27 ideas
| 24032 | Clever scholars can obscure things which are obvious even to peasants [Descartes] |
| Full Idea: Scholars are usually ingenious enough to find ways of spreading darkness even in things which are obvious by themselves, and which the peasants are not ignorant of. | |
| From: René Descartes (Rules for the Direction of the Mind [1628], 12) | |
| A reaction: Wonderful! I see it everywhere in philosophy. It is usually the result of finding ingenious and surprising grounds for scepticism. The amazing thing is not their lovely arguments, but that fools then take their conclusions seriously. Modus tollens. |
| 24033 | Most scholastic disputes concern words, where agreeing on meanings would settle them [Descartes] |
| Full Idea: The questions on which scholars argue are almost always questions of word. …If philosophers were agreed on the meaning of words, almost all their controversies would cease. | |
| From: René Descartes (Rules for the Direction of the Mind [1628], 13) | |
| A reaction: He has a low opinion of 'scholars'! It isn't that difficult to agree on the meanings of key words, in a given context. The aim isn't to get rid of the problems, but to focus on the real problems. Some words contain problems. |
| 24024 | The secret of the method is to recognise which thing in a series is the simplest [Descartes] |
| Full Idea: It is necessary, in a series of objects, to recognise which is the simplest thing, and how all the others depart from it. This rule contains the whole secret of the method. | |
| From: René Descartes (Rules for the Direction of the Mind [1628], 06) | |
| A reaction: This is an appealing thought, though deciding the criteria for 'simplest' looks tough. Are electrons, for example, simple? Is a person a simple basic thing? |
| 24018 | One truth leads us to another [Descartes] |
| Full Idea: One truth discovered helps us to discover another. | |
| From: René Descartes (Rules for the Direction of the Mind [1628], 01) | |
| A reaction: I take this to be one of the key ingredients of objectivity. People who know very little have almost no chance of objectivity. A mind full of falsehoods also blocks it. |
| 14249 | Boolos reinterprets second-order logic as plural logic [Boolos, by Oliver/Smiley] |
| Full Idea: Boolos's conception of plural logic is as a reinterpretation of second-order logic. | |
| From: report of George Boolos (On Second-Order Logic [1975]) by Oliver,A/Smiley,T - What are Sets and What are they For? n5 | |
| A reaction: Oliver and Smiley don't accept this view, and champion plural reference differently (as, I think, some kind of metalinguistic device?). |
| 10830 | Second-order logic metatheory is set-theoretic, and second-order validity has set-theoretic problems [Boolos] |
| Full Idea: The metatheory of second-order logic is hopelessly set-theoretic, and the notion of second-order validity possesses many if not all of the epistemic debilities of the notion of set-theoretic truth. | |
| From: George Boolos (On Second-Order Logic [1975], p.45) | |
| A reaction: Epistemic problems arise when a logic is incomplete, because some of the so-called truths cannot be proved, and hence may be unreachable. This idea indicates Boolos's motivation for developing a theory of plural quantification. |
| 10829 | A sentence can't be a truth of logic if it asserts the existence of certain sets [Boolos] |
| Full Idea: One may be of the opinion that no sentence ought to be considered as a truth of logic if, no matter how it is interpreted, it asserts that there are sets of certain sorts. | |
| From: George Boolos (On Second-Order Logic [1975], p.44) | |
| A reaction: My intuition is that in no way should any proper logic assert the existence of anything at all. Presumably interpretations can assert the existence of numbers or sets, but we should be able to identify something which is 'pure' logic. Natural deduction? |
| 10832 | '∀x x=x' only means 'everything is identical to itself' if the range of 'everything' is fixed [Boolos] |
| Full Idea: One may say that '∀x x=x' means 'everything is identical to itself', but one must realise that one's answer has a determinate sense only if the reference (range) of 'everything' is fixed. | |
| From: George Boolos (On Second-Order Logic [1975], p.46) | |
| A reaction: This is the problem now discussed in the recent book 'Absolute Generality', of whether one can quantify without specifying a fixed or limited domain. |
| 10834 | Weak completeness: if it is valid, it is provable. Strong: it is provable from a set of sentences [Boolos] |
| Full Idea: A weak completeness theorem shows that a sentence is provable whenever it is valid; a strong theorem, that a sentence is provable from a set of sentences whenever it is a logical consequence of the set. | |
| From: George Boolos (On Second-Order Logic [1975], p.52) | |
