Combining Texts

All the ideas for 'Exigency to Exist in Essences', 'Intro to Non-Classical Logic (1st ed)' and 'Naming and Necessity preface'

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38 ideas

4. Formal Logic / D. Modal Logic ML / 1. Modal Logic
16985 Possible worlds allowed the application of set-theoretic models to modal logic [Kripke]
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]
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]
9675 a ∈ X says a is an object in set X; a ∉ X says a is not in X [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]
9678 X⊆Y means set X is a 'subset' of set Y [Priest,G]
9679 X⊂Y means set X is a 'proper 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]
9684 Y - X is the 'relative complement' of X with respect to Y; the things in Y that are not in X [Priest,G]
9682 X∪Y indicates the 'union' of all the things in sets X and Y [Priest,G]
4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / b. Terminology of ST
9692 The 'union' of two sets is a set containing all the things in either of the sets [Priest,G]
9693 The 'intersection' of two sets is a set of the things that are in both sets [Priest,G]
9694 The 'relative complement' is things in the second set not in the first [Priest,G]
9698 The 'induction clause' says complex formulas retain the properties of their basic formulas [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]
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]
9688 A 'singleton' is a set with only one member [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 / F. Referring in Logic / 1. Naming / c. Names as referential
16982 A man has two names if the historical chains are different - even if they are the same! [Kripke]
7. Existence / A. Nature of Existence / 5. Reason for Existence
19400 Possibles demand existence, so as many of them as possible must actually exist [Leibniz]
19401 God's sufficient reason for choosing reality is in the fitness or perfection of possibilities [Leibniz]
9. Objects / F. Identity among Objects / 1. Concept of Identity
16981 With the necessity of self-identity plus Leibniz's Law, identity has to be an 'internal' relation [Kripke]
9. Objects / F. Identity among Objects / 8. Leibniz's Law
4942 The indiscernibility of identicals is as self-evident as the law of contradiction [Kripke]
10. Modality / C. Sources of Modality / 1. Sources of Necessity
16984 I don't think possible worlds reductively reveal the natures of modal operators etc. [Kripke]
10. Modality / D. Knowledge of Modality / 2. A Priori Contingent
9385 The very act of designating of an object with properties gives knowledge of a contingent truth [Kripke]
10. Modality / E. Possible worlds / 1. Possible Worlds / a. Possible worlds
19402 The actual universe is the richest composite of what is possible [Leibniz]
4943 Instead of talking about possible worlds, we can always say "It is possible that.." [Kripke]
10. Modality / E. Possible worlds / 2. Nature of Possible Worlds / a. Nature of possible worlds
16983 Probability with dice uses possible worlds, abstractions which fictionally simplify things [Kripke]