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All the ideas for 'fragments/reports' and 'The Nature of Mathematics'

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30 ideas

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)
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.
7. Existence / A. Nature of Existence / 5. Reason for Existence
Nothing could come out of nothing, and existence could never completely cease [Empedocles]
     Full Idea: From what in no wise exists, it is impossible for anything to come into being; for Being to perish completely is incapable of fulfilment and unthinkable.
     From: Empedocles (fragments/reports [c.453 BCE], B012), quoted by Anon (Lyc) - On Melissus 975b1-4
7. Existence / B. Change in Existence / 1. Nature of Change
Empedocles says things are at rest, unless love unites them, or hatred splits them [Empedocles, by Aristotle]
     Full Idea: Empedocles claims that things are alternately changing and at rest - that they are changing whenever love is creating a unity out of plurality, or hatred is creating plurality out of unity, and they are at rest in the times in between.
     From: report of Empedocles (fragments/reports [c.453 BCE]) by Aristotle - Physics 250b26
     A reaction: I suppose one must say that this an example of Ruskin's 'pathetic fallacy' - reading human emotions into the cosmos. Being constructive little creatures, we think goodness leads to construction. I'm afraid Empedocles is just wrong.
9. Objects / A. Existence of Objects / 6. Nihilism about Objects
There is no coming-to-be of anything, but only mixing and separating [Empedocles, by Aristotle]
     Full Idea: Empedocles says there is no coming-to-be of anything, but only a mingling and a divorce of what has been mingled.
     From: report of Empedocles (fragments/reports [c.453 BCE]) by Aristotle - Coming-to-be and Passing-away (Gen/Corr) 314b08
     A reaction: Aristotle comments that this prevents Empedocleans from distinguishing between superficial alteration and fundamental change of identity. Presumably, though, that wouldn't bother them.
9. Objects / E. Objects over Time / 10. Beginning of an Object
Substance is not created or destroyed in mortals, but there is only mixing and exchange [Empedocles]
     Full Idea: There is no creation of substance in any one of mortal existence, nor any end in execrable death, but only mixing and exchange of what has been mixed.
     From: Empedocles (fragments/reports [c.453 BCE], B008), quoted by Plutarch - 74: Reply to Colotes 1111f
     A reaction: also Aristotle 314b08
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 / 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.
13. Knowledge Criteria / E. Relativism / 3. Subjectivism
One vision is produced by both eyes [Empedocles]
     Full Idea: One vision is produced by both eyes
     From: Empedocles (fragments/reports [c.453 BCE], B088), quoted by Strabo - works 8.364.3
17. Mind and Body / A. Mind-Body Dualism / 3. Panpsychism
Wisdom and thought are shared by all things [Empedocles]
     Full Idea: Wisdom and power of thought, know thou, are shared in by all things.
     From: Empedocles (fragments/reports [c.453 BCE]), quoted by Sextus Empiricus - Against the Logicians (two books) II.286
     A reaction: Sextus quotes this, saying that it is 'still more paradoxical', and that it explicitly includes plants. This may mean that Empedocles was not including inanimate matter.
18. Thought / A. Modes of Thought / 1. Thought
For Empedocles thinking is almost identical to perception [Empedocles, by Theophrastus]
     Full Idea: Empedocles assumes that thinking is either identical to or very similar to sense-perception.
     From: report of Empedocles (fragments/reports [c.453 BCE], A86) by Theophrastus - On the Senses 9
     A reaction: Not to be sniffed at. We can, of course, control our thinking (though we can't control the controller) and we contemplate abstractions, but that might be seen as a sort of perception. Vision is not as visual as we think.
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.
22. Metaethics / B. Value / 2. Values / j. Evil
Empedocles said good and evil were the basic principles [Empedocles, by Aristotle]
     Full Idea: Empedocles was the first to give evil and good as principles.
     From: report of Empedocles (fragments/reports [c.453 BCE]) by Aristotle - Metaphysics 985a
     A reaction: Once you start to think that good and evil will only matter if they have causal powers, it is an easy step to the idea of a benevolent god, and a satanic anti-god. Otherwise the 'principles' could be ignored.
26. Natural Theory / A. Speculations on Nature / 1. Nature
'Nature' is just a word invented by people [Empedocles]
     Full Idea: Nature is but a word of human framing.
     From: Empedocles (fragments/reports [c.453 BCE], B008), quoted by Aristotle - Metaphysics 1015a
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / e. The One
The principle of 'Friendship' in Empedocles is the One, and is bodiless [Empedocles, by Plotinus]
     Full Idea: In Empedocles we have a dividing principle, 'Strife', set against 'Friendship' - which is the One and is to him bodiless, while the elements represent matter.
     From: report of Empedocles (fragments/reports [c.453 BCE]) by Plotinus - The Enneads 5.1.09
     A reaction: The first time I've seen the principle of Love in Empedocles identified with the One of Parmenides. Plotinus is a trustworthy reporter, I think, because he was well read, and had access to lost texts.
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / f. Ancient elements
Empedocles said that there are four material elements, and two further creative elements [Empedocles, by Aristotle]
     Full Idea: Empedocles holds that the corporeal elements are four, but that all the elements, including those which create motion, are six in number.
