42 ideas
3600 | Slow and accurate thought makes the greatest progress [Descartes] |
Full Idea: Those who go forward only very slowly can progress much further if they always keep to the right path, than those who run and wander off it. | |
From: René Descartes (A Discourse on Method [1637], §1.2) | |
A reaction: Like Descartes' 'Method'. This seems to place a low value on 'nous' or intuition. |
3601 | Most things in human life seem vain and useless [Descartes] |
Full Idea: Looking at the various activities and enterprises of mankind with the eye of a philosopher, there is hardly one which does not seem to me vain and useless. | |
From: René Descartes (A Discourse on Method [1637], §1.3) | |
A reaction: Well, yes. The obvious retort is that everything is vain and useless; or if not, then certainly metaphysics is. Useful for what? Is ornamental gardening useless, or sport? Art? What is the use of cosmology? He's right, of course. |
3602 | Almost every daft idea has been expressed by some philosopher [Descartes] |
Full Idea: There is nothing one can imagine so strange or so unbelievable that has not been said by one or other of the philosophers. | |
From: René Descartes (A Discourse on Method [1637], §2.16) | |
A reaction: Actually I think that extensive areas of logical possibilities for existence remain totally unexplored. On the other hand, most of the metaphysical beliefs of most of the human race, including the majority of philosophers, strike me as being false. |
3603 | Methodical thinking is cautious, analytical, systematic, and panoramic [Descartes, by PG] |
Full Idea: Descartes' four principles for his method of thinking are: be cautious, analyse the problem, be systematic from simple to complex, and keep an overview of the problem | |
From: report of René Descartes (A Discourse on Method [1637], §2.18) by PG - Db (ideas) |
19740 | A very hungry man cannot choose between equidistant piles of food [Aristotle] |
Full Idea: The man who, though exceedingly hungry and thirsty, and both equally, yet being equidistant from food and drink, is therefore bound to stay where he is. | |
From: Aristotle (On the Heavens [c.336 BCE], 296b33) | |
A reaction: This is, of course, Buridan's famous Ass, but this quotation has the advantage of precedence, and also of being expressed in an original quotation (which does not exist for Buridan). |
3612 | Clear and distinct conceptions are true because a perfect God exists [Descartes] |
Full Idea: That the things we grasp very clearly and very distinctly are all true, is assured only because God is or exists, and because he is a perfect Being. | |
From: René Descartes (A Discourse on Method [1637], §4.38) |
3610 | Truth is clear and distinct conception - of which it is hard to be sure [Descartes] |
Full Idea: I take it as a general rule that the things we conceive very clearly and very distinctly are all true, but that there is merely some difficulty in properly discerning which are those which we distinctly conceive. | |
From: René Descartes (A Discourse on Method [1637], §4.33) |
10282 | Logic is the study of sound argument, or of certain artificial languages (or applying the latter to the former) [Hodges,W] |
Full Idea: A logic is a collection of closely related artificial languages, and its older meaning is the study of the rules of sound argument. The languages can be used as a framework for studying rules of argument. | |
From: Wilfrid Hodges (First-Order Logic [2001], 1.1) | |
A reaction: [Hodges then says he will stick to the languages] The suspicion is that one might confine the subject to the artificial languages simply because it is easier, and avoids the tricky philosophical questions. That approximates to computer programming. |
10283 | A formula needs an 'interpretation' of its constants, and a 'valuation' of its variables [Hodges,W] |
Full Idea: To have a truth-value, a first-order formula needs an 'interpretation' (I) of its constants, and a 'valuation' (ν) of its variables. Something in the world is attached to the constants; objects are attached to variables. | |
From: Wilfrid Hodges (First-Order Logic [2001], 1.3) |
10284 | There are three different standard presentations of semantics [Hodges,W] |
Full Idea: Semantic rules can be presented in 'Tarski style', where the interpretation-plus-valuation is reduced to the same question for simpler formulas, or the 'Henkin-Hintikka style' in terms of games, or the 'Barwise-Etchemendy style' for computers. | |
From: Wilfrid Hodges (First-Order Logic [2001], 1.3) | |
