Reason [1781]) by Andrew Bowie - Introduction to German Philosophy 1 'First' | |
| A reaction: This is a solution to the paradoxes of one and many that bothered Plato. I think it is best seen in our capacity to count things, and the individuation which must precede that. Atomism and holism. |
| 5402 | Kant showed that we have a priori knowledge which is not purely analytic [Kant, by Russell] |
| Full Idea: Kant deserves credit for showing that we have a priori knowledge which is not purely 'analytic', i.e. such that the opposite would be self-contradictory. | |
| From: report of Immanuel Kant (Critique of Pure Reason [1781]) by Bertrand Russell - Problems of Philosophy Ch. 8 | |
| A reaction: It is noteworthy that a great empiricist philosopher makes this judgement. But how do you spot an a priori truth, apart from seeing that its opposite would be a contradiction? Where else can its force come from? |
| 5203 | We can think of 7 and 5 without 12, but it is still a contradiction to deny 7+5=12 [Ayer on Kant] |
| Full Idea: From the fact that one can think of the sum of seven and five without necessarily thinking of twelve, it by no means follows that the proposition '7+5=12' can be denied without self-contradiction. | |
| From: comment on Immanuel Kant (Critique of Pure Reason [1781]) by A.J. Ayer - Language,Truth and Logic Ch.4 | |
| A reaction: Kant's claim that arithmetic was synthetic always looked glib and dubious, and this pinpoints an objection very nicely. It appears that the great Kant has confused his epistemology with his ontology. |
| 5527 | That a straight line is the shortest is synthetic, as straight does not imply any quantity [Kant] |
| Full Idea: That the straight line between two points is the shortest is a synthetic proposition. For my concept of the straight contains nothing of quantity, but only a quality. The concept of shortest is additional, and cannot be extracted by analysis. | |
| From: Immanuel Kant (Critique of Pure Reason [1781], B016) | |
| A reaction: We should ask Kant to define 'straight' without mentioning 'shortest'. If you think of a long walk between two towns, it becomes obvious that the straight line will be defined by being the shortest line. |
| 5528 | That force and counter-force are equal is necessary, and a priori synthetic [Kant] |
| Full Idea: In the proposition that in all communication of motion effect and counter-effect must always be equal, not only the necessity, and thus its a priori origin, but also that it is a synthetic proposition is clear. | |
| From: Immanuel Kant (Critique of Pure Reason [1781], B017) | |
| A reaction: No, I don't follow that. God might have made Newton's Third Law that every time you push a wall it pushes you back with double force. Looks like a Humean a posteriori observation of regularity to me. |
| 5529 | The real problem of pure reason is: how are a priori synthetic judgments possible? [Kant] |
| Full Idea: The real problem of pure reason is contained in the question: How are synthetic judgments a priori possible? | |
| From: Immanuel Kant (Critique of Pure Reason [1781], B019) | |
| A reaction: If they are possible, I would say that is not 'the real problem of pure reason', but the real problem of understanding the underlying nature of reality. I doubt whether we know much of reality by 'pure' reason, but we might 'see' that it is necessary. |
| 5537 | That two lines cannot enclose a space is an intuitive a priori synthetic proposition [Kant] |
| Full Idea: The proposition that with two straight lines no space can be enclosed cannot be derived from the concept of straight lines and the number two. You are forced to take refuge in intuition, ..which is a pure a priori intuition of a synthetic proposition. | |
| From: Immanuel Kant (Critique of Pure Reason [1781], B065/A47) | |
| A reaction: A very nice example. If you gave a child two rods and told them to make a shape, they might quickly learn this from experience. Kant's proposal is nice, but I am not convinced. We learn that to create shapes you must turn corners. |
| 5546 | Are a priori concepts necessary as a precondition for something to be an object? [Kant] |
| Full Idea: The question is whether a priori concepts precede, as conditions under which alone something can be, if not intuited, nevertheless thought as objects in general. | |
| From: Immanuel Kant (Critique of Pure Reason [1781], B125/A93) | |
| A reaction: This remains a good question. Some sort of synthesis of impressions is required in order to perceive an object. To think of it as a rational inference seems wildly wrong, as it is instantaneous. How do dogs get along, I wonder…. |
| 5558 | 7+5=12 is not analytic, because 12 is not contained in 7 or 5 or their combination [Kant] |
| Full Idea: 7+5=12 is not an analytic proposition, for I do not think the number 12 either in the representation of 7 nor in that of 5 nor in the representation of the combination of the two. | |
| From: Immanuel Kant (Critique of Pure Reason [1781], B205/A164) | |
| A reaction: Unconvincing. The third option sounds analytic. Present it as: if you start at 7 and move 5 places along the natural number sequence, you have arrived at the answer (so find out its name). Or rename '12' as 'sevenplusfive'? |
| 5624 | We possess synthetic a priori knowledge in our principles which anticipate experience [Kant] |
| Full Idea: We are already in possession of synthetic a priori cognition, as is established by the principles of understanding, which anticipate experience. | |
| From: Immanuel Kant (Critique of Pure Reason [1781], B790/A762) | |
| A reaction: When put like this, I remain unconvinced that the mental states to which Kant refers should actually qualify as cognition/knowledge. If we have to look through rose-tinted spectacles, this doesn't make rose-colour a truth, or even a belief. |
| 3726 | The categorical imperative is a practical synthetic a priori proposition [Kant] |
| Full Idea: With the categorical imperative or law of morality we have a very serious difficulty, because it is a synthetic a priori practical proposition. | |
| From: Immanuel Kant (Groundwork of the Metaphysic of Morals [1785], 420.50) |
