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) |
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) |
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) |
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) |
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) |
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) |
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) |
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) |
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) |
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) |
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) |
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) |
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) |
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) |
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) |
7492 | Early societies are based on community, and modern societies on association [Tönnies, by Watson] |
Full Idea: Pre-modern societies are based on community (Gemeinschaft), whereas modern societies are based on association (Gesellschaft). | |
From: report of Ferdinand Tönnies (Community and Association [1887]) by Peter Watson - Ideas Ch.32 | |
A reaction: A very interesting distinction. The modern term implies contracts, and it strikes me as an extremely accurate description of modern liberal democracies. There is very little sense of community, but a strong sense of innumerable contracts that bind us. |
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. |