48 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. |
| 13917 | Metaphysics aims to identify categories of being, and show their interdependency [Lowe] |
| Full Idea: The central task of metaphysics is to chart the possibilities of existence by identifying the categories of being and the relations of ontological dependency in which beings of different categories stand to one another. | |
| From: E.J. Lowe (Two Notions of Being: Entity and Essence [2008], Intro) | |
| A reaction: I am beginning to think that he is right about the second one, and that dependency and grounding relations are the name of the game. I don't have Lowe's confidence that philosophers can parcel up reality in neat and true ways. |
| 13919 | Philosophy aims not at the 'analysis of concepts', but at understanding the essences of things [Lowe] |
| Full Idea: The central task of philosophy is the cultivation of insights into natures or essences, and not the 'analysis of concepts', with which it is apt to be confused. | |
| From: E.J. Lowe (Two Notions of Being: Entity and Essence [2008], 1) | |
| A reaction: This immediately strikes me as a false dichotomy. I like the idea of trying to understand the true natures of things, but how are we going to do it in our armchairs? |
| 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) |
| 16877 | A 'constructive' (as opposed to 'analytic') definition creates a new sign [Frege] |
| Full Idea: We construct a sense out of its constituents and introduce an entirely new sign to express this sense. This may be called a 'constructive definition', but we prefer to call it a 'definition' tout court. It contrasts with an 'analytic' definition. | |
| From: Gottlob Frege (Logic in Mathematics [1914], p.210) | |
| A reaction: An analytic definition is evidently a deconstruction of a past constructive definition. Fregean definition is a creative activity. |
| 11219 | Frege suggested that mathematics should only accept stipulative definitions [Frege, by Gupta] |
| Full Idea: Frege has defended the austere view that, in mathematics at least, only stipulative definitions should be countenanced. | |
| From: report of Gottlob Frege (Logic in Mathematics [1914]) by Anil Gupta - Definitions 1.3 | |
| A reaction: This sounds intriguingly at odds with Frege's well-known platonism about numbers (as sets of equinumerous sets). It makes sense for other mathematical concepts. |
| 16878 | We must be clear about every premise and every law used in a proof [Frege] |
| Full Idea: It is so important, if we are to have a clear insight into what is going on, for us to be able to recognise the premises of every inference which occurs in a proof and the law of inference in accordance with which it takes place. | |
| From: Gottlob Frege (Logic in Mathematics [1914], p.212) | |
| A reaction: Teachers of logic like natural deduction, because it reduces everything to a few clear laws, which can be stated at each step. |
| 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) |
| 16867 | Logic not only proves things, but also reveals logical relations between them [Frege] |
| Full Idea: A proof does not only serve to convince us of the truth of what is proved: it also serves to reveal logical relations between truths. Hence we find in Euclid proofs of truths that appear to stand in no need of proof because they are obvious without one. | |
| From: Gottlob Frege (Logic in Mathematics [1914], p.204) | |
| A reaction: This is a key idea in Frege's philosophy, and a reason why he is the founder of modern analytic philosophy, with logic placed at the centre of the subject. I take the value of proofs to be raising questions, more than giving answers. |
| 16863 | Does some mathematical reasoning (such as mathematical induction) not belong to logic? [Frege] |
| Full Idea: Are there perhaps modes of inference peculiar to mathematics which …do not belong to logic? Here one may point to inference by mathematical induction from n to n+1. | |
| From: Gottlob Frege (Logic in Mathematics [1914], p.203) | |
| A reaction: He replies that it looks as if induction can be reduced to general laws, and those can be reduced to logic. |
| 16862 | The closest subject to logic is mathematics, which does little apart from drawing inferences [Frege] |
| Full Idea: Mathematics has closer ties with logic than does almost any other discipline; for almost the entire activity of the mathematician consists in drawing inferences. | |
| From: Gottlob Frege (Logic in Mathematics [1914], p.203) | |
| A reaction: The interesting question is who is in charge - the mathematician or the logician? |
| 16865 | 'Theorems' are both proved, and used in proofs [Frege] |
