display all the ideas for this combination of philosophers
7 ideas
| 11083 | A sentence is necessary if it is true in a set of worlds, and nonfalse in the other worlds [Hanna] |
| Full Idea: On my view, necessity is the truth of a sentence in every member of a set of possible worlds, together with its nonfalsity in every other possible worlds. | |
| From: Robert Hanna (Rationality and Logic [2006], 6.6) |
| 11086 | Metaphysical necessity can be 'weak' (same as logical) and 'strong' (based on essences) [Hanna] |
| Full Idea: Weak metaphysical necessity is either over the set of all logically possible worlds (in which case it is the same as logical necessity), or it is of a smaller set of worlds, and is determined by the underlying essence or nature of the actual world. | |
| From: Robert Hanna (Rationality and Logic [2006], 6.6) | |
| A reaction: I take the first to be of no interest, as I have no interest in a world which is somehow rated as logically possible, but is not naturally possible. The second type should the principle aim of all human cognitive enquiry. The strong version is synthetic. |
| 11084 | Logical necessity is truth in all logically possible worlds, because of laws and concepts [Hanna] |
| Full Idea: Logical necessity is the truth of a sentence by virtue of logical laws or intrinsic conceptual connections alone, and thus true in all logically possible worlds. Put in traditional terms, logical necessity is analyticity. | |
| From: Robert Hanna (Rationality and Logic [2006], 6.6) |
| 11085 | Nomological necessity is truth in all logically possible worlds with our laws [Hanna] |
| Full Idea: Physical or nomological necessity is the truth of a sentence in all logically possible worlds governed by our actual laws of nature. | |
| From: Robert Hanna (Rationality and Logic [2006], 6.6) | |
| A reaction: Personally I think 'natural necessity' is the best label for this, as it avoids firm commitment to reductive physicalism, and it also avoids commitment to actual necessitating laws. |
| 24030 | 3+4=7 is necessary because we cannot conceive of seven without including three and four [Descartes] |
| Full Idea: When I say that four and three make seven, this connection is necessary, because one cannot conceive the number seven distinctly without including in it in a confused way the number four and the number three. | |
| From: René Descartes (Rules for the Direction of the Mind [1628], 12) | |
| A reaction: This seems to make the truths of arithmetic conceptual, and hence analytic. |
| 2301 | We know by thought that what is done cannot be undone [Descartes] |
| Full Idea: Some ideas belong exclusively to the mind, such as perceiving that what has been done cannot be undone, and everything else that is known by the light of nature. | |
| From: René Descartes (Meditations [1641], §6.82) |
| 3642 | Pythagoras' Theorem doesn't cease to be part of the essence of triangles just because we doubt it [Arnauld on Descartes] |
| Full Idea: You can't reason 'I know the triangle is right-angled, but I doubt Pythagoras' Theorem, therefore it does not belong to the essence of right-angled triangles that the square on the hypotenuse is equal to the sum of the squares on the other two sides'. | |
| From: comment on René Descartes (Meditations [1641], §6.78) by Antoine Arnauld - Objections to 'Meditations' (Fourth) 202 |