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Single Idea 6890
[filed under theme 5. Theory of Logic / G. Quantification / 1. Quantification
]
Full Idea
In formal logic, quantifiers are operators that turn an open sentence into a sentence to which a truth-value can be assigned.
Clarification
An 'open sentence' is one with a free variable, like a general formula in physics
Gist of Idea
Quantifiers turn an open sentence into one to which a truth-value can be assigned
Source
Thomas Mautner (Penguin Dictionary of Philosophy [1996], p.464)
Book Ref
Mautner,Thomas: 'Dictionary of Philosophy' [Penguin 1997], p.464
A Reaction
The standard quantifiers are 'all' and 'at least one'. The controversy is whether quantifiers actually assert existence, or whether (as McGinn says) they merely specify the subject matter of the sentence. I prefer the latter.
The
30 ideas
from Thomas Mautner
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9959
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'Real' definitions give the essential properties of things under a concept
[Mautner]
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9961
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'Contextual definitions' replace whole statements, not just expressions
[Mautner]
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9958
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Recursive definition defines each instance from a previous instance
[Mautner]
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9960
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A stipulative definition lays down that an expression is to have a certain meaning
[Mautner]
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9957
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Ostensive definitions point to an object which an expression denotes
[Mautner]
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6219
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The fallacy of composition is the assumption that what is true of the parts is true of the whole
[Mautner]
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4782
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'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]
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6881
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Analytic philosophy studies the unimportant, and sharpens tools instead of using them
[Mautner]
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6886
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Counterfactuals are not true, they are merely valid
[Mautner]
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6885
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Counterfactuals are true if in every world close to actual where p is the case, q is also the case
[Mautner]
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6884
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Counterfactuals say 'If it had been, or were, p, then it would be q'
[Mautner]
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6882
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Counterfactuals presuppose a belief (or a fact) that the condition is false
[Mautner]
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6883
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Maybe counterfactuals are only true if they contain valid inference from premisses
[Mautner]
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6896
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Double effect is the distinction between what is foreseen and what is intended
[Mautner]
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6897
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Double effect acts need goodness, unintended evil, good not caused by evil, and outweighing
[Mautner]
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6877
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Entailment is logical requirement; it may be not(p and not-q), but that has problems
[Mautner]
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5452
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'Essentialism' is opposed to existentialism, and claims there is a human nature
[Mautner]
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5449
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Essentialism is often identified with belief in 'de re' necessary truths
[Mautner]
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6898
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Fallibilism is the view that all knowledge-claims are provisional
[Mautner]
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6888
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Fuzzy logic is based on the notion that there can be membership of a set to some degree
[Mautner]
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4783
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Observing lots of green x can confirm 'all x are green' or 'all x are grue', where 'grue' is arbitrary
[Mautner, by PG]
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5439
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The 'hermeneutic circle' says parts and wholes are interdependent, and so cannot be interpreted
[Mautner]
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6880
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Strict implication says false propositions imply everything, and everything implies true propositions
[Mautner]
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6879
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'Material implication' is defined as 'not(p and not-q)', but seems to imply a connection between p and q
[Mautner]
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6899
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The references of indexicals ('there', 'now', 'I') depend on the circumstances of utterance
[Mautner]
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6878
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A person who 'infers' draws the conclusion, but a person who 'implies' leaves it to the audience
[Mautner]
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6887
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Linguistic philosophy approaches problems by attending to actual linguistic usage
[Mautner]
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6890
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Quantifiers turn an open sentence into one to which a truth-value can be assigned
[Mautner]
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6452
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'Sense-data' arrived in 1910, but it denotes ideas in Locke, Berkeley and Hume
[Mautner]
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6889
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Vagueness seems to be inconsistent with the view that every proposition is true or false
[Mautner]
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