30 ideas
9672 | Free logic is one of the few first-order non-classical logics [Priest,G] |
Full Idea: Free logic is an unusual example of a non-classical logic which is first-order. | |
From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], Pref) |
9697 | X1 x X2 x X3... x Xn indicates the 'cartesian product' of those sets [Priest,G] |
Full Idea: X1 x X2 x X3... x Xn indicates the 'cartesian product' of those sets, the set of all the n-tuples with its first member in X1, its second in X2, and so on. | |
From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.0) |
9685 | <a,b&62; is a set whose members occur in the order shown [Priest,G] |
Full Idea: <a,b> is a set whose members occur in the order shown; <x1,x2,x3, ..xn> is an 'n-tuple' ordered set. | |
From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.10) |
9675 | a ∈ X says a is an object in set X; a ∉ X says a is not in X [Priest,G] |
Full Idea: a ∈ X means that a is a member of the set X, that is, a is one of the objects in X. a ∉ X indicates that a is not in X. | |
From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.2) |
9674 | {x; A(x)} is a set of objects satisfying the condition A(x) [Priest,G] |
Full Idea: {x; A(x)} indicates a set of objects which satisfy the condition A(x). | |
From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.2) |
9673 | {a1, a2, ...an} indicates that a set comprising just those objects [Priest,G] |
Full Idea: {a1, a2, ...an} indicates that the set comprises of just those objects. | |
From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.2) |
9677 | Φ indicates the empty set, which has no members [Priest,G] |
Full Idea: Φ indicates the empty set, which has no members | |
From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.4) |
9676 | {a} is the 'singleton' set of a (not the object a itself) [Priest,G] |
Full Idea: {a} is the 'singleton' set of a, not to be confused with the object a itself. | |
From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.4) |
9679 | X⊂Y means set X is a 'proper subset' of set Y [Priest,G] |
Full Idea: X⊂Y means set X is a 'proper subset' of set Y (if and only if all of its members are members of Y, but some things in Y are not in X) | |
From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.6) |
9678 | X⊆Y means set X is a 'subset' of set Y [Priest,G] |
Full Idea: X⊆Y means set X is a 'subset' of set Y (if and only if all of its members are members of Y). | |
From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.6) |
9681 | X = Y means the set X equals the set Y [Priest,G] |
Full Idea: X = Y means the set X equals the set Y, which means they have the same members (i.e. X⊆Y and Y⊆X). | |
From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.6) |
9683 | X ∩ Y indicates the 'intersection' of sets X and Y, the objects which are in both sets [Priest,G] |
Full Idea: X ∩ Y indicates the 'intersection' of sets X and Y, which is a set containing just those things that are in both X and Y. | |
From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.8) |
9682 | X∪Y indicates the 'union' of all the things in sets X and Y [Priest,G] |
Full Idea: X ∪ Y indicates the 'union' of sets X and Y, which is a set containing just those things that are in X or Y (or both). | |
From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.8) |
9684 | Y - X is the 'relative complement' of X with respect to Y; the things in Y that are not in X [Priest,G] |
Full Idea: Y - X indicates the 'relative complement' of X with respect to Y, that is, all the things in Y that are not in X. | |
From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.8) |
9688 | A 'singleton' is a set with only one member [Priest,G] |
Full Idea: A 'singleton' is a set with only one member. | |
From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.4) |
9689 | The 'empty set' or 'null set' has no members [Priest,G] |
Full Idea: The 'empty set' or 'null set' is a set with no members. | |
From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.4) |
9690 | A set is a 'subset' of another set if all of its members are in that set [Priest,G] |
Full Idea: A set is a 'subset' of another set if all of its members are in that set. | |
From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.6) |
9691 | A 'proper subset' is smaller than the containing set [Priest,G] |
Full Idea: A set is a 'proper subset' of another set if some things in the large set are not in the smaller set | |
From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.6) |
9694 | The 'relative complement' is things in the second set not in the first [Priest,G] |
Full Idea: The 'relative complement' of one set with respect to another is the things in the second set that aren't in the first. | |
From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.8) |
9693 | The 'intersection' of two sets is a set of the things that are in both sets [Priest,G] |
Full Idea: The 'intersection' of two sets is a set containing the things that are in both sets. | |
From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.8) |
9692 | The 'union' of two sets is a set containing all the things in either of the sets [Priest,G] |
Full Idea: The 'union' of two sets is a set containing all the things in either of the sets | |
From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.8) |
9698 | The 'induction clause' says complex formulas retain the properties of their basic formulas [Priest,G] |
Full Idea: The 'induction clause' says that whenever one constructs more complex formulas out of formulas that have the property P, the resulting formulas will also have that property. | |
From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.2) |
9695 | An 'ordered pair' (or ordered n-tuple) is a set with its members in a particular order [Priest,G] |
Full Idea: An 'ordered pair' (or ordered n-tuple) is a set with its members in a particular order. | |
From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.10) |
9696 | A 'cartesian product' of sets is the set of all the n-tuples with one member in each of the sets [Priest,G] |
Full Idea: A 'cartesian product' of sets is the set of all the n-tuples with one member in each of the sets. | |
From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.10) |
9686 | A 'set' is a collection of objects [Priest,G] |
Full Idea: A 'set' is a collection of objects. | |
From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.2) |
9687 | A 'member' of a set is one of the objects in the set [Priest,G] |
Full Idea: A 'member' of a set is one of the objects in the set. | |
From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.2) |
9680 | The empty set Φ is a subset of every set (including itself) [Priest,G] |
Full Idea: The empty set Φ is a subset of every set (including itself). | |
From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.6) |
21982 | I only wish I had such eyes as to see Nobody! It's as much as I can do to see real people. [Carroll,L] |
Full Idea: "I see nobody on the road," said Alice. - "I only wish I had such eyes," the King remarked. ..."To be able to see Nobody! ...Why, it's as much as I can do to see real people." | |
From: Lewis Carroll (C.Dodgson) (Through the Looking Glass [1886], p.189), quoted by A.W. Moore - The Evolution of Modern Metaphysics 07.7 | |
A reaction: [Moore quotes this, inevitably, in a chapter on Hegel] This may be a better candidate for the birth of philosophy of language than Frege's Groundwork. |
12251 | Substantial forms are not understood, and explain nothing [Descartes] |
Full Idea: Clearly no explanation can be given by these substantial forms for any natural action, since their defenders admit that they are occult and that they do not understand them themselves, ...so they explain nothing. | |
From: René Descartes (Letters to Regius [1642], 1642.01), quoted by David S. Oderberg - Real Essentialism 267 n5 | |
A reaction: [Oderberg gives refs for attack by Locke and Hume, p.66] Descartes' target is Aristotle's hylomorphism. The problem seems to be understanding what Aristotle meant, which is much more than mere 'shape'. More like 'controlling principle'. |
16772 | An angelic mind would not experience pain, even when connected to a human body [Descartes, by Pasnau] |
Full Idea: Descartes points out that an angelic mind, even if causally connected to a human body, would not experience the same sort of bodily sensations; it would, instead, simply observe flesh being torn, like a piece of paper. | |
From: report of René Descartes (Letters to Regius [1642], III:493) by Robert Pasnau - Metaphysical Themes 1274-1671 25.6 | |
A reaction: Does that mean that the angel could not have the experience even if it wanted to have it. So they can't pick up a cup either? So they can't make themselves known to us, even if they are desperate to? So the Annunciation never happened? |