13 ideas
| 10153 | In everyday language, truth seems indefinable, inconsistent, and illogical [Tarski] |
| Full Idea: In everyday language it seems impossible to define the notion of truth or even to use this notion in a consistent manner and in agreement with the laws of logic. | |
| From: Alfred Tarski (works [1936]), quoted by Feferman / Feferman - Alfred Tarski: life and logic Int III | |
| A reaction: [1935] See Logic|Theory of Logic|Semantics of Logic for Tarski's approach to truth. |
| 19141 | Tarski thought axiomatic truth was too contingent, and in danger of inconsistencies [Tarski, by Davidson] |
| Full Idea: Tarski preferred an explicit definition of truth to axioms. He says axioms have a rather accidental character, only a definition can guarantee the continued consistency of the system, and it keeps truth in harmony with physical science and physicalism. | |
| From: report of Alfred Tarski (works [1936]) by Donald Davidson - Truth and Predication 2 n2 | |
| A reaction: Davidson's summary, gleaned from various sources in Tarski. A big challenge for modern axiom systems is to avoid inconsistency, which is extremely hard to do (given that set theory is not sure of having achieved it). |
| 10048 | There is no clear boundary between the logical and the non-logical [Tarski] |
| Full Idea: No objective grounds are known to me which permit us to draw a sharp boundary between the two groups of terms, the logical and the non-logical. | |
| From: Alfred Tarski (works [1936]), quoted by Alan Musgrave - Logicism Revisited §3 | |
| A reaction: Musgrave is pointing out that this is bad news if you want to 'reduce' something like arithmetic to logic. 'Logic' is a vague object. |
| 10694 | Logical consequence is when in any model in which the premises are true, the conclusion is true [Tarski, by Beall/Restall] |
| Full Idea: Tarski's 1936 definition of logical consequence is that in any model in which the premises are true, the conclusion is true too (so that no model can make the conclusion false). | |
| From: report of Alfred Tarski (works [1936]) by JC Beall / G Restall - Logical Consequence 3 | |
| A reaction: So the general idea is that a logical consequence is distinguished by being unstoppable. Sounds good. But then we have monotonic and non-monotonic logics, which (I'm guessing) embody different notions of consequence. |
| 10479 | Logical consequence: true premises give true conclusions under all interpretations [Tarski, by Hodges,W] |
| Full Idea: Tarski's definition of logical consequence (1936) is that in a fully interpreted formal language an argument is valid iff under any allowed interpretation of its nonlogical symbols, if the premises are true then so is the conclusion. | |
| From: report of Alfred Tarski (works [1936]) by Wilfrid Hodges - Model Theory 3 | |
| A reaction: The idea that you can only make these claims 'under an interpretation' seems to have had a huge influence on later philosophical thinking. |
| 13152 | We can talk of 'innumerable number', about the infinite points on a line [Newton] |
| Full Idea: If any man shall take the words number and sum in a larger sense, to understand things which are numberless and sumless (such as the infinite points on a line), I could allow him the contradictious phrase 'innumerable number' without absurdity. | |
| From: Isaac Newton (Letters to Bentley [1692], 1693.02.25) | |
| A reaction: [compressed] I take the key point here to be the phrase of taking number 'in a larger sense'. Like the word 'atom' in physics, the word 'number' retains its traditional reference, but has considerably shifted its scope. Amateurs must live with this. |
| 13151 | Not all infinites are equal [Newton] |
| Full Idea: It is an error that all infinites are equal. | |
| From: Isaac Newton (Letters to Bentley [1692], 1693.01.17) | |
| A reaction: There follows a discussion of the mathematicians' view of infinity. Cantor was not the first to notice that there is more than one sort of of infinity. |
| 10157 | Tarski improved Hilbert's geometry axioms, and without set-theory [Tarski, by Feferman/Feferman] |
| Full Idea: Tarski found an elegant new axiom system for Euclidean geometry that improved Hilbert's earlier version - and he formulated it without the use of set-theoretical notions. | |
| From: report of Alfred Tarski (works [1936]) by Feferman / Feferman - Alfred Tarski: life and logic Ch.9 |
| 16618 | Intellectual and moral states, and even the soul itself, depend on prime matter for their existence [Blasius, by Pasnau] |
| Full Idea: Blasius argued that prime matter is the subject of all our intellectual and moral states. This implies that such states cannot exist apart from the body, which seems to imply further that the soul itself cannot exist apart from the body. | |
| From: report of Blasius of Parma (Les quaestiones de anima (lectures on the soul) [1385], I.8 p.65) by Robert Pasnau - Metaphysical Themes 1274-1671 06.3 | |
| A reaction: It seems that, under pressure, Blasius recanted this view in lectures given eleven years later. |
| 15863 | The principles of my treatise are designed to fit with a belief in God [Newton] |
| Full Idea: When I wrote my treatise about our system, I had an eye upon such principles as might work with considering men, for the belief of a deity. | |
| From: Isaac Newton (Letters to Bentley [1692], 1692.12.10) | |
| A reaction: Harré quotes this, and it shows that the rather passive view of nature Newton developed was to be supplemented by the active power of God. Without God, we need a more active view of nature. |
| 8340 | I do not pretend to know the cause of gravity [Newton] |
| Full Idea: You sometimes speak of gravity as essential and inherent in matter. Pray do no ascribe that notion to me; for the cause of gravity is what I do not pretend to know. | |
| From: Isaac Newton (Letters to Bentley [1692], 1693.01.17) | |
| A reaction: I take science to be a two-stage operation - first we discern the regularities, and then we explain them. Evolution was spotted, then explained by Darwin. Cancer from cigarettes was spotted, but hasn't been explained. Regularity is the beginning. |
| 13150 | The motions of the planets could only derive from an intelligent agent [Newton] |
| Full Idea: The motions which the planets now have could not spring from any natural cause alone, but were impressed by an intelligent agent. | |
| From: Isaac Newton (Letters to Bentley [1692], 1692.12.10) | |
| A reaction: He is writing to a cleric, but seems to be quite sincere about this. Elsewhere he just says he doesn't know what causes gravity. |
| 12178 | That gravity should be innate and essential to matter is absurd [Newton] |
| Full Idea: That gravity should be innate, inherent and essential to matter ...is to me so great an absurdity that I believe no man who has in philosophical matters a competent faculty of thinking can ever fall into it. | |
| From: Isaac Newton (Letters to Bentley [1692], 1693.02.25) | |
| A reaction: He is replying to some sermons, and he pays vague lip service to a possible divine force. Nevertheless, this is thoroughgoing anti-essentialism, and he talks of external 'laws' in the next sentence. Newton still sought the cause of gravity. |