16 ideas
| 14782 | 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. |
| 14787 | 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) |
| 9331 | How do we determine which of the sentences containing a term comprise its definition? [Horwich] |
| Full Idea: How are we to determine which of the sentences containing a term comprise its definition? | |
| From: Paul Horwich (Stipulation, Meaning and Apriority [2000], §2) | |
| A reaction: Nice question. If I say 'philosophy is the love of wisdom' and 'philosophy bores me', why should one be part of its definition and the other not? What if I stipulated that the second one is part of my definition, and the first one isn't? |
| 14783 | 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) |
| 14788 | 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. |
| 14786 | 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) |
| 9333 | A priori belief is not necessarily a priori justification, or a priori knowledge [Horwich] |
| Full Idea: It is one thing to believe something a priori and another for this belief to be epistemically justified. The latter is required for a priori knowledge. | |
| From: Paul Horwich (Stipulation, Meaning and Apriority [2000], §8) | |
| A reaction: Personally I would agree with this, because I don't think anything should count as knowledge if it doesn't have supporting reasons, but fans of a priori knowledge presumably think that certain basic facts are just known. They are a priori justified. |
| 9342 | Understanding needs a priori commitment [Horwich] |
| Full Idea: Understanding is itself based on a priori commitment. | |
| From: Paul Horwich (Stipulation, Meaning and Apriority [2000], §12) | |
| A reaction: This sounds plausible, but needs more justification than Horwich offers. This is the sort of New Rationalist idea I associate with Bonjour. The crucial feature of the New lot is, I take it, their fallibilism. All understanding is provisional. |
| 9332 | Meaning is generated by a priori commitment to truth, not the other way around [Horwich] |
| Full Idea: Our a priori commitment to certain sentences is not really explained by our knowledge of a word's meaning. It is the other way around. We accept a priori that the sentences are true, and thereby provide it with meaning. | |
| From: Paul Horwich (Stipulation, Meaning and Apriority [2000], §8) | |
| A reaction: This sounds like a lovely trump card, but how on earth do you decide that a sentence is true if you don't know what it means? Personally I would take it that we are committed to the truth of a proposition, before we have a sentence for it. |
| 9341 | Meanings and concepts cannot give a priori knowledge, because they may be unacceptable [Horwich] |
| Full Idea: A priori knowledge of logic and mathematics cannot derive from meanings or concepts, because someone may possess such concepts, and yet disagree with us about them. | |
| From: Paul Horwich (Stipulation, Meaning and Apriority [2000], §12) | |
| A reaction: A good argument. The thing to focus on is not whether such ideas are a priori, but whether they are knowledge. I think we should employ the word 'intuition' for a priori candidates for knowledge, and demand further justification for actual knowledge. |
| 9334 | If we stipulate the meaning of 'number' to make Hume's Principle true, we first need Hume's Principle [Horwich] |
| Full Idea: If we stipulate the meaning of 'the number of x's' so that it makes Hume's Principle true, we must accept Hume's Principle. But a precondition for this stipulation is that Hume's Principle be accepted a priori. | |
| From: Paul Horwich (Stipulation, Meaning and Apriority [2000], §9) | |
| A reaction: Yet another modern Quinean argument that all attempts at defining things are circular. I am beginning to think that the only a priori knowledge we have is of when a group of ideas is coherent. Calling it 'intuition' might be more accurate. |
| 9339 | A priori knowledge (e.g. classical logic) may derive from the innate structure of our minds [Horwich] |
| Full Idea: One potential source of a priori knowledge is the innate structure of our minds. We might, for example, have an a priori commitment to classical logic. | |
| From: Paul Horwich (Stipulation, Meaning and Apriority [2000], §11) | |
| A reaction: Horwich points out that to be knowledge it must also say that we ought to believe it. I'm wondering whether if we divided the whole territory of the a priori up into intuitions and then coherent justifications, the whole problem would go away. |
| 14789 | 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. |
| 14785 | 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. |
| 14784 | 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. |
| 1422 | God's existence is either necessary or impossible, and no one has shown that the concept of God is contradictory [Malcolm] |
| Full Idea: God's existence is either impossible or necessary. It can be the former only if the concept of such a being is self-contradictory or in some way logically absurd. Assuming that this is not so, it follows that He necessarily exists. | |
| From: Norman Malcolm (Anselm's Argument [1959], §2) | |
| A reaction: The concept of God suggests paradoxes of omniscience, omnipotence and free will, so self-contradiction seems possible. How should we respond if the argument suggests God is necessary, but evidence suggests God is highly unlikely? |