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All the ideas for 'The Statesman', 'Mechanisms' and 'The Nature of Mathematics'

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24 ideas

1. Philosophy / F. Analytic Philosophy / 2. Analysis by Division
Whenever you perceive a community of things, you should also hunt out differences in the group [Plato]
     Full Idea: The rule is that when one perceives first the community between the members of a group of many things, one should not desist until one sees in it all those differences that are located in classes.
     From: Plato (The Statesman [c.356 BCE], 285b)
     A reaction: He goes on to recommend the opposite as well - see community even when there appears to be nothing but differences. I take this to be analysis, just as much as modern linguistic approaches are. Analyse the world, not language.
1. Philosophy / G. Scientific Philosophy / 3. Scientism
Philosophy is an experimental science, resting on common experience [Peirce]
     Full Idea: Philosophy, although it uses no microscopes or other apparatus of special observation, is really an experimental science, resting on that experience which is common to us all.
     From: Charles Sanders Peirce (The Nature of Mathematics [1898], I)
     A reaction: The 'experimental' either implies that thought-experiments are central to the subject, or that philosophers are discussing the findings of scientists, but at a high level of theory and abstraction. Peirce probably means the latter. I can't disagree.
2. Reason / B. Laws of Thought / 3. Non-Contradiction
Self-contradiction doesn't reveal impossibility; it is inductive impossibility which reveals self-contradiction [Peirce]
     Full Idea: It is an anacoluthon to say that a proposition is impossible because it is self-contradictory. It rather is thought so to appear self-contradictory because the ideal induction has shown it to be impossible.
     From: Charles Sanders Peirce (The Nature of Mathematics [1898], III)
2. Reason / D. Definition / 2. Aims of Definition
To reveal a nature, divide down, and strip away what it has in common with other things [Plato]
     Full Idea: Let's take the kind posited and cut it in two, .then follow the righthand part of what we've cut, and hold onto things that the sophist is associated with until we strip away everything he has in common with other things, then display his peculiar nature.
     From: Plato (The Statesman [c.356 BCE], 264e)
     A reaction: This seems to be close to Aristotle's account of definition, when he is trying to get at what-it-is-to-be some thing. But if you strip away everything the definiendum has in common with other things, will anything remain?
No one wants to define 'weaving' just for the sake of weaving [Plato]
     Full Idea: I don't suppose that anyone with any sense would want to hunt down the definition of 'weaving' for the sake of weaving itself.
     From: Plato (The Statesman [c.356 BCE], 285d)
     A reaction: The point seems to be that the definition brings out the connections between weaving and other activities and objects, thus enlarging our understanding.
5. Theory of Logic / C. Ontology of Logic / 3. If-Thenism
Logic, unlike mathematics, is not hypothetical; it asserts categorical ends from hypothetical means [Peirce]
     Full Idea: Mathematics is purely hypothetical: it produces nothing but conditional propositions. Logic, on the contrary, is categorical in its assertions. True, it is a normative science, and not a mere discovery of what really is. It discovers ends from means.
     From: Charles Sanders Peirce (The Nature of Mathematics [1898], II)
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
Mathematics is close to logic, but is even more abstract [Peirce]
     Full Idea: The whole of the theory of numbers belongs to logic; or rather, it would do so, were it not, as pure mathematics, pre-logical, that is, even more abstract than logic.
     From: Charles Sanders Peirce (The Nature of Mathematics [1898], IV)
     A reaction: Peirce seems to flirt with logicism, but rejects in favour of some subtler relationship. I just don't believe that numbers are purely logical entities.
10. Modality / B. Possibility / 1. Possibility
Some logical possibility concerns single propositions, but there is also compatibility between propositions [Peirce]
     Full Idea: Many say everything is logically possible which involves no contradiction. In this sense two contradictory propositions may be severally possible. In the substantive sense, the contradictory of a possible proposition is impossible (if we were omniscient).
