35 ideas
| 2352 | The job of the philosopher is to distinguish facts about the world from conventions [Putnam] |
| Full Idea: It is the job of the philosopher to distinguish what is fact and what is convention in our theorising about the world. | |
| From: Hilary Putnam (Representation and Reality [1988], §7 p.112) | |
| A reaction: This may well be the entire truth about philosophy. It begins with the Nomos-Physis debate in ancient Athens, and it turns out to be the key issue in almost every area of metaphysics, epistemology, aesthetics and morality. |
| 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. |
| 2345 | Semantic notions do not occur in Tarski's definitions, but assessing their correctness involves translation [Putnam] |
| Full Idea: Although no semantic notions are used in Tarski's truth definitions themselves, they are used in deciding when such a definition is correct, namely the notion of translation. | |
| From: Hilary Putnam (Representation and Reality [1988], §4 p.66) |
| 2347 | Asserting the truth of an indexical statement is not the same as uttering the statement [Putnam] |
| Full Idea: If you say "I am going to drive this car", and I say "That's true", that is very different from my saying "I am going to drive this car". | |
| From: Hilary Putnam (Representation and Reality [1988], §4 p.68) |
| 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 |
| 19393 | What is not active is nothing [Leibniz] |
| Full Idea: We can now show from the inner truths of metaphysics that what is not active is nothing. | |
| From: Gottfried Leibniz (True Method in Philosophy and Theology [1686], p.64) | |
| A reaction: This is Leibniz's rebellion against the Cartesian idea that all that matters for natural existence is spatial extension. I agree (tentatively) with Leibniz's vision of nature here. Modern physics reveals a seething turmoil beneath the placid exterior. |
| 2349 | Realists believe truth is correspondence, independent of humans, is bivalent, and is unique [Putnam] |
| Full Idea: Metaphysical realism about truth is a bundle of ideas: that it is a matter of Correspondence, that it exhibits Independence (of humans), Bivalence, and Uniqueness (there is only one ultimate truth). | |
| From: Hilary Putnam (Representation and Reality [1988], §7 p.107) |
| 2351 | Aristotle says an object (e.g. a lamp) has identity if its parts stay together when it is moved [Putnam] |
| Full Idea: The parts of a lamp stay together when it is moved (which is one of Aristotle's criteria for objecthood). | |
| From: Hilary Putnam (Representation and Reality [1988], §7 p.110) | |
| A reaction: Metaphysics 1052a26 (just after the cross-reference) says a thing may be unified 'if its movement is single'. |
| 2331 | Functionalism says robots and people are the same at one level of abstraction [Putnam] |
| Full Idea: My "functionalism" insisted that a robot, a human being, a silicon creature and a disembodied spirit could all work much the same way when described at the relevant level of abstraction, and it is wrong to think the essence of mind is hardware. | |
| From: Hilary Putnam (Representation and Reality [1988], Int p.xii) | |
| A reaction: This is the key point about the theory - that it is an abstract theory of mind, saying nothing about substances. It drew, however, some misguided criticisms suggesting silly implementations. |
| 2071 | If concepts have external meaning, computational states won't explain psychology [Putnam] |
| Full Idea: Computational models of the brain/mind will not suffice for cognitive psychology. We cannot individuate concepts and beliefs without reference to the environment. Meanings aren't "in the head". | |
| From: Hilary Putnam (Representation and Reality [1988], p.73) | |
| A reaction: Mr Functionalism quits! |
| 2332 | Functionalism can't explain reference and truth, which are needed for logic [Putnam] |
| Full Idea: Functionalism has as much trouble with physical accounts of reference as of meaning. Reference is the main tool used in formal theories of truth. But 'truth' isn't folk psychology, it is central to logic, which everyone wants. | |
| From: Hilary Putnam (Representation and Reality [1988], Int p.xiv) | |
| A reaction: All logic is defined in terms of truth and falsehood resulting from reasoning, but it could be that 'true' and 'false' have no more content that 1 and 0 in binary electronics. They are distinct, but empty. |
| 2348 | Is there just one computational state for each specific belief? [Putnam] |
| Full Idea: The idea that there is one computational state that every being who believes that there are lots of cats in the neighbourhood is in must be false. | |
| From: Hilary Putnam (Representation and Reality [1988], §5 p.84) | |
| A reaction: It is tempting to say that the mental states of such people must have SOMETHING in common, until you realise that all you can specify is that all their states are about cats. |
| 2344 | If we are going to eliminate folk psychology, we must also eliminate folk logic [Putnam] |
| Full Idea: Why don't the eliminationists speak of "folk logic" as well as "folk psychology"? | |
| From: Hilary Putnam (Representation and Reality [1988], §4 p.60) | |
| A reaction: I think Putnam considers that if you can prove 'truth' to be a necessary feature of mental life, that connects mind and world, but marking a sentence as 'T' doesn't make any connections. |
| 2074 | Can we give a scientific, computational account of folk psychology? [Putnam] |
| Full Idea: The desire that grips Fodor, as it once gripped me, is the desire to make belief-desire psychology "scientific" by simply identifying it outright with computational psychology. | |
| From: Hilary Putnam (Representation and Reality [1988], p.7) | |
