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All the ideas for 'A Discourse on Method', 'On boundary numbers and domains of sets' and 'The Sentiment of Rationality'

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43 ideas

1. Philosophy / A. Wisdom / 1. Nature of Wisdom
It is wisdom to believe what you desire, because belief is needed to achieve it [James]
     Full Idea: Clearly it is often the part of wisdom to believe what one desires; for the belief is one of indispensable preliminary conditions of the realisation of its object.
     From: William James (The Sentiment of Rationality [1882], p.43)
     A reaction: Roughly, action is impossible without optimism about possible success. This may count as instinct, rather than 'wisdom'.
1. Philosophy / D. Nature of Philosophy / 1. Philosophy
All good philosophers start from a dumb conviction about which truths can be revealed [James]
     Full Idea: Every philosopher whose initiative counts for anything in the evolution of thought has taken his stand on a sort of dumb conviction that the truth must lie in one direction rather than another, and a preliminary assurance that this can be made to work.
     From: William James (The Sentiment of Rationality [1882], p.40)
     A reaction: I would refer to this as 'intuition', which I think of as reasons (probably good reasons) which cannot yet be articulated. Hence I like this idea very much, except for the word 'dumb'. It is more like a rational vision, yet to be filled in.
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.
1. Philosophy / D. Nature of Philosophy / 7. Despair over Philosophy
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.
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.
1. Philosophy / E. Nature of Metaphysics / 3. Metaphysical Systems
A complete system is just a classification of the whole world's ingredients [James]
     Full Idea: A completed theoretic philosophy can never be anything more than a completed classification of the world's ingredients.
     From: William James (The Sentiment of Rationality [1882], p.23)
     A reaction: I assume this is not just the physical ingredients, but must also include our conceptual scheme - but then we must first decide which is the best conceptual scheme to classify, and that's where the real action is. [He scorns such classifation later].
2. Reason / A. Nature of Reason / 4. Aims of Reason
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)
2. Reason / A. Nature of Reason / 5. Objectivity
A single explanation must have a single point of view [James]
     Full Idea: A single explanation of a fact only explains it from a single point of view.
     From: William James (The Sentiment of Rationality [1882], p.23)
     A reaction: I take this to imply that multiple viewpoints lead us towards objectivity. The single viewpoint of an expert is of much greater value than that of a novice, on the whole.
2. Reason / B. Laws of Thought / 6. Ockham's Razor
Our greatest pleasure is the economy of reducing chaotic facts to one single fact [James]
     Full Idea: Our pleasure at finding that a chaos of facts is the expression of single underlying fact is like a musician's relief at discovering harmony. …The passion for economy of means in thought is the philosophic passion par excellence.
     From: William James (The Sentiment of Rationality [1882], p.21)
     A reaction: We do, though, possess an inner klaxon warning against stupid simplistic reductions. Reducing all the miseries of life to the workings of the Devil is not satisfactory, even it it is economical. Simplicities are dangerously tempting.
2. Reason / F. Fallacies / 4. Circularity
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)
3. Truth / A. Truth Problems / 8. Subjective Truth
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)
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
Zermelo showed that the ZF axioms in 1930 were non-categorical [Zermelo, by Hallett,M]
     Full Idea: Zermelo's paper sets out to show that the standard set-theoretic axioms (what he calls the 'constitutive axioms', thus the ZF axioms minus the axiom of infinity) have an unending sequence of different models, thus that they are non-categorical.
     From: report of Ernst Zermelo (On boundary numbers and domains of sets [1930]) by Michael Hallett - Introduction to Zermelo's 1930 paper p.1209
     A reaction: Hallett says later that Zermelo is working with second-order set theory. The addition of an Axiom of Infinity seems to have aimed at addressing the problem, and the complexities of that were pursued by Gödel.
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / h. Axiom of Replacement VII
Replacement was added when some advanced theorems seemed to need it [Zermelo, by Maddy]
     Full Idea: Zermelo included Replacement in 1930, after it was noticed that the sequence of power sets was needed, and Replacement gave the ordinal form of the well-ordering theorem, and justification for transfinite recursion.
     From: report of Ernst Zermelo (On boundary numbers and domains of sets [1930]) by Penelope Maddy - Believing the Axioms I §1.8
     A reaction: Maddy says that this axiom suits the 'limitation of size' theorists very well, but is not so good for the 'iterative conception'.