A reaction: I haven't yet got the hang of the latter two, but I note them to map the territory. |
10285 | I |= φ means that the formula φ is true in the interpretation I [Hodges,W] |
Full Idea: I |= φ means that the formula φ is true in the interpretation I. | |
From: Wilfrid Hodges (First-Order Logic [2001], 1.5) | |
A reaction: [There should be no space between the vertical and the two horizontals!] This contrasts with |-, which means 'is proved in'. That is a syntactic or proof-theoretic symbol, whereas |= is a semantic symbol (involving truth). |
10288 | Down Löwenheim-Skolem: if a countable language has a consistent theory, that has a countable model [Hodges,W] |
Full Idea: Downward Löwenheim-Skolem (the weakest form): If L is a first-order language with at most countably many formulas, and T is a consistent theory in L. Then T has a model with at most countably many elements. | |
From: Wilfrid Hodges (First-Order Logic [2001], 1.10) |
10289 | Up Löwenheim-Skolem: if infinite models, then arbitrarily large models [Hodges,W] |
Full Idea: Upward Löwenheim-Skolem: every first-order theory with infinite models has arbitrarily large models. | |
From: Wilfrid Hodges (First-Order Logic [2001], 1.10) |
10287 | If a first-order theory entails a sentence, there is a finite subset of the theory which entails it [Hodges,W] |
Full Idea: Compactness Theorem: suppose T is a first-order theory, ψ is a first-order sentence, and T entails ψ. Then there is a finite subset U of T such that U entails ψ. | |
From: Wilfrid Hodges (First-Order Logic [2001], 1.10) | |
A reaction: If entailment is possible, it can be done finitely. |
10286 | A 'set' is a mathematically well-behaved class [Hodges,W] |
Full Idea: A 'set' is a mathematically well-behaved class. | |
From: Wilfrid Hodges (First-Order Logic [2001], 1.6) |
3605 | We can believe a thing without knowing we believe it [Descartes] |
Full Idea: The action of thought by which one believes a thing, being different from that by which one knows that one believes it, they often exist the one without the other. | |
From: René Descartes (A Discourse on Method [1637], §3.23) |
1583 | In morals Descartes accepts the conventional, but rejects it in epistemology [Roochnik on Descartes] |
Full Idea: Descartes' procedure for treating values (accepting normal conventions when faced with uncertainty) is the exact antithesis of that used to attain knowledge. | |
From: comment on René Descartes (A Discourse on Method [1637], §3.23) by David Roochnik - The Tragedy of Reason p.73 |
3607 | In thinking everything else false, my own existence remains totally certain [Descartes] |
Full Idea: While I decided to think that everything was false, it followed necessarily that I who thought thus must be something; the truth 'I think therefore I am' was so certain that the most extravagant scepticism could never shake it. | |
From: René Descartes (A Discourse on Method [1637], §4.32) |
3617 | I aim to find the principles and causes of everything, using the seeds within my mind [Descartes] |
Full Idea: I have tried to find in general the principles or first causes of everything which is or which may be in the world, ..without taking them from any other source than from certain seeds of truth which are naturally in our minds. | |
From: René Descartes (A Discourse on Method [1637], §6.64) |
3611 | Understanding, rather than imagination or senses, gives knowledge [Descartes] |
Full Idea: Neither our imagination nor our senses could ever assure us of anything, if our understanding did not intervene. | |
From: René Descartes (A Discourse on Method [1637], §4.37) |
3606 | I was searching for reliable rock under the shifting sand [Descartes] |
Full Idea: My whole plan had for its aim simply to give me assurance, and the rejection of shifting ground and sand in order to find rock or clay. | |
From: René Descartes (A Discourse on Method [1637], §3.29) | |
A reaction: I take this to be characteristic of an age when religion is being quietly rocked by the revival of ancient scepticism. If he'd settled for fallibilism, our civilization would have gone differently. |
3604 | When rebuilding a house, one needs alternative lodgings [Descartes] |
Full Idea: Before beginning to rebuild the house in which one lives…. one must also provide oneself with some other accommodation in which to be lodge conveniently while the work is going on. | |
From: René Descartes (A Discourse on Method [1637], §3.22) |
3618 | Only experiments can settle disagreements between rival explanations [Descartes] |