| A reaction: An "outright" identification looks very implausible. It seems that we should accept that belief-desire psychology is a very good guide to normal brain events, but a bad guide to unusual brain events. See Ideas 2987 and 7519. |
| 2343 | Reference may be different while mental representation is the same [Putnam] |
| Full Idea: The 'mental representations' of Earth speakers and Twin Earth speakers were not in any way different; the reference was different because the substances were different. Reference is fixed by the environment itself. | |
| From: Hilary Putnam (Representation and Reality [1988], §2 p.32) | |
| A reaction: There seems to be an elementary distinction here between what you think you are referring to, and what you are in fact referring to. "That man is the Prince of Wales" (pointing at the butler). |
| 2346 | Meaning and translation (which are needed to define truth) both presuppose the notion of reference [Putnam] |
| Full Idea: The notion of meaning, and hence of translation (needed to define truth), presupposes the notion of reference. | |
| From: Hilary Putnam (Representation and Reality [1988], §4 p.67) | |
| A reaction: It is plausible to see reference as the fundamental notion of language. With no anchors in reality, language would be 'private', in LW's sense. |
| 2354 | "Meaning is use" is not a definition of meaning [Putnam] |
| Full Idea: "Meaning is use" is not a definition of meaning. | |
| From: Hilary Putnam (Representation and Reality [1988], §7 p.119) | |
| A reaction: I agree. It probably fails to define meaning because it is false. A corkscrew is not the action of opening a wine bottle. |
| 2336 | Holism seems to make fixed definition more or less impossible [Putnam] |
| Full Idea: Holism immediately suggests that most terms cannot be defined, at least not in a way that is fixed once and for all. | |
| From: Hilary Putnam (Representation and Reality [1988], §1 p.09) | |
| A reaction: Perhaps there exists a single perfect definition for each holistic system, only graspable by a transcendent intellect. Or why can't there be a matching holistic system of definitions? |
| 2334 | Meaning holism tried to show that you can't get fixed meanings built out of observation terms [Putnam] |
| Full Idea: The doctrine of Quine called "meaning holism" offered arguments refuting logical positivist attempts to show that every term we can understand can be defined using a limited group of "observation terms". | |
| From: Hilary Putnam (Representation and Reality [1988], §1 p.08) | |
| A reaction: To seems a rather large jump from saying that sentences come in groups to full-blown 'holism' (involving every sentence). |
| 2335 | Understanding a sentence involves background knowledge and can't be done in isolation [Putnam] |
| Full Idea: If I say "Hawks fly", I do not intend my hearer to deduce that a hawk with a broken wing will fly. What we expect depends on the whole network of belief. Language describes experience as a network, not sentence by sentence. | |
| From: Hilary Putnam (Representation and Reality [1988], §1 p.09) | |
| A reaction: The shortcut through this is 'exactly what did you mean when you said "Hawks fly"?'. That is, get me closer to your proposition. |
| 2340 | We should separate how the reference of 'gold' is fixed from its conceptual content [Putnam] |
| Full Idea: The effect of my account, as of Kripke's, is to separate the question of how the reference of terms such as 'gold' is fixed from the question of their conceptual content. | |
| From: Hilary Putnam (Representation and Reality [1988], §2 p.38) | |
| A reaction: Too simple. 'Gold' isn't a proper name, like 'Hilary', which needs no more content than a serial number. Baptising a gold sample needs much more information than baptising a person. |
| 2341 | Like names, natural kind terms have their meaning fixed by extension and reference [Putnam] |
| Full Idea: It seems that the dominant "component" of natural kind words is the extension. The referential factor does almost all the work, and natural kind terms resemble names. | |
| From: Hilary Putnam (Representation and Reality [1988], §3 p.49) | |
| A reaction: My concept of 'tiger' does not mainly consist of the tigers. Does the concept contract as the tiger population dwindles? Prototypes, exemplars etc. See 'Concepts' |
| 2338 | Reference (say to 'elms') is a social phenomenon which we can leave to experts [Putnam] |
| Full Idea: Reference is a social phenomenon. Individual speakers do not have to know how to distinguish robins, or elms, or aluminium. They can always rely on experts to do this for them. | |
| From: Hilary Putnam (Representation and Reality [1988], §2 p.22) | |
| A reaction: It can't just be a social phenomenon. The experts don't just enquire about standard usage, or defer to Hilary Putnam. |
| 2339 | Aristotle implies that we have the complete concepts of a language in our heads, but we don't [Putnam] |
| Full Idea: What is wrong with the Aristotelian picture (of meaning and reference based on concepts) is that it suggest that everything that is necessary for the use of language is stored in each individual mind, but no individual language works this way. | |
| From: Hilary Putnam (Representation and Reality [1988], §2 p.25) | |
| A reaction: Languages must partly work that way. You can't talk without a conceptual storehouse. In a small society I would expect every adult to know the full vocabulary. |
| 2342 | "Water" is a natural kind term, but "H2O" is a description [Putnam] |
| Full Idea: "Water" functions as a natural kind term, but "H2O" is a description, synonymous with an account of its atoms. | |
| From: Hilary Putnam (Representation and Reality [1988], §3 p.50) |