Combining Philosophers

All the ideas for Hermarchus, Anon (Dham) and Michael D. Resnik

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17 ideas

1. Philosophy / A. Wisdom / 3. Wisdom Deflated
Our life is the creation of our mind [Anon (Dham)]
     Full Idea: What we are today comes from our thoughts of yesterday, and our present thoughts build our life of tomorrow: our life is the creation of our mind.
     From: Anon (Dham) (The DhammaPada [c.250 BCE], §1.1)
     A reaction: I may adopt this as a second epigraph for the database. This idea records the subjective view, which now comes up against evolutionary psychology. Maybe philosophy is opposed to science, because it is committed to exploring the subjective view?
4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / e. Axioms of PL
Axioms are often affirmed simply because they produce results which have been accepted [Resnik]
     Full Idea: Many axioms have been proposed, not on the grounds that they can be directly known, but rather because they produce a desired body of previously recognised results.
     From: Michael D. Resnik (Maths as a Science of Patterns [1997], One.5.1)
     A reaction: This is the perennial problem with axioms - whether we start from them, or whether we deduce them after the event. There is nothing wrong with that, just as we might infer the existence of quarks because of their results.
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
Mathematical realism says that maths exists, is largely true, and is independent of proofs [Resnik]
     Full Idea: Mathematical realism is the doctrine that mathematical objects exist, that much contemporary mathematics is true, and that the existence and truth in question is independent of our constructions, beliefs and proofs.
     From: Michael D. Resnik (Maths as a Science of Patterns [1997], Three.12.9)
     A reaction: As thus defined, I would call myself a mathematical realist, but everyone must hesitate a little at the word 'exist' and ask, how does it exist? What is it 'made of'? To say that it exists in the way that patterns exist strikes me as very helpful.
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
Mathematical constants and quantifiers only exist as locations within structures or patterns [Resnik]
     Full Idea: In maths the primary subject-matter is not mathematical objects but structures in which they are arranged; our constants and quantifiers denote atoms, structureless points, or positions in structures; they have no identity outside a structure or pattern.
     From: Michael D. Resnik (Maths as a Science of Patterns [1997], Three.10.1)
     A reaction: This seems to me a very promising idea for the understanding of mathematics. All mathematicians acknowledge that the recognition of patterns is basic to the subject. Even animals recognise patterns. It is natural to invent a language of patterns.
Sets are positions in patterns [Resnik]
     Full Idea: On my view, sets are positions in certain patterns.
     From: Michael D. Resnik (Maths as a Science of Patterns [1997], Three.10.5)
     A reaction: I have always found the ontology of a 'set' puzzling, because they seem to depend on prior reasons why something is a member of a given set, which cannot always be random. It is hard to explain sets without mentioning properties.
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / d. Platonist structuralism
Structuralism must explain why a triangle is a whole, and not a random set of points [Resnik]
     Full Idea: An objection is that structuralism fails to explain why certain mathematical patterns are unified wholes while others are not; for instance, some think that an ontological account of mathematics must explain why a triangle is not a 'random' set of points.
     From: Michael D. Resnik (Maths as a Science of Patterns [1997], Three.10.4)
     A reaction: This is an indication that we are not just saying that we recognise patterns in nature, but that we also 'see' various underlying characteristics of the patterns. The obvious suggestion is that we see meta-patterns.
There are too many mathematical objects for them all to be mental or physical [Resnik]
     Full Idea: If we take mathematics at its word, there are too many mathematical objects for it to be plausible that they are all mental or physical objects.
     From: Michael D. Resnik (Maths as a Science of Patterns [1997], One.1)
     A reaction: No one, of course, has ever claimed that they are, but this is a good starting point for assessing the ontology of mathematics. We are going to need 'rules', which can deduce the multitudinous mathematical objects from a small ontology.
Maths is pattern recognition and representation, and its truth and proofs are based on these [Resnik]
     Full Idea: I argue that mathematical knowledge has its roots in pattern recognition and representation, and that manipulating representations of patterns provides the connection between the mathematical proof and mathematical truth.
     From: Michael D. Resnik (Maths as a Science of Patterns [1997], One.1)
     A reaction: The suggestion that patterns are at the basis of the ontology of mathematics is the most illuminating thought I have encountered in the area. It immediately opens up the possibility of maths being an entirely empirical subject.
