|
15649
|
In semantic theories of truth, the predicate is in an object-language, and the definition in a metalanguage [Halbach]
|
|
Full Idea:
In semantic theories of truth (Tarski or Kripke), a truth predicate is defined for an object-language. This definition is carried out in a metalanguage, which is typically taken to include set theory or another strong theory or expressive language.
|
|
From:
Volker Halbach (Axiomatic Theories of Truth (2005 ver) [2005], 1)
|
|
A reaction:
Presumably the metalanguage includes set theory because that connects it with mathematics, and enables it to be formally rigorous. Tarski showed, in his undefinability theorem, that the meta-language must have increased resources.
|
|
13331
|
Part and whole contribute asymmetrically to one another, so must differ [Fine,K]
|
|
Full Idea:
The whole identity of a part is relevant to whether it is a part, but the identity of the whole makes a part a part. The whole part belongs to the whole as a part. The standard account in terms of time-slices fails to respect this part/whole asymmetry.
|
|
From:
Kit Fine (Things and Their Parts [1999], §2)
|
|
A reaction:
Hard to follow, but I think the asymmetry is that the wholeness of the part contributes to the wholeness of the whole, while the wholeness of the whole contributes to the parthood of the part. Wholeness does different jobs in different directions. OK?
|
|
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.
|
|
13332
|
Hierarchical set membership models objects better than the subset or aggregate relations do [Fine,K]
|
|
Full Idea:
It is the hierarchical conception of sets and their members, rather than the linear conception of set and subset or of aggregate and component, that provides us with the better model for the structure of part-whole in its application to material things.
|
|
From:
Kit Fine (Things and Their Parts [1999], §5)
|
|
A reaction:
His idea is to give some sort of internal structure. He says of {a,b,c,d} that we can create subsets {a,b} and {c,d} from that. But {{a,b},{c,d}} has given member sets, and he is looking for 'natural' divisions between the members.
|
|
13333
|
The matter is a relatively unstructured version of the object, like a set without membership structure [Fine,K]
|
|
Full Idea:
The wood is, as it were, a relatively unstructured version of the tree, just as the set {a,b,c,d} is an unstructured counterpart of the set {{a,b},{c,d}}.
|
|
From:
Kit Fine (Things and Their Parts [1999], §5)
|
|
A reaction:
He is trying to give a modern logicians' account of the Aristotelian concept of 'form' (as applied to matter). It is part of the modern project that objects must be connected to the formalism of mereology or set theory. If it works, are we thereby wiser?
|
|
13326
|
A 'temporary' part is a part at one time, but may not be at another, like a carburetor [Fine,K]
|
|
Full Idea:
First, a thing can be a part in a way that is relative to a time, for example, that a newly installed carburettor is now part of my car, whereas earlier it was not. (This will be called a 'temporary' part).
|
|
From:
Kit Fine (Things and Their Parts [1999], Intro)
|
|
A reaction:
[Cf Idea 13327 for the 'second' concept of part] I'm immediately uneasy. Being a part seems to be a univocal concept. He seems to be distinguishing parts which are necessary for identity from those which aren't. Fine likes to define by example.
|
|
13327
|
A 'timeless' part just is a part, not a part at some time; some atoms are timeless parts of a water molecule [Fine,K]
|
|
Full Idea:
Second, an object can be a part of another in a way that is not relative to time ('timeless'). It is not appropriate to ask when it is a part. Thus pants and jacket are parts of the suit, atoms of a water molecule, and two pints part of a quart of milk.
|
|
From:
Kit Fine (Things and Their Parts [1999], Intro)
|
|
A reaction:
[cf Idea 13326 for the other concept of 'part'] Again I am uneasy that 'part' could have two meanings. A Life Member is a member in the same way that a normal paid up member is a member.
|
|
13329
|
An 'aggregative' sum is spread in time, and exists whenever a component exists [Fine,K]
|
|
Full Idea:
In the 'aggregative' understanding of a sum, it is spread out in time, so that exists whenever any of its components exists (just as it is located at any time wherever any of its components are located).
|
|
From:
Kit Fine (Things and Their Parts [1999], §1)
|
|
A reaction:
This works particularly well for something like an ancient forest, which steadily changes its trees. On that view, though, the ship which has had all of its planks replaced will be the identical single sum of planks all the way through. Fine agrees.
|
|
13330
|
An 'compound' sum is not spread in time, and only exists when all the components exists [Fine,K]
|
|
Full Idea:
In the 'compound' notion of sum, the mereological sum is spread out only in space, not also in time. For it to exist at a time, all of its components must exist at the time.
|
|
From:
Kit Fine (Things and Their Parts [1999], §1)
|
|
A reaction:
It is hard to think of anything to which this applies, apart from for a classical mereologist. Named parts perhaps, like Tom, Dick and Harry. Most things preserve sum identity despite replacement of parts by identical components.
|
|
13328
|
Two sorts of whole have 'rigid embodiment' (timeless parts) or 'variable embodiment' (temporary parts) [Fine,K]
|
|
Full Idea:
I develop a version of hylomorphism, in which the theory of 'rigid embodiment' provides an account of the timeless relation of part, and the theory of 'variable embodiment' is an account of the temporary relation. We must accept two new kinds of whole.
|
|
From:
Kit Fine (Things and Their Parts [1999], Intro)
|
|
A reaction:
[see Idea 13326 and Idea 13327 for the two concepts of 'part'] This is easier to take than the two meanings for 'part'. Since Aristotle, everyone has worried about true wholes (atoms, persons?) and looser wholes (houses).
|