     From: Charles Sanders Peirce (The Nature of Mathematics [1898], III)
12. Knowledge Sources / A. A Priori Knowledge / 3. Innate Knowledge / b. Recollection doctrine
The soul gets its goodness from god, and its evil from previous existence. [Plato]
     Full Idea: From its composer the soul possesses all beautiful things, but from its former condition, everything that proves to be harsh and unjust in heaven.
     From: Plato (The Statesman [c.356 BCE], 273b)
     A reaction: A neat move to explain the origins of evil (or rather, to shift the problem of evil to a long long way from here). This view presumably traces back to the views of Empedocles on good and evil. Can the soul acquire evil in its current existence?
12. Knowledge Sources / D. Empiricism / 1. Empiricism
Experience is indeed our only source of knowledge, provided we include inner experience [Peirce]
     Full Idea: If Mill says that experience is the only source of any kind of knowledge, I grant it at once, provided only that by experience he means personal history, life. But if he wants me to admit that inner experience is nothing, he asks what cannot be granted.
     From: Charles Sanders Peirce (The Nature of Mathematics [1898])
     A reaction: Notice from Idea 14785 that Peirce has ideas in mind, and not just inner experiences like hunger. Empiricism certainly begins to look more plausible if we expand the notion of experience. It must include what we learned from prior experience.
12. Knowledge Sources / D. Empiricism / 5. Empiricism Critique
The world is one of experience, but experiences are always located among our ideas [Peirce]
     Full Idea: The real world is the world of sensible experience, and it is part of the process of sensible experience to locate its facts in the world of ideas.
     From: Charles Sanders Peirce (The Nature of Mathematics [1898], III)
     A reaction: This is the neatest demolition of the sharp dividing line between empiricism and rationalism that I have ever encountered.
14. Science / B. Scientific Theories / 2. Aim of Science
Empiricist theories are sets of laws, which give explanations and reductions [Glennan]
     Full Idea: In the empiricist tradition theories were understood to be deductive closures of sets of laws, explanations were understood as arguments from covering laws, and reduction was understood as a deductive relationship between laws of different theories.
     From: Stuart Glennan (Mechanisms [2008], 'Intro')
     A reaction: A lovely crisp summary of the whole tradition of philosophy of science from Comte through to Hempel. Mechanism and essentialism are the new players in the game.
14. Science / D. Explanation / 2. Types of Explanation / i. Explanations by mechanism
Modern mechanism need parts with spatial, temporal and function facts, and diagrams [Glennan]
     Full Idea: Modern champions of mechanisms say models should identify both the parts and their spatial, temporal and functional organisation, ...and the practical importance of diagrams in addition to or in place of linguistic representations of mechanisms.
     From: Stuart Glennan (Mechanisms [2008], 'Discover')
     A reaction: Apparently chemists obtain much more refined models by using mathematics than they did by diagrams or 3D models (let alone verbal descriptions). For that reason, I'm thinking that 'model' might be a better term than 'mechanism'.
Mechanistic philosophy of science is an alternative to the empiricist law-based tradition [Glennan]
     Full Idea: To a significant degree, a mechanistic philosophy of science can be seen as an alternative to an earlier logical empiricist tradition in philosophy of science that gave pride of place to laws of nature.
     From: Stuart Glennan (Mechanisms [2008], 'Intro')
     A reaction: Lovely! Someone who actually spells out what's going on here. Most philosophers are far too coy about explaining what their real game is. Mechanism is fine in chemistry and biology. How about in 'mathematical' physics, or sociology?
Mechanisms are either systems of parts or sequences of activities [Glennan]
     Full Idea: There are two sorts of mechanisms: systems consist of collections of parts that interact to produce some behaviour, and processes are sequences of activities which produce some outcome.
     From: Stuart Glennan (Mechanisms [2008], 'Intro')
     A reaction: [compressed] The second one is important because it is more generic, and under that account all kinds the features of the world that need to be explained can be subsumed. E.g. hyperinflation in an economy is a 'mechanism'.
