display all the ideas for this combination of texts
5 ideas
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) |
4730 | For Aristotle, the subject-predicate structure of Greek reflected a substance-accident structure of reality [Aristotle, by O'Grady] |
Full Idea: Aristotle apparently believed that the subject-predicate structure of Greek reflected the substance-accident nature of reality. | |
From: report of Aristotle (works [c.330 BCE]) by Paul O'Grady - Relativism Ch.4 | |
A reaction: We need not assume that Aristotle is wrong. It is a chicken-and-egg. There is something obvious about subject-predicate language, if one assumes that unified objects are part of nature, and not just conventional. |
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) |