19 ideas
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? |
13913 | The four 'perfect syllogisms' are called Barbara, Celarent, Darii and Ferio [Engelbretsen/Sayward] |
Full Idea: There are four 'perfect syllogisms': Barbara (every M is P, every S is M, so every S is P); Celarent (no M is P, every S is M, so no S is P); Darii (every M is P, some S is M, so some S is P); Ferio (no M is P, some S is M, so some S is not P). | |
From: Engelbretsen,G/Sayward,C (Philosophical Logic: Intro to Advanced Topics [2011], 8) | |
A reaction: The four names are mnemonics from medieval universities. |
13914 | Syllogistic logic has one rule: what is affirmed/denied of wholes is affirmed/denied of their parts [Engelbretsen/Sayward] |
Full Idea: It has often been claimed (e.g. by Leibniz) that a single rule governs all syllogistic validity, called 'dictum de omni et null', which says that what is affirmed or denied of any whole is affirmed or denied of any part of that whole. | |
From: Engelbretsen,G/Sayward,C (Philosophical Logic: Intro to Advanced Topics [2011], 8) | |
A reaction: This seems to be the rule which is captured by Venn Diagrams. |
13915 | Syllogistic can't handle sentences with singular terms, or relational terms, or compound sentences [Engelbretsen/Sayward] |
Full Idea: Three common kinds of sentence cannot be put into syllogistic ('categorical') form: ones using singular terms ('Mars is red'), ones using relational terms ('every painter owns some brushes'), and compound sentences. | |
From: Engelbretsen,G/Sayward,C (Philosophical Logic: Intro to Advanced Topics [2011], 8) |
13916 | Term logic uses expression letters and brackets, and '-' for negative terms, and '+' for compound terms [Engelbretsen/Sayward] |
Full Idea: Term logic begins with expressions and two 'term functors'. Any simple letter is a 'term', any term prefixed by a minus ('-') is a 'negative term', and any pair of terms flanking a plus ('+') is a 'compound term'. Parenthese are used for grouping. | |
From: Engelbretsen,G/Sayward,C (Philosophical Logic: Intro to Advanced Topics [2011], 8) | |
A reaction: [see Engelbretsen and Sayward for the full formal system] |
13850 | In modern logic all formal validity can be characterised syntactically [Engelbretsen/Sayward] |
Full Idea: One of the key ideas of modern formal logic is that all formally valid inferences can be specified in strictly syntactic terms. | |
From: Engelbretsen,G/Sayward,C (Philosophical Logic: Intro to Advanced Topics [2011], Ch.2) |
13849 | Classical logic rests on truth and models, where constructivist logic rests on defence and refutation [Engelbretsen/Sayward] |
Full Idea: Classical logic rests on the concepts of truth and falsity (and usually makes use of a semantic theory based on models), whereas constructivist logic accounts for inference in terms of defense and refutation. | |
From: Engelbretsen,G/Sayward,C (Philosophical Logic: Intro to Advanced Topics [2011], Intro) | |
A reaction: My instincts go with the classical view, which is that inferences do not depend on the human capacity to defend them, but sit there awaiting revelation. My view isn't platonist, because I take the inferences to be rooted in the physical world. |
13851 | Unlike most other signs, = cannot be eliminated [Engelbretsen/Sayward] |
Full Idea: Unlike ∨, →, ↔, and ∀, the sign = is not eliminable from a logic. | |
From: Engelbretsen,G/Sayward,C (Philosophical Logic: Intro to Advanced Topics [2011], Ch.3) |
13852 | Axioms are ω-incomplete if the instances are all derivable, but the universal quantification isn't [Engelbretsen/Sayward] |
Full Idea: A set of axioms is said to be ω-incomplete if, for some universal quantification, each of its instances is derivable from those axioms but the quantification is not thus derivable. | |
From: Engelbretsen,G/Sayward,C (Philosophical Logic: Intro to Advanced Topics [2011], 7) |
16678 | Without magnitude a thing would retain its parts, but they would have no location [Buridan] |
Full Idea: If magnitude were removed from matter by divine power, it would still have parts distinct from one another, but they would not be positioned either outside one another or inside one another, because position would be removed. | |
From: Jean Buridan (Questions on Aristotle's Physics [1346], I.8 f. 11va), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 14.4 | |
A reaction: This shows why Quantity is such an important category for scholastic philosopher. |
16793 | A thing is (less properly) the same over time if each part is succeeded by another [Buridan] |
Full Idea: Less properly, one thing is said to be numerically the same as another according to the continuity of distinct parts, one in succession after another. In this way the Seine is said to be the same river after a thousand years. | |
From: Jean Buridan (Questions on Aristotle's Physics [1346], I.10, f. 13vb), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 29.3 | |
A reaction: This is a rather good solution to the difficulty of the looser non-transitive notion of a thing being 'the same'. The Ship of Theseus endures (in the simple case) as long as you remember to replace each departing plank. Must some parts be originals? |
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. |
16577 | Induction is not demonstration, because not all of the instances can be observed [Buridan] |
Full Idea: Inductions are not demonstrations, because they do not conclude on account of their form, since it is not possible to make an induction from all cases. | |
From: Jean Buridan (Questions on Aristotle's Physics [1346], I.15 f. 18vb), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 02.3 | |
A reaction: Thus showing that demonstration really is meant to be as conclusive as a mathematical proof, and that Aristotle seems to think such a thing is possible in physical science. |
16576 | Science is based on induction, for general truths about fire, rhubarb and magnets [Buridan] |
Full Idea: Induction should be regarded as a principle of natural science. For otherwise you could not prove that every fire is hot, that all rhubarb is purgative of bile, that every magnet attracts iron. | |
From: Jean Buridan (Questions on Aristotle's Physics [1346], I.15 f. 18vb), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 02.3 | |
A reaction: He is basing this on Aristotle, and refers to 'Physics' 190a33-b11. |