17th century mechanists explained everything by the kinetic physical fundamentals [Glennan]
     Full Idea: 17th century mechanists said that interactions governed by chemical, electrical or gravitational forces would have to be explicable in terms of the operation of some atomistic (or corpuscular) kinetic mechanism.
     From: Stuart Glennan (Mechanisms [2008], 'Intro')
     A reaction: Glennan says science has rejected this, so modern mechanists do not reduce mechanisms to anything in particular.
Unlike the lawlike approach, mechanistic explanation can allow for exceptions [Glennan]
     Full Idea: One of the advantages of the move from nomological to mechanistic modes of explanation is that the latter allows for explanations involving exception-ridden generalizations.
     From: Stuart Glennan (Mechanisms [2008], 'regular')
     A reaction: The lawlike approach has endless problems with 'ceteris paribus' ('all things being equal') laws, where specifying all the other 'things' seems a bit tricky.
19. Language / F. Communication / 1. Rhetoric
The question of whether or not to persuade comes before the science of persuasion [Plato]
     Full Idea: The science of whether one must persuade or not must rule over the science capable of persuading.
     From: Plato (The Statesman [c.356 BCE], 304c)
     A reaction: Plato probably thinks that reason has to be top of the pyramid, but there is always the Nietzschean/romantic question of why we should place such a value on what is rational.
21. Aesthetics / A. Aesthetic Experience / 5. Natural Beauty
Non-physical beauty can only be shown clearly by speech [Plato]
     Full Idea: The bodiless things, being the most beautiful and the greatest, are only shown with clarity by speech and nothing else.
     From: Plato (The Statesman [c.356 BCE], 286a)
     A reaction: Unfortunately this will be true of warped and ugly ideas as well.
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / b. Defining ethics
Ethics is the science of aims [Peirce]
     Full Idea: Ethics is the science of aims.
     From: Charles Sanders Peirce (The Nature of Mathematics [1898], II)
     A reaction: Intriguing slogan. He is discussing the aims of logic. I think what he means is that ethics is the science of value. 'Science' may be optimistic, but I would sort of agree with his basic idea.
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / f. The Mean
The arts produce good and beautiful things by preserving the mean [Plato]
     Full Idea: It is by preserving the mean that arts produce everything that is good and beautiful.
     From: Plato (The Statesman [c.356 BCE], 284b)
24. Political Theory / D. Ideologies / 5. Democracy / a. Nature of democracy
Democracy is the worst of good constitutions, but the best of bad constitutions [Plato, by Aristotle]
     Full Idea: Plato judged that when the constitution is decent, democracy is the worst of them, but when they are bad it is the best.
     From: report of Plato (The Statesman [c.356 BCE], 302e) by Aristotle - Politics 1289b07
     A reaction: Aristotle denies that a good oligarchy is superior. What of technocracy? The challenge is to set up institutions which ensure the health of the democracy. The big modern problem is populists who lie.
26. Natural Theory / C. Causation / 4. Naturalised causation
Since causal events are related by mechanisms, causation can be analysed in that way [Glennan]
     Full Idea: Causation can be analyzed in terms of mechanisms because (except for fundamental causal interactions) causally related events will be connected by intervening mechanisms.
     From: Stuart Glennan (Mechanisms [2008], 'causation')
     A reaction: This won't give us the metaphysics of causation (which concerns the fundamentals), but this strikes me as a very coherent and interesting proposal. He mentions electron interaction as non-mechanistic causation.
28. God / A. Divine Nature / 2. Divine Nature
Only divine things can always stay the same, and bodies are not like that [Plato]
     Full Idea: It is fitting for only the most divine things of all to be always the same and in the same state and in the same respects, and the nature of body is not of this ordering.
     From: Plato (The Statesman [c.356 BCE], 269b)