Congruence is the strongest relationship of patterns, equivalence comes next, and mutual occurrence is the weakest [Resnik]
     Full Idea: Of the equivalence relationships which occur between patterns, congruence is the strongest, equivalence the next, and mutual occurrence the weakest. None of these is identity, which would require the same position.
     From: Michael D. Resnik (Maths as a Science of Patterns [1997], Three.10.3)
     A reaction: This gives some indication of how an account of mathematics as a science of patterns might be built up. Presumably the recognition of these 'degrees of strength' cannot be straightforward observation, but will need an a priori component?
11. Knowledge Aims / C. Knowing Reality / 3. Idealism / a. Idealism
The world is just the illusion of an appearance [Anon (Dham)]
     Full Idea: When a man considers this world as a bubble of froth, and as the illusion of an appearance, then the king of death has no power over him.
     From: Anon (Dham) (The DhammaPada [c.250 BCE], §13.170)
     A reaction: Strictly, of course, this says you can 'consider' things this way. Perhaps we could substitute 'pretends', but the world's great religions don't go in for that sort of thing. Berkeley would be shocked to learn he was approaching Buddhism.
22. Metaethics / B. Value / 2. Values / g. Love
Hate is conquered by love [Anon (Dham)]
     Full Idea: Hate is not conquered by hate: hate is conquered by love. This is the law eternal.
     From: Anon (Dham) (The DhammaPada [c.250 BCE], §1.5)
     A reaction: [N.B. This thought was not invented by Jesus] The challenge to this view might be the tit-for-tat strategy of game theory, which says that hate is actually conquered by a combination of hate and love, judiciously applied.
22. Metaethics / C. The Good / 3. Pleasure / f. Dangers of pleasure
Even divine pleasure will not satisfy the wise, as it is insatiable, and leads to pain [Anon (Dham)]
     Full Idea: Since a shower of gold coins could not satisfy craving desires and the end of all pleasure is pain, how could a wise man find satisfaction even in the pleasures of the gods?
     From: Anon (Dham) (The DhammaPada [c.250 BCE], §14.186)
     A reaction: I'm never sure how so many ancient thinkers arrived at this implausible view. They seem to think that no one knows when to stop, and that every drink leads to hangover. What is actually wrong with moderate sensible pleasure?
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / e. Character
The foolish gradually fill with evil, like a slowly-filled water-jar [Anon (Dham)]
     Full Idea: The falling of drops of water will in time fill a water-jar. Even so the foolish man becomes full of evil, although he gather it little by little.
     From: Anon (Dham) (The DhammaPada [c.250 BCE], §9.121)
     A reaction: This coincides closely with Aristotle's view of moral education. Maybe a wise man can maintain one small vice. Not all slopes are slippery.
The wise gradually fill with good, like a slowly-filled water-jar [Anon (Dham)]
     Full Idea: The falling of drops of water will in time fill a water-jar. Even so the wise man becomes full of good, although he gather it little by little.
     From: Anon (Dham) (The DhammaPada [c.250 BCE], §9.122)
     A reaction: Again, this is like Aristotle's proposal of how to educate people in virtue. In my experience, there is no guarantee that small acts of politeness and charity will eventually guarantee goodness of character. Thought is also needed.
23. Ethics / C. Virtue Theory / 4. External Goods / d. Friendship
Don't befriend fools; either find superior friends, or travel alone [Anon (Dham)]
     Full Idea: If on the great journey of life a man cannot find one who is better or at least as good as himself, let him joyfully travel alone: a fool cannot help him on his journey.
     From: Anon (Dham) (The DhammaPada [c.250 BCE], §5.61)
     A reaction: This is a slightly disturbing aspect of Buddhism, possibly leading to contradiction. It urges friendship and love, but the finest people will have virtually no friends, and solitude is presented as a finer state than friendship.
25. Social Practice / F. Life Issues / 6. Animal Rights
Animals are dangerous and nourishing, and can't form contracts of justice [Hermarchus, by Sedley]
     Full Idea: Hermarchus said that animal killing is justified by considerations of human safety and nourishment and by animals' inability to form contractual relations of justice with us.
     From: report of Hermarchus (fragments/reports [c.270 BCE]) by David A. Sedley - Hermarchus
     A reaction: Could the last argument be used to justify torturing animals? Or could we eat a human who was too brain-damaged to form contracts?
29. Religion / C. Spiritual Disciplines / 3. Buddhism
Speak the truth, yield not to anger, give what you can to him who asks [Anon (Dham)]
     Full Idea: Speak the truth, yield not to anger, give what you can to him who asks: these three steps lead you to the gods
     From: Anon (Dham) (The DhammaPada [c.250 BCE], §17.224)
     A reaction: I don't recall either the Old or New Testament, or the Koran, placing great emphasis on speaking the truth. The injunction to give is not so simple. Give to greedy children, to alcoholics, to criminals, to the rich, to fools, to yourself?