| 16916 | A priori synthetic knowledge is only of appearances, not of things in themselves [Kant] |
| Full Idea: Through intuition we can only know objects as they appear to us (to our senses), not as they may be in themselves; and this presupposition is absolutely necessary if synthetic propositions a priori are to be granted as possible. | |
| From: Immanuel Kant (Prolegomena to Any Future Metaphysic [1781], 283) | |
| A reaction: This idea is basic to understanding Kant, and especially his claim that arithmetic is a priori synthetic. |
| 9225 | Hegel reputedly claimed to know a priori that there are five planets [Hegel, by Field,H] |
| Full Idea: Hegel is reputed to have claimed to have deduced on a priori grounds that the number of planets is exactly five. | |
| From: report of Georg W.F.Hegel (works [1812]) by Hartry Field - Recent Debates on the A Priori 1 | |
| A reaction: Even if this is a wicked travesty of Hegel, it will do nicely to represent the extremes of claims to a priori synthetic knowledge. Field doesn't offer any evidence. I would love it to be true. |
| 23500 | My main problem is the order of the world, and whether it is knowable a priori [Wittgenstein] |
| Full Idea: The great problem around which everything turns that I write is: is there an order in the world a priori, and if so what does it consist in? | |
| From: Ludwig Wittgenstein (Notebooks 1914-1916 [1915], 15.06.01) | |
| A reaction: Morris identifies this as a 'Kantian question'. I trace it back to stoicism. This question has never bothered me. It just seems weird to think that you can infer reality from the examination of your own thinking. Perhaps I should take it more seriously? |
| 23479 | The Tractatus aims to reveal the necessities, without appealing to synthetic a priori truths [Wittgenstein, by Morris,M] |
| Full Idea: We can see the 'Tractatus' as an attempt to make sense of what is necessarily true of the world - in general, and not just in the mathematical case - without appealing to synthetic a priori truths. | |
| From: report of Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921]) by Michael Morris - Guidebook to Wittgenstein's Tractatus 2H | |
| A reaction: Morris sees the Tractatus as firmly in the Kantian tradition, and exploring Kant's main project in the first Critique. |
| 23501 | There is no a priori order of things [Wittgenstein] |
| Full Idea: Whatever we can describe at all could be other than it is. There is no a priori order of things. | |
| From: Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 5.634) | |
| A reaction: This is his rejection of Kant's dream, of inferring truths about the world by self-examination. However, compare Idea 23495. He clings to the faith that logic reveals 'something' about reality. |
| 2619 | Whether geometry can be applied to reality is an empirical question outside of geometry [Ayer] |
| Full Idea: Whether a geometry can be applied to the actual physical world or not, is an empirical question which falls outside the scope of the geometry itself. | |
| From: A.J. Ayer (Language,Truth and Logic [1936], Ch.4) | |
| A reaction: This is a key objection to rationalism by empiricists. You may say that geometry applies to your car, but your car may have been pulverised while you were talking. Why, though, did Einstein find non-Euclidean geometry so useful? |
| 2513 | We don't have a clear enough sense of meaning to pronounce some sentences meaningless or just analytic [Katz] |
| Full Idea: Linguistic meaning is not rich enough to show either that all metaphysical sentences are meaningless or that all alleged synthetic a priori propositions are just analytic a priori propositions. | |
| From: Jerrold J. Katz (Realistic Rationalism [2000], Int.xx) |
| 2794 | Knowing that a cow is not a horse seems to be a synthetic a priori truth [Dancy,J] |
| Full Idea: The fact that a cow is not a horse is a candidate for a priori synthetic truth. It doesn't seem to be analytic, because you can know what a cow is without knowing what a horse is. | |
| From: Jonathan Dancy (Intro to Contemporary Epistemology [1985], 14.3) |
| 3341 | Logical positivism amounts to no more than 'there is no synthetic a priori' [Benardete,JA] |
| Full Idea: Logical positivism has been concisely summarised as 'there is no synthetic a priori'. | |
| From: José A. Benardete (Metaphysics: the logical approach [1989], Ch.18) |
| 3344 | Assertions about existence beyond experience can only be a priori synthetic [Benardete,JA] |
| Full Idea: No one thinks that the proposition that something exists that transcends all possible experience harbours a logical inconsistency. Its denial cannot therefore be an analytic proposition, so it must be synthetic, though only knowable on a priori grounds. | |
| From: José A. Benardete (Metaphysics: the logical approach [1989], Ch.18) |
| 3345 | Appeals to intuition seem to imply synthetic a priori knowledge [Benardete,JA] |
| Full Idea: Appeals to intuition - no matter how informal - can hardly fail to smack of the synthetic a priori. | |
| From: José A. Benardete (Metaphysics: the logical approach [1989], Ch.18) |
| 3349 | If we know truths about prime numbers, we seem to have synthetic a priori knowledge of Platonic objects [Benardete,JA] |
| Full Idea: Assume that we know to be true propositions of the form 'There are exactly x prime numbers between y and z', and synthetic a priori truths about Platonic objects are delivered to us on a silver platter. | |
| From: José A. Benardete (Metaphysics: the logical approach [1989], Ch.18) |
| 3887 | Maybe our knowledge of truth and causation is synthetic a priori [Scruton] |
| Full Idea: 'Every event has a cause' and 'truth is correspondence to facts' are candidates for being synthetic a priori knowledge. | |
| From: Roger Scruton (Modern Philosophy:introduction and survey [1994], 13.2) |
| 3876 | If my team is losing 3-1, I have synthetic a priori knowledge that they need two goals for a draw [PG] |
| Full Idea: If my football team is losing 3-1, I seem to have synthetic a priori knowledge that they need two goals to achieve a draw | |
| From: PG (Db (ideas) [2031]) |