6 ideas
18758 | Validity is provable, but invalidity isn't, because the model is infinite [Church, by McGee] |
Full Idea: Church showed that logic has a proof procedure, but no decision procedure. If an argument is invalid, there is a model with true premises and false conclusion, but the model will typically be infinite, so there is no way to display it concretely. | |
From: report of Alonzo Church (A Note on the entscheidungsproblem [1936]) by Vann McGee - Logical Consequence 5 |
14794 | Instead of seeking Truth, we should seek belief that is beyond doubt [Peirce] |
Full Idea: Your problems would be greatly simplified, if, instead of saying that you want to know the Truth, you were simply to say that you want to attain a state of belief unassailable beyond doubt. | |
From: Charles Sanders Peirce (Essentials of Pragmatism [1905], I) | |
A reaction: This is not the same as saying that belief beyond doubt IS truth. He is merely offering a strategy for scientists to side-step the sort of scepticism raised by Descartes and radical empiricists. |
14792 | A 'conception', the rational implication of a word, lies in its bearing upon the conduct of life [Peirce] |
Full Idea: The present writer framed the theory that a 'conception', that is, the rational purport of a word or other expression, lies exclusively in its conceivable bearing upon the conduct of life. | |
From: Charles Sanders Peirce (Essentials of Pragmatism [1905], I) |
14793 | The definition of a concept is just its experimental implications [Peirce] |
Full Idea: If one can define accurately all the conceivable experimental phenomena which the affirmation or denial of a concept could imply, one will have therein a complete definition of the concept, and there is absolutely nothing more in it. | |
From: Charles Sanders Peirce (Essentials of Pragmatism [1905], I) | |
A reaction: Strictly, I would have thought you could only affirm or deny a complete proposition, rather than a concept. What should I do with the concept of a 'unicorn'? Note that all theories, such as empiricism or pragmatism, begin with an account of our concepts. |
1748 | Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius] |
Full Idea: Archelaus was the first person to say that the universe is boundless. | |
From: report of Archelaus (fragments/reports [c.450 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 02.Ar.3 |
5989 | Archelaus said life began in a primeval slime [Archelaus, by Schofield] |
Full Idea: Archelaus wrote that life on Earth began in a primeval slime. | |
From: report of Archelaus (fragments/reports [c.450 BCE]) by Malcolm Schofield - Archelaus | |
A reaction: This sounds like a fairly clearcut assertion of the production of life by evolution. Darwin's contribution was to propose the mechanism for achieving it. We should honour the name of Archelaus for this idea. |