What do "the domain of the metalanguage" and "the world of that metalanguage" refer to? — TonesInDeepFreeze
A language itself doesn't have a domain nor a world. Rather, an interpretation of a language has a domain of discourse — TonesInDeepFreeze
Consider the sentence: 'Snow is white' is true if and only if snow is white. — TonesInDeepFreeze
Tarski's T-sentence is the Metalanguage — RussellA
The LHS is the Object Language (OL). — RussellA
In the OL, we can say that the domain — RussellA
The OL is interpreted in the ML. — RussellA
The domain of the OL on the LHS of the biconditional is "cooking", "cleaning", "bar", "fog", etc — RussellA
The domain of the ML on the RHS of the biconditional is cooking, cleaning, bar, fog, etc — RussellA
the T-sentence relates the domain of the OL with the domain of the ML — RussellA
1) In the world is the achromatic object color of greatest lightness characteristically perceived to belong to objects that reflect diffusely nearly all incident energy throughout the visible spectrum. Designate this "white"
2) In the world is precipitation in the form of small white ice crystals formed directly from the water vapor of the air at a temperature of less than 32°F (0°C). Designate this as "snow" — RussellA
3) "Snow is white" is true IFF what has been designated "snow" has what has been designated "white" — RussellA
I observe the world and see something cold, white and frozen and a relation between them, the relation snow. — RussellA
The T-sentence is a biconditional, meaning that the truth of the proposition "snow is white" is conditional on something. — RussellA
"snow" being "white" — RussellA
Of course the word 'snow' is not the word 'white'. And of course the word 'white' is not an adjective regarding the word 'snow'. — TonesInDeepFreeze
'Snow is white' is true iff what 'snow' stands for has the property that 'white' stands for. — TonesInDeepFreeze
'Snow is white' is true iff what 'snow' stands for hasthe property that'white' standsfor [it, among other things]. — TonesInDeepFreeze
It seems that we both agree that the T-sentence is missing a necessary condition on the RHS of the biconditional. — RussellA
Talk of properties when glossing use of a logical predicate is eliminable? — bongo fury
The nominalist cancels out the property and treats the predicate as bearing a one-many relation directly to the several things it applies to or denotes. — Goodman, p49
A second thread of Hochberg's article comes to something like this: a common predicate applies to several different things in virtue of a common property they possess. Now I doubt very much that Hochberg intends to deny that any two or more things have some property in common; thus for him as for the nominalist there are no two or more things such that application of a common predicate is precluded. Advocates of properties usually hold that sometimes more than one property may be common to exactly the same things; but Hochberg does not seem to be arging this point either. Rather, he seems to hold that a predicate applies initially to a property as its name, and then only derivatively to the things that have that property. The nominalist cancels out the property and treats the predicate as bearing a one-many relation directly to the several things it applies to or denotes. I cannot see that anything Hochberg says in any way discredits such a treatment or shows the need for positing properties as intervening entities.
I didn't say anything like that. — TonesInDeepFreeze
Whatever is meant by 'predicate' and 'property' there, you asked about model theory. — TonesInDeepFreeze
unary predicate — bongo fury
unary relations — bongo fury
I mean one-place? — bongo fury
Don't want more! — bongo fury
Get involved in philosophical discussions about knowledge, truth, language, consciousness, science, politics, religion, logic and mathematics, art, history, and lots more. No ads, no clutter, and very little agreement — just fascinating conversations.