Combining Texts

Ideas for 'Thinking About Mathematics', 'Women of Trachis' and 'The Essence of Reference'

unexpand these ideas     |    start again     |     choose another area for these texts

display all the ideas for this combination of texts

4 ideas

5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
8729 Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro]
     Full Idea: Intuitionists in mathematics deny excluded middle, because it is symptomatic of faith in the transcendent existence of mathematical objects and/or the truth of mathematical statements.
     From: Stewart Shapiro (Thinking About Mathematics [2000], 1.2)
     A reaction: There are other problems with excluded middle, such as vagueness, but on the whole I, as a card-carrying 'realist', am committed to the law of excluded middle.
5. Theory of Logic / F. Referring in Logic / 1. Naming / e. Empty names
10429 It is best to say that a name designates iff there is something for it to designate [Sainsbury]
     Full Idea: It is better to say that 'For all x ("Hesperus" stands for x iff x = Hesperus)', than to say '"Hesperus" stands for Hesperus', since then the expression can be a name with no bearer (e.g. "Vulcan").
     From: Mark Sainsbury (The Essence of Reference [2006], 18.2)
     A reaction: In cases where it is unclear whether the name actually designates something, it seems desirable that the name is at least allowed to function semantically.
5. Theory of Logic / F. Referring in Logic / 2. Descriptions / b. Definite descriptions
10425 Definite descriptions may not be referring expressions, since they can fail to refer [Sainsbury]
     Full Idea: Almost everyone agrees that intelligible definite descriptions may lack a referent; this has historically been a reason for not counting them among referring expressions.
     From: Mark Sainsbury (The Essence of Reference [2006], 18.2)
     A reaction: One might compare indexicals such as 'I', which may be incapable of failing to refer when spoken. However 'look at that!' frequently fails to communicate reference.
10438 Definite descriptions are usually rigid in subject, but not in predicate, position [Sainsbury]
     Full Idea: Definite descriptions used with referential intentions (usually in subject position) are normally rigid, ..but in predicate position they are normally not rigid, because there is no referential intention.
     From: Mark Sainsbury (The Essence of Reference [2006], 18.5)
     A reaction: 'The man in the blue suit is the President' seems to fit, but 'The President is the head of state' doesn't. Seems roughly right, but language is always too complex for philosophers.