| A reaction: So the weak version says |- φ → |= φ, and the strong versions says Γ |- φ → Γ |= φ. Presumably it is stronger if it can specify the source of the inference. |
| 13841 | Why should compactness be definitive of logic? [Boolos, by Hacking] |
| Full Idea: Boolos asks why on earth compactness, whatever its virtues, should be definitive of logic itself. | |
| From: report of George Boolos (On Second-Order Logic [1975]) by Ian Hacking - What is Logic? §13 |
| 24035 | Unity is something shared by many things, so in that respect they are equals [Descartes] |
| Full Idea: Unity is that common nature in which all things that are compared with each other must participate equally. | |
| From: René Descartes (Rules for the Direction of the Mind [1628], 14) | |
| A reaction: A lovely explanation of the concept of 'units' for counting. Fregeans hate units, but we Grecian thinkers love them. |
| 24036 | I can only see the proportion of two to three if there is a common measure - their unity [Descartes] |
| Full Idea: I do not recognise what the proportion of magnitude is between two and three, unless I consider a third term, namely unity, which is the common measure of the one and the other. | |
| From: René Descartes (Rules for the Direction of the Mind [1628], 14) | |
| A reaction: A striking defence of the concept of the need for the unit in arithmetic. To say 'three is half as big again', you must be discussing the same size of 'half' in each instance. |
| 10833 | Many concepts can only be expressed by second-order logic [Boolos] |
| Full Idea: The notions of infinity and countability can be characterized by second-order sentences, though not by first-order sentences (as compactness and Skolem-Löwenheim theorems show), .. as well as well-ordering, progression, ancestral and identity. | |
| From: George Boolos (On Second-Order Logic [1975], p.48) |
| 24029 | Among the simples are the graspable negations, such as rest and instants [Descartes] |
| Full Idea: Among the simple things, we must also place their negation and deprivation, insofar as they fall under out intelligence, because the idea of nothingness, of the instant, of rest, is no less true an idea than that of existence, of duration, of motion. | |
| From: René Descartes (Rules for the Direction of the Mind [1628], 12) | |
| A reaction: He sees the 'simple' things as the foundation of all knowledge, because they are self-evident. Not sure about 'no less true', since the specific nothings are parasitic on the somethings. |
| 24030 | 3+4=7 is necessary because we cannot conceive of seven without including three and four [Descartes] |
| Full Idea: When I say that four and three make seven, this connection is necessary, because one cannot conceive the number seven distinctly without including in it in a confused way the number four and the number three. | |
| From: René Descartes (Rules for the Direction of the Mind [1628], 12) | |
| A reaction: This seems to make the truths of arithmetic conceptual, and hence analytic. |
| 24019 | If we accept mere probabilities as true we undermine our existing knowledge [Descartes] |
| Full Idea: It is better never to study than to be unable to distinguish the true from the false, and be obliged to accept as certain what is doubtful. One risks losing the knowledge one already has. Hence we reject all those knowledges which are only probable. | |
| From: René Descartes (Rules for the Direction of the Mind [1628], 02) | |
| A reaction: This is usually seen nowadays (and I agree) that this is a false dichotomy. Knowledge can't be all-or-nothing. We should accept probabilities as probable, not as knowledge. Probability became a science after Descartes. |
| 24020 | We all see intuitively that we exist, where intuition is attentive, clear and distinct rational understanding [Descartes] |
| Full Idea: By intuition I mean the conception of an attentive mind, so distinct and clear that it has no doubt about what it understands, …a conception that is borne of the sole light of reason. Thus everyone can see intuitively that he exists. | |
| From: René Descartes (Rules for the Direction of the Mind [1628], 03) | |
| A reaction: By 'intuition' he means self-evident certainty, whereas my concept is of a judgement of which I am reasonably confident, but without sufficient grounds for certainty. This is an early assertion of the Cogito, with a clear statement of its grounding. |
| 24031 | When Socrates doubts, he know he doubts, and that truth is possible [Descartes] |
| Full Idea: If Socrates says he doubts everything, it necessarily follows that he at least understands that he doubts, and that he knows that something can be true or false: for these are notions that necessarily accompany doubt. | |
| From: René Descartes (Rules for the Direction of the Mind [1628], 12) | |
| A reaction: An early commitment to the Cogito. But note that the inescapable commitment is not just to his existence, but also to his own reasoning, and his own commitment, and to the possibility of truth. Many, many things are undeniable. |