Full Idea: I observe almost no individual effect without immediately knowing that it can be deduced in many different ways, ..and I know of no way to resolve this but by experiments such that the results are different according to different explanations. | |
From: René Descartes (A Discourse on Method [1637], §6.65) |
3615 | Little reason is needed to speak, so animals have no reason at all [Descartes] |
Full Idea: Animals not only have less reason than men, but they have none at all; for we see that very little of it is required in order to be able to speak. | |
From: René Descartes (A Discourse on Method [1637], §5.58) |
3609 | I am a thinking substance, which doesn't need a place or material support [Descartes] |
Full Idea: I concluded that I was a substance, of which the whole essence or nature consists in thinking, and which, in order to exist, needs no place and depends on no material thing. | |
From: René Descartes (A Discourse on Method [1637], §4.33) | |
A reaction: To me that sounds like "I concluded that I wasn't a human being", which highlights the bizarre wishful thinking that seems to have gripped the human race for the first few thousand years of its serious thinking. |
3608 | I can deny my body and the world, but not my own existence [Descartes] |
Full Idea: I could pretend that I had no body, and that there was no world or place that I was in, but I could not, for all that, pretend that I did not exist. | |
From: René Descartes (A Discourse on Method [1637], §4.32) | |
A reaction: He makes the (in my opinion) appalling blunder of thinking that because he can pretend that he has no body, that therefore he might not have one. I can pretend that gold is an unusual form of cheese. However, "I don't exist" certainly sounds wrong. |
3613 | Reason is universal in its responses, but a physical machine is constrained by its organs [Descartes] |
Full Idea: Whereas reason is a universal instrument which can serve on any kind of occasion, the organs of a machine need a disposition for each action; so it is impossible to have enough different organs in a machine to respond to all the occurrences of life. | |
From: René Descartes (A Discourse on Method [1637], §5.57) | |
A reaction: How can Descartes know that reason is 'universal' rather than just 'very extensive'? Is there any information which cannot be encoded in a computer? It doesn't feel as if there any intrinsic restrictions to reason, but note Idea 4688. |
3616 | The soul must unite with the body to have appetites and sensations [Descartes] |
Full Idea: It is not sufficient that the reasonable soul should be lodged in the body like a pilot in a ship, unless perhaps to move its limbs, but it needs to be united more closely with the body in order to have sensations and appetites, and so be a true man. | |
From: René Descartes (A Discourse on Method [1637], §5.59) | |
A reaction: The idea that the pineal gland is the link suggests that Descartes has the 'pilot' view, but this idea shows that he believes in very close and complex interaction between mind and body. But how can a mind 'have' appetites if it has no physical needs? |
3614 | A machine could speak in response to physical stimulus, but not hold a conversation [Descartes] |
Full Idea: One may conceive of a machine made so as to emit words, and even emit them in response to a change in its bodily organs, such as being touched, but not to reply to the sense of everything said in its presence, as the most unintelligent men can. | |
From: René Descartes (A Discourse on Method [1637], §5.56) | |
A reaction: A critique of the Turing Test, written in 1637! You have to admire. Because of the advent of the microprocessor, we can 'conceive' more sophisticated, multi-level machines than Descartes could come up with. |
398 | Each thing that has a function is for the sake of that function [Aristotle] |
Full Idea: Each thing that has a function is for the sake of that function. | |
From: Aristotle (On the Heavens [c.336 BCE], 286a08) | |
A reaction: This is the central idea of Aristotle's Ethics. Did it originate with Plato, or Socrates, the young pupil Aristotle? I suspect the strong influence of Aristotle on later Plato. A major idea. Functions link the facts to life. |
1581 | Greeks elevate virtues enormously, but never explain them [Descartes] |
Full Idea: The ancient pagans place virtues on a high plateau and make them appear the most valuable thing in the world, but they do not sufficiently instruct us about how to know them. | |
From: René Descartes (A Discourse on Method [1637], §1.8) |