5. Theory of Logic / L. Paradox / 3. Antinomies
The antinomy of endless advance and of completion is resolved in well-ordered transfinite numbers [Zermelo]
     Full Idea: Two opposite tendencies of thought, the idea of creative advance and of collection and completion (underlying the Kantian 'antinomies') find their symbolic representation and their symbolic reconciliation in the transfinite numbers based on well-ordering.
     From: Ernst Zermelo (On boundary numbers and domains of sets [1930], §5)
     A reaction: [a bit compressed] It is this sort of idea, from one of the greatest set-theorists, that leads philosophers to think that the philosophy of mathematics may offer solutions to metaphysical problems. As an outsider, I am sceptical.
7. Existence / E. Categories / 2. Categorisation
Classification can only ever be for a particular purpose [James]
     Full Idea: Every way of classifying a thing is but a way of handling it for some particular purpose. Conceptions, 'kinds', are teleological instruments.
     From: William James (The Sentiment of Rationality [1882], p.24)
     A reaction: Could there not be ways of classifying which suit all of our purposes? If there were a naturally correct way to classifying things, then any pragmatist would probably welcome that. (I don't say there is such a way).
11. Knowledge Aims / A. Knowledge / 4. Belief / a. Beliefs
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)
11. Knowledge Aims / B. Certain Knowledge / 1. Certainty
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
11. Knowledge Aims / B. Certain Knowledge / 4. The Cogito
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)
12. Knowledge Sources / A. A Priori Knowledge / 6. A Priori from Reason
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)
12. Knowledge Sources / C. Rationalism / 1. Rationalism
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)
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / a. Foundationalism
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.
13. Knowledge Criteria / D. Scepticism / 6. Scepticism Critique
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)
14. Science / A. Basis of Science / 1. Observation
Scientific genius extracts more than other people from the same evidence [James]
     Full Idea: What is the use of being a genius, unless with the same scientific evidence as other men, one can reach more truth than they?
     From: William James (The Sentiment of Rationality [1882], p.40)
     A reaction: This is aimed at Clifford's famous principle. He isn't actually contraverting the principle, but it is a nice point about evidence. Simple empiricists think detectives only have to stare at the evidence and the solution creates itself.
14. Science / A. Basis of Science / 3. Experiment
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)
14. Science / A. Basis of Science / 6. Falsification
Experimenters assume the theory is true, and stick to it as long as result don't disappoint [James]
     Full Idea: Each tester of the truth of a theory …acts as if it were true, and expects the result to disappoint him if his assumption is false. The longer disappointment is delayed, the stronger grows his faith in his theory.
     From: William James (The Sentiment of Rationality [1882], p.42)
     A reaction: This is almost exactly Popper's falsificationist proposal for science, which interestingly shows the close relationship of his view to pragmatism. Believe it as long as it is still working.
14. Science / C. Induction / 3. Limits of Induction
We can't know if the laws of nature are stable, but we must postulate it or assume it [James]
     Full Idea: That nature will follow tomorrow the same laws that she follows today is a truth which no man can know; but in the interests of cognition as well as of action we must postulate or assume it.
     From: William James (The Sentiment of Rationality [1882], p.39)
     A reaction: The stability of nature is something to be assessed, not something taken for granted. If you arrive in a new city and it all seems quiet, you keep your fingers crossed and treat it as stable. But revolution or coup could be just round the corner.
14. Science / C. Induction / 6. Bayes's Theorem
Trying to assess probabilities by mere calculation is absurd and impossible [James]
     Full Idea: The absurd abstraction of an intellect verbally formulating all its evidence and carefully estimating the probability thereof solely by the size of a vulgar fraction, is as ideally inept as it is practically impossible.
     From: William James (The Sentiment of Rationality [1882], p.40)
     A reaction: James probably didn't know about Bayes, but this is directed at the Bayesian approach. My view is that full rational assessment of coherence is a much better bet than a Bayesian calculation. Factors must be weighted.
14. Science / D. Explanation / 2. Types of Explanation / j. Explanations by reduction
We have a passion for knowing the parts of something, rather than the whole [James]
     Full Idea: Alongside the passion for simplification …is the passion for distinguishing; it is the passion to be acquainted with the parts rather than to comprehend the whole.
     From: William James (The Sentiment of Rationality [1882], p.22)
     A reaction: As I child I dismantled almost every toy I was given. This seems to be the motivation for a lot of analytic philosophy, but Aristotle also tended to think that way.