| Full Idea: Usually a truth is only called a 'theorem' when it has not merely been obtained by inference, but is used in turn as a premise for a number of inferences in the science. ….Proofs use non-theorems, which only occur in that proof. | |
| From: Gottlob Frege (Logic in Mathematics [1914], p.204) |
| 16866 | Tracing inference backwards closes in on a small set of axioms and postulates [Frege] |
| Full Idea: We can trace the chains of inference backwards, …and the circle of theorems closes in more and more. ..We must eventually come to an end by arriving at truths can cannot be inferred, …which are the axioms and postulates. | |
| From: Gottlob Frege (Logic in Mathematics [1914], p.204) | |
| A reaction: The rival (more modern) view is that that all theorems are equal in status, and axioms are selected for convenience. |
| 16868 | The essence of mathematics is the kernel of primitive truths on which it rests [Frege] |
| Full Idea: Science must endeavour to make the circle of unprovable primitive truths as small as possible, for the whole of mathematics is contained in this kernel. The essence of mathematics has to be defined by this kernel of truths. | |
| From: Gottlob Frege (Logic in Mathematics [1914], p.204-5) | |
| A reaction: [compressed] I will make use of this thought, by arguing that mathematics may be 'explained' by this kernel. |
| 16871 | A truth can be an axiom in one system and not in another [Frege] |
| Full Idea: It is possible for a truth to be an axiom in one system and not in another. | |
| From: Gottlob Frege (Logic in Mathematics [1914], p.205) | |
| A reaction: Frege aspired to one huge single system, so this is a begrudging concession, one which modern thinkers would probably take for granted. |
| 16870 | Axioms are truths which cannot be doubted, and for which no proof is needed [Frege] |
| Full Idea: The axioms are theorems, but truths for which no proof can be given in our system, and no proof is needed. It follows from this that there are no false axioms, and we cannot accept a thought as an axiom if we are in doubt about its truth. | |
| From: Gottlob Frege (Logic in Mathematics [1914], p.205) | |
| A reaction: He struggles to be as objective as possible, but has to concede that whether we can 'doubt' the axiom is one of the criteria. |
| 16869 | To create order in mathematics we need a full system, guided by patterns of inference [Frege] |
| Full Idea: We cannot long remain content with the present fragmentation [of mathematics]. Order can be created only by a system. But to construct a system it is necessary that in any step forward we take we should be aware of the logical inferences involved. | |
| From: Gottlob Frege (Logic in Mathematics [1914], p.205) |
| 16864 | If principles are provable, they are theorems; if not, they are axioms [Frege] |
| Full Idea: If the law [of induction] can be proved, it will be included amongst the theorems of mathematics; if it cannot, it will be included amongst the axioms. | |
| From: Gottlob Frege (Logic in Mathematics [1914], p.203) | |
| A reaction: This links Frege with the traditional Euclidean view of axioms. The question, then, is how do we know them, given that we can't prove them. |
| 13918 | Holes, shadows and spots of light can coincide without being identical [Lowe] |
| Full Idea: Holes are things of such a kind that they can coincide without being identical - as are, for example, shadows and spots of light. | |
| From: E.J. Lowe (Two Notions of Being: Entity and Essence [2008], 1) | |
| A reaction: His point is that they thereby fail one of the standard tests for being an 'object'. |
| 9388 | Every concept must have a sharp boundary; we cannot allow an indeterminate third case [Frege] |
| Full Idea: Of any concept, we must require that it have a sharp boundary. Of any object it must hold either that it falls under the concept or it does not. We may not allow a third case in which it is somehow indeterminate whether an object falls under a concept. | |
| From: Gottlob Frege (Logic in Mathematics [1914], p.229), quoted by Ian Rumfitt - The Logic of Boundaryless Concepts p.1 n1 | |
| A reaction: This is the voice of the classical logician, which has echoed by Russell. I'm with them, I think, in the sense that logic can only work with precise concepts. The jury is still out. Maybe we can 'precisify', without achieving total precision. |
| 13921 | All things must have an essence (a 'what it is'), or we would be unable to think about them [Lowe] |
| Full Idea: Things must have an essence, in the sense of 'what it is to be the individual of that kind', or it would make no sense to say we can talk or think comprehendingly about things at all. If we don't know what it is, how can we think about it? | |
| From: E.J. Lowe (Two Notions of Being: Entity and Essence [2008], 2) | |
