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Single Idea 18828

[filed under theme 10. Modality / B. Possibility / 1. Possibility ]

Full Idea

Two possibilities are incompatible when no possibility determines both.

Gist of Idea

If two possibilities can't share a determiner, they are incompatible

Source

Ian Rumfitt (The Boundary Stones of Thought [2015], 7.1)

Book Ref

Rumfitt,Ian: 'The Boundary Stones of Thought' [OUP 2015], p.185

A Reaction

This strikes me as just the right sort of language for building up a decent metaphysical picture of the world, which needs to incorporate possibilities as well as actualities.

Related Ideas

Idea 18826 'True at a possibility' means necessarily true if what is said had obtained [Rumfitt]

Idea 18829 The truth grounds for 'not A' are the possibilities incompatible with truth grounds for A [Rumfitt]

The 37 ideas from 'The Boundary Stones of Thought'

18803 Semantics for propositions: 1) validity preserves truth 2) non-contradition 3) bivalence 4) truth tables [Rumfitt]
18799 Intuitionists can accept Double Negation Elimination for decidable propositions [Rumfitt]
18798 It is the second-order part of intuitionistic logic which actually negates some classical theorems [Rumfitt]
18805 Classical logic rules cannot be proved, but various lines of attack can be repelled [Rumfitt]
18804 The case for classical logic rests on its rules, much more than on the Principle of Bivalence [Rumfitt]
18802 In specifying a logical constant, use of that constant is quite unavoidable [Rumfitt]
18800 Introduction rules give deduction conditions, and Elimination says what can be deduced [Rumfitt]
18808 Normal deduction presupposes the Cut Law [Rumfitt]
18807 Monotonicity means there is a guarantee, rather than mere inductive support [Rumfitt]
18809 Logical truths are just the assumption-free by-products of logical rules [Rumfitt]
18815 Logic is higher-order laws which can expand the range of any sort of deduction [Rumfitt]
18814 'Absolute necessity' would have to rest on S5 [Rumfitt]
18813 Logical consequence is a relation that can extended into further statements [Rumfitt]
18816 Metaphysical modalities respect the actual identities of things [Rumfitt]
18817 We understand conditionals, but disagree over their truth-conditions [Rumfitt]
18819 The idea that there are unrecognised truths is basic to our concept of truth [Rumfitt]
18820 In English 'evidence' is a mass term, qualified by 'little' and 'more' [Rumfitt]
18821 Possibilities are like possible worlds, but not fully determinate or complete [Rumfitt]
18824 Since possibilities are properties of the world, calling 'red' the determination of a determinable seems right [Rumfitt]
18825 S5 is the logic of logical necessity [Rumfitt]
18826 'True at a possibility' means necessarily true if what is said had obtained [Rumfitt]
18827 If truth-tables specify the connectives, classical logic must rely on Bivalence [Rumfitt]
18828 If two possibilities can't share a determiner, they are incompatible [Rumfitt]
18829 The truth grounds for 'not A' are the possibilities incompatible with truth grounds for A [Rumfitt]
18831 Medieval logicians said understanding A also involved understanding not-A [Rumfitt]
18830 Most set theorists doubt bivalence for the Continuum Hypothesis, but still use classical logic [Rumfitt]
18834 Infinitesimals do not stand in a determinate order relation to zero [Rumfitt]
18835 Logic doesn't have a metaphysical basis, but nor can logic give rise to the metaphysics [Rumfitt]
18836 A set may well not consist of its members; the empty set, for example, is a problem [Rumfitt]
18837 A set can be determinate, because of its concept, and still have vague membership [Rumfitt]
18839 An object that is not clearly red or orange can still be red-or-orange, which sweeps up problem cases [Rumfitt]
18838 The extension of a colour is decided by a concept's place in a network of contraries [Rumfitt]
18840 When faced with vague statements, Bivalence is not a compelling principle [Rumfitt]
18842 Maybe an ordinal is a property of isomorphic well-ordered sets, and not itself a set [Rumfitt]
18843 The iterated conception of set requires continual increase in axiom strength [Rumfitt]
18845 If the totality of sets is not well-defined, there must be doubt about the Power Set Axiom [Rumfitt]
18846 Cantor and Dedekind aimed to give analysis a foundation in set theory (rather than geometry) [Rumfitt]