19 ideas
5300 | Philosophers have interpreted the world, but the point is to change it [Marx] |
Full Idea: The philosophers have only interpreted the world, in various ways; the point is to change it. | |
From: Karl Marx (Theses on Feuerbach [1846], §XI) | |
A reaction: The 'point' of what? Personally I am more with Aristotle - that the aim is to create a society in which we can all aspire to contemplate like gods. As an interim statement of aim, though, one must respect Marx. But was he a philosopher? |
5297 | Whether human thinking can be 'true' must be decided in practice, not theory [Marx] |
Full Idea: The question whether objective truth can be attributed to human thinking is not a question of theory but is a practical question; man must prove the truth of his thinking in practice. | |
From: Karl Marx (Theses on Feuerbach [1846], §II) | |
A reaction: This would appear to be an assertion of the pragmatic view of truth well before Peirce. The obvious objections arise, such as whether falsehood (Plato's 'noble lie') might not have equal practical success, and whether truth might be disastrous. |
8623 | Proof reveals the interdependence of truths, as well as showing their certainty [Euclid, by Frege] |
Full Idea: Euclid gives proofs of many things which anyone would concede to him without question. ...The aim of proof is not merely to place the truth of a proposition beyond doubt, but also to afford us insight into the dependence of truths upon one another. | |
From: report of Euclid (Elements of Geometry [c.290 BCE]) by Gottlob Frege - Grundlagen der Arithmetik (Foundations) §02 | |
A reaction: This connects nicely with Shoemaker's view of analysis (Idea 8559), which I will adopt as my general view. I've always thought of philosophy as the aspiration to wisdom through the cartography of concepts. |
13907 | If you pick an arbitrary triangle, things proved of it are true of all triangles [Euclid, by Lemmon] |
Full Idea: Euclid begins proofs about all triangles with 'let ABC be a triangle', but ABC is not a proper name. It names an arbitrarily selected triangle, and if that has a property, then we can conclude that all triangles have the property. | |
From: report of Euclid (Elements of Geometry [c.290 BCE]) by E.J. Lemmon - Beginning Logic 3.2 | |
A reaction: Lemmon adds the proviso that there must be no hidden assumptions about the triangle we have selected. You must generalise the properties too. Pick a triangle, any triangle, say one with three angles of 60 degrees; now generalise from it. |
6297 | Euclid's geometry is synthetic, but Descartes produced an analytic version of it [Euclid, by Resnik] |
Full Idea: Euclid's geometry is a synthetic geometry; Descartes supplied an analytic version of Euclid's geometry, and we now have analytic versions of the early non-Euclidean geometries. | |
From: report of Euclid (Elements of Geometry [c.290 BCE]) by Michael D. Resnik - Maths as a Science of Patterns One.4 | |
A reaction: I take it that the original Euclidean axioms were observations about the nature of space, but Descartes turned them into a set of pure interlocking definitions which could still function if space ceased to exist. |
9603 | An assumption that there is a largest prime leads to a contradiction [Euclid, by Brown,JR] |
Full Idea: Assume a largest prime, then multiply the primes together and add one. The new number isn't prime, because we assumed a largest prime; but it can't be divided by a prime, because the remainder is one. So only a larger prime could divide it. Contradiction. | |
From: report of Euclid (Elements of Geometry [c.290 BCE]) by James Robert Brown - Philosophy of Mathematics Ch.1 | |
A reaction: Not only a very elegant mathematical argument, but a model for how much modern logic proceeds, by assuming that the proposition is false, and then deducing a contradiction from it. |
9894 | A unit is that according to which each existing thing is said to be one [Euclid] |
Full Idea: A unit is that according to which each existing thing is said to be one. | |
From: Euclid (Elements of Geometry [c.290 BCE], 7 Def 1) | |
A reaction: See Frege's 'Grundlagen' §29-44 for a sustained critique of this. Frege is good, but there must be something right about the Euclid idea. If I count stone, paper and scissors as three, each must first qualify to be counted as one. Psychology creeps in. |
8738 | Postulate 2 says a line can be extended continuously [Euclid, by Shapiro] |
Full Idea: Euclid's Postulate 2 says the geometer can 'produce a finite straight line continuously in a straight line'. | |
From: report of Euclid (Elements of Geometry [c.290 BCE]) by Stewart Shapiro - Thinking About Mathematics 4.2 | |
A reaction: The point being that this takes infinity for granted, especially if you start counting how many points there are on the line. The Einstein idea that it might eventually come round and hit you on the back of the head would have charmed Euclid. |
22278 | Euclid relied on obvious properties in diagrams, as well as on his axioms [Potter on Euclid] |
Full Idea: Euclid's axioms were insufficient to derive all the theorems of geometry: at various points in his proofs he appealed to properties that are obvious from the diagrams but do not follow from the stated axioms. | |
From: comment on Euclid (Elements of Geometry [c.290 BCE]) by Michael Potter - The Rise of Analytic Philosophy 1879-1930 03 'aim' | |
A reaction: I suppose if the axioms of a system are based on self-evidence, this would licence an appeal to self-evidence elsewhere in the system. Only pedants insist on writing down what is obvious to everyone! |