| A reaction: Lowe presents this as a sort of Master Argument for essences. I think he is working with the wrong notion of essence. All he means is that things must have identities to be objects of thought. Why equate identity with essence, and waste a good concept? |
| 13922 | Knowing an essence is just knowing what the thing is, not knowing some further thing [Lowe] |
| Full Idea: To know something's essence is not to be acquainted with some further thing of a special kind, but simply to understand what exactly that thing is. | |
| From: E.J. Lowe (Two Notions of Being: Entity and Essence [2008], 2) | |
| A reaction: I think he is wrong about this, or at least is working with an unhelpful notion of essence. Identity is one thing, and essence is another. I take essences to be certain selected features of things, which explain their nature. |
| 13920 | Each thing has to be of a general kind, because it belongs to some category [Lowe] |
| Full Idea: Any individual thing must be a thing of some general kind - because, at the very least, it must belong to some ontological category. | |
| From: E.J. Lowe (Two Notions of Being: Entity and Essence [2008], 2) | |
| A reaction: Where does the law that 'everything must have a category' come from? I'm baffled by remarks of this kind. Where do we get the categories from? From observing the individuals. So which has priority? Not the categories. Is God a kind? |
| 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? |
| 16876 | We need definitions to cram retrievable sense into a signed receptacle [Frege] |
| Full Idea: If we need such signs, we also need definitions so that we can cram this sense into the receptacle and also take it out again. | |
| From: Gottlob Frege (Logic in Mathematics [1914], p.209) | |
| A reaction: Has anyone noticed that Frege is the originator of the idea of the mental file? Has anyone noticed the role that definition plays in his account? |
| 16875 | We use signs to mark receptacles for complex senses [Frege] |
| Full Idea: We often need to use a sign with which we associate a very complex sense. Such a sign seems a receptacle for the sense, so that we can carry it with us, while being always aware that we can open this receptacle should we need what it contains. | |
| From: Gottlob Frege (Logic in Mathematics [1914], p.209) | |
| A reaction: This exactly the concept of a mental file, which I enthusiastically endorse. Frege even talks of 'opening the receptacle'. For Frege a definition (which he has been discussing) is the assigment of a label (the 'definiendum') to the file (the 'definiens'). |
| 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. |
| 16879 | A sign won't gain sense just from being used in sentences with familiar components [Frege] |
| Full Idea: No sense accrues to a sign by the mere fact that it is used in one or more sentences, the other constituents of which are known. | |
| From: Gottlob Frege (Logic in Mathematics [1914], p.213) | |
| A reaction: Music to my ears. I've never grasped how meaning could be grasped entirely through use. |
| 16873 | Thoughts are not subjective or psychological, because some thoughts are the same for us all [Frege] |
| Full Idea: A thought is not something subjective, is not the product of any form of mental activity; for the thought that we have in Pythagoras's theorem is the same for everybody. | |
| From: Gottlob Frege (Logic in Mathematics [1914], p.206) | |
| A reaction: When such thoughts are treated as if the have objective (platonic) existence, I become bewildered. I take a thought (or proposition) to be entirely psychological, but that doesn't stop two people from having the same thought. |
| 16872 | A thought is the sense expressed by a sentence, and is what we prove [Frege] |
| Full Idea: The sentence is of value to us because of the sense that we grasp in it, which is recognisably the same in a translation. I call this sense the thought. What we prove is not a sentence, but a thought. | |
| From: Gottlob Frege (Logic in Mathematics [1914], p.206) | |
| A reaction: The 'sense' is presumably the German 'sinn', and a 'thought' in Frege is what we normally call a 'proposition'. So the sense of a sentence is a proposition, and logic proves propositions. I'm happy with that. |
| 16874 | The parts of a thought map onto the parts of a sentence [Frege] |
| Full Idea: A sentence is generally a complex sign, so the thought expressed by it is complex too: in fact it is put together in such a way that parts of a thought correspond to parts of the sentence. | |
| From: Gottlob Frege (Logic in Mathematics [1914], p.207) | |
| A reaction: This is the compositional view of propositions, as opposed to the holistic view. |
| 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) |
| 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. |