17 ideas
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) |
7544 | Many people imagine that to experience is to understand [Goethe] |
Full Idea: There are many people who imagine that what they experience they also understand. | |
From: Wolfgang von Goethe (Maxims and Reflections [1825], 889) | |
A reaction: This should be posted over the arrivals gate of every international airport, for returning holiday-makers. It seems to place Goethe on the rationalist side of the debate with empiricism. It is hard to explain 'understanding' in Humean terms. |
7541 | Man never understands how anthropomorphic he is [Goethe] |
Full Idea: Man never understands how anthropomorphic he is. | |
From: Wolfgang von Goethe (Maxims and Reflections [1825], 203) | |
A reaction: Nice. It is true, even when it is pointed out to us. No matter how hard we try to realise how very different animals are from us, we can't help identifying with them. Religious people even do it with inanimate creation. |
7543 | We gain self-knowledge through action, not thought - especially when doing our duty [Goethe] |
Full Idea: How can we learn self-knowledge? Never by taking thought, but rather by action. Try to do your duty and you'll soon discover what you're like. | |
From: Wolfgang von Goethe (Maxims and Reflections [1825], 442) | |
A reaction: Good! I even like the unfashionable bit about duty. If you just do what you want, you will discover your interests, but not so much about your capacities. However, when you have to do something less comfortable, it is very revealing. |
7540 | Beauty is a manifestation of secret natural laws [Goethe] |
Full Idea: Beauty is a manifestation of secret natural laws which without this appearance would have remained eternally hidden from us. | |
From: Wolfgang von Goethe (Maxims and Reflections [1825], 183) | |
A reaction: An interesting defence of beauty as an objective feature of the world. I'm not sure. Much beauty is indeed the result of growth or erosion expressing underlying laws, but then I have always thought there was a sexual component to visual beauty. |
7538 | The happiest people link the beginning and end of life [Goethe] |
Full Idea: The happiest man is one who can link the end of his life with its beginning. | |
From: Wolfgang von Goethe (Maxims and Reflections [1825], 140) | |
A reaction: [from 'Art and Antiquity']. A nice thought, which chimes in with the idea that a good life is like a complete story or a work of art (Idea 7501), or that it is 'eudaimon'. |
7542 | The best form of government teaches us to govern ourselves [Goethe] |
Full Idea: You ask which form of government is the best? Whichever teaches us to govern ourselves. | |
From: Wolfgang von Goethe (Maxims and Reflections [1825], 353) | |
A reaction: Not a fashionable view, since the rise of freedom as the highest political ideal, but I identify with the idea that a good government should educate, and should try to facilitate virtue as well as pleasure. |
7539 | To get duties from people without rights, you must pay them well [Goethe] |
Full Idea: If you demand duties from people and will not concede them rights, you have to pay them well. | |
From: Wolfgang von Goethe (Maxims and Reflections [1825], 180) | |
A reaction: [from 'Art and Antiquity']. ...or have great power over them. Goethe gives the optimistic liberal view, rather than the Marxist view. |
13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
Full Idea: In a single day there lies open to men of learning more than there ever does to the unenlightened in the longest of lifetimes. | |
From: Posidonius (fragments/reports [c.95 BCE]), quoted by Seneca the Younger - Letters from a Stoic 078 | |
A reaction: These remarks endorsing the infinite superiority of the educated to the uneducated seem to have been popular in late antiquity. It tends to be the religions which discourage great learning, especially in their emphasis on a single book. |
20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |
Full Idea: Posidonius defined time thus: it is an interval of motion, or the measure of speed and slowness. | |
From: report of Posidonius (fragments/reports [c.95 BCE]) by John Stobaeus - Anthology 1.08.42 | |
A reaction: Hm. Can we define motion or speed without alluding to time? Looks like we have to define them as a conjoined pair, which means we cannot fully understand either of them. |