14 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) |
| 10779 | A comprehension axiom is 'predicative' if the formula has no bound second-order variables [Linnebo] |
| Full Idea: If φ contains no bound second-order variables, the corresponding comprehension axiom is said to be 'predicative'; otherwise it is 'impredicative'. | |
| From: Øystein Linnebo (Plural Quantification Exposed [2003], §1) | |
| A reaction: ['Predicative' roughly means that a new predicate is created, and 'impredicative' means that it just uses existing predicates] |
| 10781 | A 'pure logic' must be ontologically innocent, universal, and without presuppositions [Linnebo] |
| Full Idea: I offer these three claims as a partial analysis of 'pure logic': ontological innocence (no new entities are introduced), universal applicability (to any realm of discourse), and cognitive primacy (no extra-logical ideas are presupposed). | |
| From: Øystein Linnebo (Plural Quantification Exposed [2003], §1) |
| 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) |
| 10783 | Plural quantification depends too heavily on combinatorial and set-theoretic considerations [Linnebo] |
| Full Idea: If my arguments are correct, the theory of plural quantification has no right to the title 'logic'. ...The impredicative plural comprehension axioms depend too heavily on combinatorial and set-theoretic considerations. | |
| From: Øystein Linnebo (Plural Quantification Exposed [2003], §4) |
| 10778 | Can second-order logic be ontologically first-order, with all the benefits of second-order? [Linnebo] |
| Full Idea: According to its supporters, second-order logic allow us to pay the ontological price of a mere first-order theory and get the corresponding monadic second-order theory for free. | |
| From: Øystein Linnebo (Plural Quantification Exposed [2003], §0) |
| 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. |
| 10782 | The modern concept of an object is rooted in quantificational logic [Linnebo] |
| Full Idea: Our modern general concept of an object is given content only in connection with modern quantificational logic. | |
| From: Øystein Linnebo (Plural Quantification Exposed [2003], §2) | |
| A reaction: [He mentions Frege, Carnap, Quine and Dummett] This is the first thing to tell beginners in modern analytical metaphysics. The word 'object' is very confusing. I think I prefer 'entity'. |
| 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) |
| 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. |
| 15998 | Perfect love is not in spite of imperfections; the imperfections must be loved as well [Kierkegaard] |
| Full Idea: To love another in spite of his weaknesses and errors and imperfections is not perfect love. No, to love is to find him lovable in spite of, and together with, his weaknesses and errors and imperfections. | |
| From: Søren Kierkegaard (Works of Love [1847], p.158) | |
| A reaction: A true romantic at heart, Kierkegaard ideally posits perfect love as unconditional love, and not just of good attributes, predicates and conditions. However, the real question for both me and Kierkegaard is, is perfect love desirable or even possible?[SY] |