     From: report of Empedocles (fragments/reports [c.453 BCE]) by Aristotle - Coming-to-be and Passing-away (Gen/Corr) 314a16
Empedocles says bone is water, fire and earth in ratio 2:4:2 [Empedocles, by Inwood]
     Full Idea: Empedocles used numerical ratios to explain different kinds of matter; for example, bone is two parts water, four parts fire, two parts earth; and blood is an equal blend of all four elements.
     From: report of Empedocles (fragments/reports [c.453 BCE]) by Brad Inwood - Empedocles
     A reaction: Why isn't the ration 1:2:1? This presumably shows the influence of Pythagoras (who had also been based in Italy, like Empedocles), as well as that of the earlier naturalistic philosophers. It was a very good theory, though wrong.
Fire, Water, Air and Earth are elements, being simple as well as homoeomerous [Empedocles, by Aristotle]
     Full Idea: Empedocles says that Fire, Water, Air and Earth are four elements, and are thus 'simple' rather than flesh, bone and bodies which, like these, are 'homoeomeries'.
     From: report of Empedocles (fragments/reports [c.453 BCE]) by Aristotle - Coming-to-be and Passing-away (Gen/Corr) 314a26
     A reaction: The translation is not quite clear. I take it that flesh and bone may look simple, because they are homoeomerous, but they are not really - but what is his evidence for that? Compare Idea 13208.
All change is unity through love or division through hate [Empedocles]
     Full Idea: These elements never cease their continuous exchange, sometimes uniting under the influence of Love, so that all become One, at other times again moving apart through the hostile force of Hate.
     From: Empedocles (fragments/reports [c.453 BCE], B017), quoted by Simplicius - On Aristotle's 'Physics' 158.1-
The elements combine in coming-to-be, but how do the elements themselves come-to-be? [Aristotle on Empedocles]
     Full Idea: Empedocles says it is evident that all the other bodies down to the 'elements' have their coming-to-be and their passing-away: but it is not clear how the 'elements' themselves, severally in their aggregated masses, come-to-be and pass-away.
     From: comment on Empedocles (fragments/reports [c.453 BCE]) by Aristotle - Coming-to-be and Passing-away (Gen/Corr) 325b20
     A reaction: Presumably the elements are like axioms - and are just given. How do electrons and quarks come-to-be?
Love and Strife only explain movement if their effects are distinctive [Aristotle on Empedocles]
     Full Idea: It is not an adequate explanation to say that 'Love and Strife set things moving', unless the very nature of Love is a movement of this kind and the very nature of Strife a movement of that kind.
     From: comment on Empedocles (fragments/reports [c.453 BCE]) by Aristotle - Coming-to-be and Passing-away (Gen/Corr) 333b23
     A reaction: I take this to be of interest for showing Aristotle's quest for explanations, and his unwillingness to be fobbed off with anything superficial. I take a task of philosophy to be to push explanations further than others wish to go.
If the one Being ever diminishes it would no longer exist, and what could ever increase it? [Empedocles]
     Full Idea: Besides these elements, nothing else comes into being, nor does anything cease. For if they had been perishing continuously, they would Be no more; and what could increase the Whole? And whence could it have come?
     From: Empedocles (fragments/reports [c.453 BCE], B017), quoted by Simplicius - On Aristotle's 'Physics' 158.1-
27. Natural Reality / G. Biology / 3. Evolution
Maybe bodies are designed by accident, and the creatures that don't work are destroyed [Empedocles, by Aristotle]
     Full Idea: Is it just an accident that teeth and other parts of the body seem to have some purpose, and creatures survive because they happen to be put together in a useful way? Everything else has been destroyed, as Empedocles says of his 'cow with human head'.
     From: report of Empedocles (fragments/reports [c.453 BCE], 61) by Aristotle - Physics 198b29
     A reaction: Good grief! Has no one ever noticed that Empedocles proposed the theory of evolution? It isn't quite natural selection, because we aren't told what does the 'destroying', but it is a little flash of genius that was quietly forgotten.
28. God / A. Divine Nature / 2. Divine Nature
God is a pure, solitary, and eternal sphere [Empedocles]
     Full Idea: God is equal in all directions to himself and altogether eternal, a rounded Sphere enjoying a circular solitude.
     From: Empedocles (fragments/reports [c.453 BCE], B028), quoted by John Stobaeus - Anthology 1.15.2
God is pure mind permeating the universe [Empedocles]
     Full Idea: God is mind, holy and ineffable, and only mind, which darts through the whole cosmos with its swift thought.
     From: Empedocles (fragments/reports [c.453 BCE], B134), quoted by Ammonius - On 'De Interpretatione' 4.5.249.6
28. God / A. Divine Nature / 4. Divine Contradictions
In Empedocles' theory God is ignorant because, unlike humans, he doesn't know one of the elements (strife) [Aristotle on Empedocles]
     Full Idea: It is a consequence of Empedocles' view that God is the most unintelligent thing, for he alone is ignorant of one of the elements, namely strife, whereas mortal creatures are familiar with them all.
     From: comment on Empedocles (fragments/reports [c.453 BCE]) by Aristotle - De Anima 410b08
29. Religion / A. Polytheistic Religion / 2. Greek Polytheism
It is wretched not to want to think clearly about the gods [Empedocles]
     Full Idea: Wretched is he who cares not for clear thinking about the gods.
     From: Empedocles (fragments/reports [c.453 BCE], B132), quoted by Clement - Miscellanies 5.140.5.1