8673 | Euclid's parallel postulate defines unique non-intersecting parallel lines [Euclid, by Friend] |
Full Idea: Euclid's fifth 'parallel' postulate says if there is an infinite straight line and a point, then there is only one straight line through the point which won't intersect the first line. This axiom is independent of Euclid's first four (agreed) axioms. | |
From: report of Euclid (Elements of Geometry [c.290 BCE]) by Michèle Friend - Introducing the Philosophy of Mathematics 2.2 | |
A reaction: This postulate was challenged in the nineteenth century, which was a major landmark in the development of modern relativist views of knowledge. |
10250 | Euclid needs a principle of continuity, saying some lines must intersect [Shapiro on Euclid] |
Full Idea: Euclid gives no principle of continuity, which would sanction an inference that if a line goes from the outside of a circle to the inside of circle, then it must intersect the circle at some point. | |
From: comment on Euclid (Elements of Geometry [c.290 BCE]) by Stewart Shapiro - Philosophy of Mathematics 6.1 n2 | |
A reaction: Cantor and Dedekind began to contemplate discontinuous lines. |
10302 | Euclid says we can 'join' two points, but Hilbert says the straight line 'exists' [Euclid, by Bernays] |
Full Idea: Euclid postulates: One can join two points by a straight line; Hilbert states the axiom: Given any two points, there exists a straight line on which both are situated. | |
From: report of Euclid (Elements of Geometry [c.290 BCE]) by Paul Bernays - On Platonism in Mathematics p.259 |
14157 | Modern geometries only accept various parts of the Euclid propositions [Russell on Euclid] |
Full Idea: In descriptive geometry the first 26 propositions of Euclid hold. In projective geometry the 1st, 7th, 16th and 17th require modification (as a straight line is not a closed series). Those after 26 depend on the postulate of parallels, so aren't assumed. | |
From: comment on Euclid (Elements of Geometry [c.290 BCE]) by Bertrand Russell - The Principles of Mathematics §388 |
1600 | Euclid's common notions or axioms are what we must have if we are to learn anything at all [Euclid, by Roochnik] |
Full Idea: The best known example of Euclid's 'common notions' is "If equals are subtracted from equals the remainders are equal". These can be called axioms, and are what "the man who is to learn anything whatever must have". | |
From: report of Euclid (Elements of Geometry [c.290 BCE], 72a17) by David Roochnik - The Tragedy of Reason p.149 |
22598 | The authentic self exists at the level of class, rather than the individual [Marx, by Dunt] |
Full Idea: Instead of focusing on the individual, Marxism suggested that the authentic self was at the social level in the form of class. | |
From: report of Karl Marx (Theses on Feuerbach [1846]) by Ian Dunt - How to be a Liberal 6 | |
A reaction: [not sure of the best source in Marx] This idea is expressed here by a defender of liberal individualism. Dunt persuasively attacks any concept of the self as part of some group, rather than as being an individual. |
7861 | Libet says the processes initiated in the cortex can still be consciously changed [Libet, by Papineau] |
Full Idea: Libet himself points out that the conscious decisions still have the power to 'endorse' or 'cancel', so to speak, the processes initiated by the earlier cortical activity: no action will result if the action's execution is consciously countermanded. | |
From: report of Benjamin Libet (Unconscious Cerebral Initiative [1985]) by David Papineau - Thinking about Consciousness 1.4 | |
A reaction: This is why Libet's findings do not imply 'epiphenomenalism'. It seems that part of a decisive action is non-conscious, undermining the all-or-nothing view of consciousness. Searle tries to smuggle in free will at this point (Idea 3817). |
6660 | Libet found conscious choice 0.2 secs before movement, well after unconscious 'readiness potential' [Libet, by Lowe] |
Full Idea: Libet found that a subject's conscious choice to move was about a fifth of a second before movement, and thus later than the onset of the brain's so-called 'readiness potential', which seems to imply that unconscious processes initiates action. | |
From: report of Benjamin Libet (Unconscious Cerebral Initiative [1985]) by E.J. Lowe - Introduction to the Philosophy of Mind Ch.9 | |
A reaction: Of great interest to philosophers! It seems to make conscious choices epiphenomenal. The key move, I think, is to give up the idea of consciousness as being all-or-nothing. My actions are still initiated by 'me', but 'me' shades off into unconsciousness. |
5298 | The human essence is not found in individuals but in social relations [Marx] |
Full Idea: The human essence is no abstraction inherent in each single individual; in its reality it is the ensemble of the social relations. | |
From: Karl Marx (Theses on Feuerbach [1846], §VI) | |
A reaction: This is a key Marxist doctrine, and the central difference from Aristotle. Personally I am more with Aristotle, but the truth obviously lies somewhere in between. Man must be a 'social being', or there wouldn't be any social relations. |
5299 | Religious feeling is social in origin [Marx] |
Full Idea: The "religious sentiment" (discussed by Feuerbach) is itself a social product. | |
From: Karl Marx (Theses on Feuerbach [1846], §VII) | |
A reaction: Recent brain research has identified a part of the brain which is only active during religious thought and experience. It is easy to produce cynical political accounts of religion, but in its time it was also quite a good scientific account of nature. |