30 ideas
| 2945 | Most philosophers start with reality and then examine knowledge; Descartes put the study of knowledge first [Lehrer] |
| Full Idea: Some philosophers (e.g Plato) begin with an account of reality, and then appended an account of how we can know it, ..but Descartes turned the tables, insisting that we must first decide what we can know. | |
| From: Keith Lehrer (Theory of Knowledge (2nd edn) [2000], I p.2) |
| 2946 | You cannot demand an analysis of a concept without knowing the purpose of the analysis [Lehrer] |
| Full Idea: An analysis is always relative to some objective. It makes no sense to simply demand an analysis of goodness, knowledge, beauty or truth, without some indication of the purpose of the analysis. | |
| From: Keith Lehrer (Theory of Knowledge (2nd edn) [2000], I p.7) | |
| A reaction: Your dismantling of a car will go better if you know what a car is for, but you can still take it apart in ignorance. |
| 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 |
| 16554 | Activities have place, rate, duration, entities, properties, modes, direction, polarity, energy and range [Machamer/Darden/Craver] |
| Full Idea: Activities can be identified spatiotemporally, and individuated by rate, duration, and types of entity and property that engage in them. They also have modes of operation, directionality, polarity, energy requirements and a range. | |
| From: Machamer,P/Darden,L/Craver,C (Thinking About Mechanisms [2000], 3) | |
| A reaction: This is their attempt at making 'activity' one of the two central concepts of ontology, along with 'entity'. A helpful analysis. It just seems to be one way of slicing the cake. |
| 16556 | Penicillin causes nothing; the cause is what penicillin does [Machamer/Darden/Craver] |
| Full Idea: It is not the penicillin that causes the pneumonia to disappear, but what the penicillin does. | |
| From: Machamer,P/Darden,L/Craver,C (Thinking About Mechanisms [2000], 3.1) | |
| A reaction: This is a very neat example for illustrating how we slip into 'entity' talk, when the reality we are addressing actually concerns processes. Without the 'what it does', penicillin can't participate in causation at all. |
| 16562 | We understand something by presenting its low-level entities and activities [Machamer/Darden/Craver] |
| Full Idea: The intelligibility of a phenomenon consists in the mechanisms being portrayed in terms of a field's bottom out entities and activities. | |
| From: Machamer,P/Darden,L/Craver,C (Thinking About Mechanisms [2000], 7) | |
| A reaction: In other words, we understand complex things by reducing them to things we do understand. It would, though, be illuminating to see a nest of interconnected activities, even if we understood none of them. |
| 9329 | Justification is coherence with a background system; if irrefutable, it is knowledge [Lehrer] |
| Full Idea: Justification is coherence with a background system which, when irrefutable, converts to knowledge. | |
| From: Keith Lehrer (Consciousness,Represn, and Knowledge [2006]) | |
| A reaction: A problem (as the theory stands here) would be whether you have to be aware that the coherence is irrefutable, which would seem to require a pretty powerful intellect. If one needn't be aware of the irrefutability, how does it help my justification? |
| 16563 | The explanation is not the regularity, but the activity sustaining it [Machamer/Darden/Craver] |
| Full Idea: It is not regularities that explain but the activities that sustain the regularities. | |
| From: Machamer,P/Darden,L/Craver,C (Thinking About Mechanisms [2000], 7) | |
| A reaction: Good, but we had better not characterise the 'activities' in terms of regularities. |
| 16555 | Functions are not properties of objects, they are activities contributing to mechanisms [Machamer/Darden/Craver] |
| Full Idea: It is common to speak of functions as properties 'had by' entities, …but they should rather be understood in terms of the activities by virtue of which entities contribute to the workings of a mechanism. | |
| From: Machamer,P/Darden,L/Craver,C (Thinking About Mechanisms [2000], 3) | |
| A reaction: I'm certainly quite passionately in favour of cutting down on describing the world almost entirely in terms of entities which have properties. An 'activity', though, is a bit of an elusive concept. |
| 16528 | Mechanisms are not just push-pull systems [Machamer/Darden/Craver] |
| Full Idea: One should not think of mechanisms as exclusively mechanical (push-pull) systems. | |
| From: Machamer,P/Darden,L/Craver,C (Thinking About Mechanisms [2000], 1) | |
| A reaction: The difficulty seems to be that you could broaden the concept of 'mechanism' indefinitely, so that it covered history, mathematics, populations, cultural change, and even mathematics. Where to stop? |
| 16529 | Mechanisms are systems organised to produce regular change [Machamer/Darden/Craver] |
| Full Idea: Mechanisms are entities and activities organized such that they are productive of regular change from start or set-up to finish or termination conditions. | |