| 24025 | Clear and distinct truths must be known all at once (unlike deductions) [Descartes] |
| Full Idea: We require two conditions for intuition, namely that the proposition appear clear and distinct, and then that it be understood all at once and not successively. Deduction, on the other hand, implies a certain movement of the mind. | |
| From: René Descartes (Rules for the Direction of the Mind [1628], 11) | |
| A reaction: A nice distinction. Presumably with deduction you grasp each step clearly, and then the inference and conclusion, and you can then forget the previous steps because you have something secure. |
| 24022 | Our souls possess divine seeds of knowledge, which can bear spontaneous fruit [Descartes] |
| Full Idea: The human soul possesses something divine in which are deposited the first seeds of useful knowledge, which, in spite of the negligence and embarrassment of poorly done studies, bear spontaneous fruit. | |
| From: René Descartes (Rules for the Direction of the Mind [1628], 04) | |
| A reaction: This makes clear the religious underpinning which is required for his commitment to such useful innate ideas (such as basic geometry) |
| 24034 | If someone had only seen the basic colours, they could deduce the others from resemblance [Descartes] |
| Full Idea: Let there be a man who has sometimes seen the fundamental colours, and never the intermediate and mixed colours; it may be that by a sort of deduction he will represent those he has not seen, by their resemblance to the others. | |
| From: René Descartes (Rules for the Direction of the Mind [1628], 14) | |
| A reaction: Thus Descartes solved Hume's shade of blue problem, by means of 'a sort of deduction' from resemblance, where Hume was paralysed by his need to actually experience it. Dogmatic empiricism is a false doctrine! |
| 24021 | The method starts with clear intuitions, followed by a process of deduction [Descartes] |
| Full Idea: If the method shows clearly how we must use intuition to avoid mistaking the false for the true, and how deduction must operate to lead us to the knowledge of all things, it will be complete in my opinion. | |
| From: René Descartes (Rules for the Direction of the Mind [1628], 04) | |
| A reaction: A perfect statement of his foundationalist view. It needs a clear and distinct basis, and the steps of building must be strictly logical. Of course, most of our knowledge relies on induction, rather than deduction. |
| 24027 | Nerves and movement originate in the brain, where imagination moves them [Descartes] |
| Full Idea: The motive power or the nerves themselves originate in the brain, which contains the imagination, which moves them in a thousand ways, as the common sense is moved by the external sense. | |
| From: René Descartes (Rules for the Direction of the Mind [1628], 12) | |
| A reaction: This sounds a lot more physicalist than his later explicit dualism in Meditations. Even in that work the famous passage on the ship's pilot acknowledged tight integration of mind and brain. |
| 24026 | Our four knowledge faculties are intelligence, imagination, the senses, and memory [Descartes] |
| Full Idea: There are four faculties in us which we can use to know: intelligence, imagination, the senses, and memory. | |
| From: René Descartes (Rules for the Direction of the Mind [1628], 12) | |
| A reaction: Philosophers have to attribute faculties to the mind, even if the psychologists and neuroscientists won't accept them. We must infer the sources of our modes of understanding. He is cautious about imagination. |
| 24028 | The force by which we know things is spiritual, and quite distinct from the body [Descartes] |
| Full Idea: This force by which we properly know objects is purely spiritual, and is no less distinct from the body than is the blood from the bones. | |
| From: René Descartes (Rules for the Direction of the Mind [1628], 12) | |
| A reaction: This firmly contradicts any physicalism I thought I detected in Idea 24027! He uses the word 'spiritual' of the mind here, which I don't think he uses in later writings. |
| 468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
| Full Idea: In singing and playing the lyre, a boy will be likely to reveal not only courage and moderation, but also justice. | |
| From: Damon (fragments/reports [c.460 BCE], B4), quoted by (who?) - where? |
| 24023 | All the sciences searching for order and measure are related to mathematics [Descartes] |
| Full Idea: I have discovered that all the sciences which have as their aim the search for order and measure are related to mathematics. | |
| From: René Descartes (Rules for the Direction of the Mind [1628], 04) | |
| A reaction: Note that he sound a more cautious note than Galileo's famous remark. It leaves room for biology to still be a science, even when it fails to be mathematical. |