Combining Texts

All the ideas for 'Clitophon', 'Intro to Non-Classical Logic (1st ed)' and 'Senses of Essence'

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35 ideas

2. Reason / D. Definition / 6. Definition by Essence
11178 The essence or definition of an essence involves either a class of properties or a class of propositions [Fine,K]
4. Formal Logic / E. Nonclassical Logics / 6. Free Logic
9672 Free logic is one of the few first-order non-classical logics [Priest,G]
4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / a. Symbols of ST
9697 X1 x X2 x X3... x Xn indicates the 'cartesian product' of those sets [Priest,G]
9685 <a,b&62; is a set whose members occur in the order shown [Priest,G]
9675 a ∈ X says a is an object in set X; a ∉ X says a is not in X [Priest,G]
9674 {x; A(x)} is a set of objects satisfying the condition A(x) [Priest,G]
9673 {a1, a2, ...an} indicates that a set comprising just those objects [Priest,G]
9677 Φ indicates the empty set, which has no members [Priest,G]
9676 {a} is the 'singleton' set of a (not the object a itself) [Priest,G]
9679 X⊂Y means set X is a 'proper subset' of set Y [Priest,G]
9678 X⊆Y means set X is a 'subset' of set Y [Priest,G]
9681 X = Y means the set X equals the set Y [Priest,G]
9683 X ∩ Y indicates the 'intersection' of sets X and Y, the objects which are in both sets [Priest,G]
9682 X∪Y indicates the 'union' of all the things in sets X and Y [Priest,G]
9684 Y - X is the 'relative complement' of X with respect to Y; the things in Y that are not in X [Priest,G]
4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / b. Terminology of ST
9694 The 'relative complement' is things in the second set not in the first [Priest,G]
9693 The 'intersection' of two sets is a set of the things that are in both sets [Priest,G]
9692 The 'union' of two sets is a set containing all the things in either of the sets [Priest,G]
9698 The 'induction clause' says complex formulas retain the properties of their basic formulas [Priest,G]
9688 A 'singleton' is a set with only one member [Priest,G]
9687 A 'member' of a set is one of the objects in the set [Priest,G]
9695 An 'ordered pair' (or ordered n-tuple) is a set with its members in a particular order [Priest,G]
9696 A 'cartesian product' of sets is the set of all the n-tuples with one member in each of the sets [Priest,G]
9686 A 'set' is a collection of objects [Priest,G]
9689 The 'empty set' or 'null set' has no members [Priest,G]
9690 A set is a 'subset' of another set if all of its members are in that set [Priest,G]
9691 A 'proper subset' is smaller than the containing set [Priest,G]
4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / c. Basic theorems of ST
9680 The empty set Φ is a subset of every set (including itself) [Priest,G]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
11175 Logical concepts rest on certain inferences, not on facts about implications [Fine,K]
5. Theory of Logic / F. Referring in Logic / 3. Property (λ-) Abstraction
11176 The property of Property Abstraction says any suitable condition must imply a property [Fine,K]
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
11174 A logical truth is true in virtue of the nature of the logical concepts [Fine,K]
9. Objects / D. Essence of Objects / 1. Essences of Objects
11177 Can the essence of an object circularly involve itself, or involve another object? [Fine,K]
9. Objects / D. Essence of Objects / 3. Individual Essences
11173 Being a man is a consequence of his essence, not constitutive of it [Fine,K]
9. Objects / D. Essence of Objects / 4. Essence as Definition
11179 If there are alternative definitions, then we have three possibilities for essence [Fine,K]
22. Metaethics / B. Value / 2. Values / f. Altruism
1590 The just man does not harm his enemies, but benefits everyone [Plato]