| From: Machamer,P/Darden,L/Craver,C (Thinking About Mechanisms [2000], 1) | |
| A reaction: This is their initial formal definition of a mechanism. Note that a mere 'activity' can be included. Presumably the mechanism might have an outcome that was not the intended outcome. Does a random element disqualify it? Are hands mechanisms? |
| 16530 | A mechanism explains a phenomenon by showing how it was produced [Machamer/Darden/Craver] |
| Full Idea: To give a description of a mechanism for a phenomenon is to explain that phenomenon, i.e. to explain how it was produced. | |
| From: Machamer,P/Darden,L/Craver,C (Thinking About Mechanisms [2000], 1) | |
| A reaction: To 'show how' something happens needs a bit of precisification. It is probably analytic that 'showing how' means 'revealing the mechanism', though 'mechanism' then becomes the tricky concept. |
| 16553 | Our account of mechanism combines both entities and activities [Machamer/Darden/Craver] |
| Full Idea: We emphasise the activities in mechanisms. This is explicitly dualist. Substantivalists speak of entities with dispositions to act. Process ontologists reify activities and try to reduce entities to processes. We try to capture both intuitions. | |
| From: Machamer,P/Darden,L/Craver,C (Thinking About Mechanisms [2000], 3) | |
| A reaction: [A quotation of selected fragments] The problem here seems to be the raising of an 'activity' to a central role in ontology, when it doesn't seem to be primitive, and will typically be analysed in a variety of ways. |
| 16559 | Descriptions of explanatory mechanisms have a bottom level, where going further is irrelevant [Machamer/Darden/Craver] |
| Full Idea: Nested hierachical descriptions of mechanisms typically bottom out in lowest level mechanisms. …Bottoming out is relative …the explanation comes to an end, and description of lower-level mechanisms would be irrelevant. | |
| From: Machamer,P/Darden,L/Craver,C (Thinking About Mechanisms [2000], 5.1) | |
| A reaction: This seems to me exactly the right story about mechanism, and it is a story I am associating with essentialism. The relevance is ties to understanding. The lower level is either fully understood, or totally baffling. |
| 16564 | There are four types of bottom-level activities which will explain phenomena [Machamer/Darden/Craver] |
| Full Idea: There are four bottom-out kinds of activities: geometrico-mechanical, electro-chemical, electro-magnetic and energetic. These are abstract means of production that can be fruitfully applied in particular cases to explain phenomena. | |
| From: Machamer,P/Darden,L/Craver,C (Thinking About Mechanisms [2000], 7) | |
| A reaction: I like that. It gives a nice core for a metaphysics for physicalists. I suspect that 'mechanical' can be reduced to something else, and that 'energetic' will disappear in the final story. |
| 16561 | We can abstract by taking an exemplary case and ignoring the detail [Machamer/Darden/Craver] |
| Full Idea: Abstractions may be constructed by taking an exemplary case or instance and removing detail. | |
| From: Machamer,P/Darden,L/Craver,C (Thinking About Mechanisms [2000], 5.3) | |
| A reaction: I love 'removing detail'. That's it. Simple. I think this process is the basis of our whole capacity to formulate abstract concepts. Forget Frege - he's just describing the results of the process. How do we decide what is 'detail'? Essentialism! |
| 9330 | Generalization seems to be more fundamental to minds than spotting similarities [Lehrer] |
| Full Idea: There is a level of generalization we share with other animals in the responses to objects that suggest that generalization is a more fundamental operation of the mind than the observation of similarities. | |
| From: Keith Lehrer (Consciousness,Represn, and Knowledge [2006]) | |
| A reaction: He derives this from Reid (1785) - Lehrer's hero - who argued against Hume that we couldn't spot similarities if we hadn't already generalized to produce the 'respect' of the similarity. Interesting. I think Reid must be right. |
| 9328 | All conscious states can be immediately known when attention is directed to them [Lehrer] |
| Full Idea: I am inclined to think that all conscious states can be immediately known when attention is directed to them. | |
| From: Keith Lehrer (Consciousness,Represn, and Knowledge [2006]) | |
| A reaction: This strikes me as a very helpful suggestion, for eliminating lots of problem cases for introspective knowledge which have been triumphally paraded in recent times. It might, though, be tautological, if it is actually a definition of 'conscious states'. |
| 16558 | Laws of nature have very little application in biology [Machamer/Darden/Craver] |
| Full Idea: The traditional notion of a law of nature has few, if any, applications in neurobiology or molecular biology. | |
| From: Machamer,P/Darden,L/Craver,C (Thinking About Mechanisms [2000], 3.2) | |
| A reaction: This is a simple and self-evident fact, and bad news for anyone who want to build their entire ontology around laws of nature. I take such a notion to be fairly empty, except as a convenient heuristic device. |