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Ideas for 'Axiomatic Theories of Truth (2005 ver)', 'Cratylus' and 'Intermediate Logic'

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4 ideas

5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
13357 Truth-functors are usually held to be defined by their truth-tables [Bostock]
     Full Idea: The usual view of the meaning of truth-functors is that each is defined by its own truth-table, independently of any other truth-functor.
     From: David Bostock (Intermediate Logic [1997], 2.7)
5. Theory of Logic / E. Structures of Logic / 5. Functions in Logic
13812 A 'zero-place' function just has a single value, so it is a name [Bostock]
     Full Idea: We can talk of a 'zero-place' function, which is a new-fangled name for a familiar item; it just has a single value, and so it has the same role as a name.
     From: David Bostock (Intermediate Logic [1997], 8.2)
13811 A 'total' function ranges over the whole domain, a 'partial' function over appropriate inputs [Bostock]
     Full Idea: Usually we allow that a function is defined for arguments of a suitable kind (a 'partial' function), but we can say that each function has one value for any object whatever, from the whole domain that our quantifiers range over (a 'total' function).
     From: David Bostock (Intermediate Logic [1997], 8.2)
     A reaction: He points out (p.338) that 'the father of..' is a functional expression, but it wouldn't normally take stones as input, so seems to be a partial function. But then it doesn't even take all male humans either. It only takes fathers!
5. Theory of Logic / E. Structures of Logic / 7. Predicates in Logic
15651 Instead of saying x has a property, we can say a formula is true of x - as long as we have 'true' [Halbach]
     Full Idea: Quantification over (certain) properties can be mimicked in a language with a truth predicate by quantifying over formulas. Instead of saying that Tom has the property of being a poor philosopher, we can say 'x is a poor philosopher' is true of Tom.
     From: Volker Halbach (Axiomatic Theories of Truth (2005 ver) [2005], 1.1)
     A reaction: I love this, and think it is very important. He talks of 'mimicking' properties, but I see it as philosophers mistakenly attributing properties, when actually what they were doing is asserting truths involving certain predicates.