394 | An unworn sandal is in vain, but nothing in nature is in vain [Aristotle] |
Full Idea: We say of a sandal which is not worn that it is in vain; God and nature, however, do nothing in vain. | |
From: Aristotle (On the Heavens [c.336 BCE], 271a33) |
396 | There has to be some goal, and not just movement to infinity [Aristotle] |
Full Idea: There has to be some goal, and not just movement to infinity. | |
From: Aristotle (On the Heavens [c.336 BCE], 277a26) |
16102 | Aether moves in circles and is imperishable; the four elements perish, and move in straight lines [Aristotle, by Gill,ML] |
Full Idea: For Aristotle, aether and the four sublunary elements obey different physical laws. Aether moves naturally in a circle and, unlike its lower counterparts, is not a source of perishability. The four sublunary elements move naturally in straight lines. | |
From: report of Aristotle (On the Heavens [c.336 BCE]) by Mary Louise Gill - Aristotle on Substance Ch.2 | |
A reaction: I think it is anachronistic for Gill to talk of 'obeying' and 'laws'. She should have said that they have different 'natures'. We can be amused by Greek errors, until we stare hard at the problems they were trying to solve. |
17463 | An element is what bodies are analysed into, and won't itself divide into something else [Aristotle] |
Full Idea: An element is a body into which other bodies may be analyzed, present in them potentially or in actuality (which of these is still disputable), and not itself divisible into bodies different in form. That is what all men mean by element. | |
From: Aristotle (On the Heavens [c.336 BCE], 302a05), quoted by Weisberg/Needham/Hendry - Philosophy of Chemistry 1.1 | |
A reaction: This is the classic definition of an element, which endured for a long time, and has been replaced by an 'actual components' view. Obviously analysis nowadays goes well beyond the atoms. |
16686 | God has established laws throughout nature, and implanted ideas of them within us [Descartes] |
Full Idea: I have noticed certain laws that God has so established in nature, and of which he has implanted such notions in our souls, that …we cannot doubt that they are exactly observed in everything that exists or occurs in the world. | |
From: René Descartes (A Discourse on Method [1637], pt 5), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 15.5 | |
A reaction: This is the view of laws which still seems to be with us (and needs extirpating) - that some outside agency imposes them on nature. I suspect that even Richard Feynman thought of laws like that, because he despised philosophy, and was thus naïve. |
399 | If the more you raise some earth the faster it moves, why does the whole earth not move? [Aristotle] |
Full Idea: If you raise some earth and release it, it moves and won't stay put, and the more you raise it the faster it moves, so why does the whole earth not move? | |
From: Aristotle (On the Heavens [c.336 BCE], 294a12) |
20918 | Void is a kind of place, so it can't explain place [Aristotle] |
Full Idea: It is absurd to explain place by the void, as though this latter were not itself some kind of place. | |
From: Aristotle (On the Heavens [c.336 BCE], 309b24) | |
A reaction: Presumably this is aimed at Democritus. |
402 | The Earth must be spherical, because it casts a convex shadow on the moon [Aristotle] |
Full Idea: A lunar eclipse always has a convex dividing line, so, if it is eclipsed by the interposition of the earth, the circumference of the earth, being spherical, is responsible for the shape. | |
From: Aristotle (On the Heavens [c.336 BCE], 297b29) |
403 | The earth must be round and of limited size, because moving north or south makes different stars visible [Aristotle] |
Full Idea: Clearly the earth is round and not of great size, because when we move north or south we find that very different stars are visible. | |
From: Aristotle (On the Heavens [c.336 BCE], 297b30) |
1498 | Everyone agrees that the world had a beginning, but thinkers disagree over whether it will end [Aristotle] |
Full Idea: All thinkers agree that the world had a beginning, but some claim that, having come into existence, it is everlasting. | |
From: Aristotle (On the Heavens [c.336 BCE], 279b12) |
395 | It seems possible that there exists a limited number of other worlds apart from this one [Aristotle] |
Full Idea: One might indeed be puzzled whether, just as the world about us exists, nothing prevents there being others as well, certainly more than one, though not an unlimited number | |
From: Aristotle (On the Heavens [c.336 BCE], 274a26) |