15. Nature of Minds / A. Nature of Mind / 1. Mind / b. Purpose of mind
The mind has evolved entirely for practical interests, seen in our reflex actions [James]
     Full Idea: It is far too little recognised how entirely the intellect is built up of practical interests. The theory of evolution is beginning to do very good service by its reduction of all mentality to the type of reflex action.
     From: William James (The Sentiment of Rationality [1882], p.34)
     A reaction: Hands evolved for manipulating tools end up playing the piano. Minds evolved for action can be afflicted with boredom. He's not wrong, but he is risking the etymological fallacy (origin = purpose). I take navigation to be the original purpose of mind.
15. Nature of Minds / A. Nature of Mind / 7. Animal Minds
Dogs' curiosity only concerns what will happen next [James]
     Full Idea: A dog's curiosity about the movements of his master or a strange object only extends as far as the point of what is going to happen next.
     From: William James (The Sentiment of Rationality [1882], p.31)
     A reaction: Good. A nice corrective to people like myself who are tempted to inflate animal rationality, in order to emphasise human evolutionary continuity with them. It is hard to disagree with his observation. But dogs do make judgements! True/false!
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)
16. Persons / B. Nature of the Self / 3. Self as Non-physical
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.
17. Mind and Body / A. Mind-Body Dualism / 1. Dualism
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.
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.
17. Mind and Body / A. Mind-Body Dualism / 2. Interactionism
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?
18. Thought / A. Modes of Thought / 5. Rationality / a. Rationality
How can the ground of rationality be itself rational? [James]
     Full Idea: Can that which is the ground of rationality in all else be itself properly called rational?
     From: William James (The Sentiment of Rationality [1882], p.25)
     A reaction: This is the perennial problem in deciding grounds, and in deciding what to treat as primitive. The stoics see the whole of nature as rational. Cf how can the ground of what is physical be itself physical?
18. Thought / A. Modes of Thought / 5. Rationality / b. Human rationality
It seems that we feel rational when we detect no irrationality [James]
     Full Idea: I think there are very good grounds for upholding the view that the feeling of rationality is constituted merely by the absence of any feelings of irrationality.
     From: William James (The Sentiment of Rationality [1882], p.20)
     A reaction: A very interesting proposal. Nothing is more basic to logic (well, plausible versions of logic) than the principle of non-contradiction - perhaps because it is the foundation of our natural intellectual equipment.
18. Thought / B. Mechanics of Thought / 6. Artificial Thought / c. Turing Test
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.
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / d. Biological ethics
Evolution suggests prevailing or survival as a new criterion of right and wrong [James]
     Full Idea: The philosophy of evolution offers us today a new criterion, which is objective and fixed, as an ethical test between right and wrong: That is to be called good which is destined to prevail or survive.
     From: William James (The Sentiment of Rationality [1882], p.44)
     A reaction: Perceptive for its time. Herbert Spencer may have suggested the idea. James dismisses it, because it implies a sort of fatalism, whereas genuine moral choices are involved in what survives.
23. Ethics / C. Virtue Theory / 1. Virtue Theory / d. Virtue theory critique
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)
26. Natural Theory / C. Causation / 8. Particular Causation / d. Selecting the cause
Understanding by means of causes is useless if they are not reduced to a minimum number [James]
     Full Idea: The knowledge of things by their causes, which is often given as a definition of rational knowledge, is useless unless the causes converge to a minimum number, while still producing the maximum number of effects.
     From: William James (The Sentiment of Rationality [1882], p.21)
     A reaction: This is certainly the psychological motivation for trying to identify 'the' cause of something, but James always tries to sell such things as subjective. 'Useless' to one person is a subjective criterion; useless to anyone is much more objective.
26. Natural Theory / D. Laws of Nature / 7. Strictness of Laws
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.
29. Religion / B. Monotheistic Religion / 4. Christianity / a. Christianity
Early Christianity says God recognises the neglected weak and tender impulses [James]
     Full Idea: In what did the emancipating message of primitive Christianity consist but in the announcement that God recognizes those weak and tender impulses which paganism had so rudely overlooked.
     From: William James (The Sentiment of Rationality [1882], p.36)
     A reaction: Nietzsche says these are the virtues of a good slave. Previous virtues were dominated by military needs, but the new virtues are those of large cities, where communal living with strangers is the challenge.