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Single Idea 6879

[filed under theme 5. Theory of Logic / B. Logical Consequence / 8. Material Implication ]

Full Idea

'Material implication' is a term introduced by Russell which is defined as 'the conjunction of p and not-q is false', but carries a strong implication that p implies q, and so there must be some kind of connection between them, which is misleading.

Gist of Idea

'Material implication' is defined as 'not(p and not-q)', but seems to imply a connection between p and q

Source

Thomas Mautner (Penguin Dictionary of Philosophy [1996], p.270)

Book Ref

Mautner,Thomas: 'Dictionary of Philosophy' [Penguin 1997], p.270

A Reaction

Mautner says statements of the form 'if p then q' are better called 'conditionals' than 'material implications'. Clearly there is a need for more precise terminology here, as the underlying concepts seem simple enough.

The 30 ideas from 'Penguin Dictionary of Philosophy'

9959 'Real' definitions give the essential properties of things under a concept [Mautner]
9961 'Contextual definitions' replace whole statements, not just expressions [Mautner]
9958 Recursive definition defines each instance from a previous instance [Mautner]
9960 A stipulative definition lays down that an expression is to have a certain meaning [Mautner]
9957 Ostensive definitions point to an object which an expression denotes [Mautner]
6219 The fallacy of composition is the assumption that what is true of the parts is true of the whole [Mautner]
4782 'All x are y' is equivalent to 'all non-y are non-x', so observing paper is white confirms 'ravens are black' [Mautner, by PG]
6881 Analytic philosophy studies the unimportant, and sharpens tools instead of using them [Mautner]
6886 Counterfactuals are not true, they are merely valid [Mautner]
6885 Counterfactuals are true if in every world close to actual where p is the case, q is also the case [Mautner]
6884 Counterfactuals say 'If it had been, or were, p, then it would be q' [Mautner]
6882 Counterfactuals presuppose a belief (or a fact) that the condition is false [Mautner]
6883 Maybe counterfactuals are only true if they contain valid inference from premisses [Mautner]
6896 Double effect is the distinction between what is foreseen and what is intended [Mautner]
6897 Double effect acts need goodness, unintended evil, good not caused by evil, and outweighing [Mautner]
6877 Entailment is logical requirement; it may be not(p and not-q), but that has problems [Mautner]
5452 'Essentialism' is opposed to existentialism, and claims there is a human nature [Mautner]
5449 Essentialism is often identified with belief in 'de re' necessary truths [Mautner]
6898 Fallibilism is the view that all knowledge-claims are provisional [Mautner]
6888 Fuzzy logic is based on the notion that there can be membership of a set to some degree [Mautner]
4783 Observing lots of green x can confirm 'all x are green' or 'all x are grue', where 'grue' is arbitrary [Mautner, by PG]
5439 The 'hermeneutic circle' says parts and wholes are interdependent, and so cannot be interpreted [Mautner]
6880 Strict implication says false propositions imply everything, and everything implies true propositions [Mautner]
6879 'Material implication' is defined as 'not(p and not-q)', but seems to imply a connection between p and q [Mautner]
6899 The references of indexicals ('there', 'now', 'I') depend on the circumstances of utterance [Mautner]
6878 A person who 'infers' draws the conclusion, but a person who 'implies' leaves it to the audience [Mautner]
6887 Linguistic philosophy approaches problems by attending to actual linguistic usage [Mautner]
6890 Quantifiers turn an open sentence into one to which a truth-value can be assigned [Mautner]
6452 'Sense-data' arrived in 1910, but it denotes ideas in Locke, Berkeley and Hume [Mautner]
6889 Vagueness seems to be inconsistent with the view that every proposition is true or false [Mautner]