Basic Question: What's the difference between logical forms and truth conditions?
Hello,
I have a basic question: what's the difference between logical forms and truth conditions?
The logical form of 'all dogs are animals' is 'for every x, if x is a dog, then x is an animal.'
It seems that the truth condition of it is the same.
What makes the difference?
I have a basic question: what's the difference between logical forms and truth conditions?
The logical form of 'all dogs are animals' is 'for every x, if x is a dog, then x is an animal.'
It seems that the truth condition of it is the same.
What makes the difference?
Comments (9)
The truth condition of "all dogs are animals" would be as follows:
"All dogs are animals" is true if and only if for every x, if x is a dog, then x is an animal.
This seems to be the same as the logical form of "all dogs are animals".
A better approach is probably this: just why are you asking this question? The context can help us answer in a targeted way pertinent to your concerns. Are you asking something relative to a class you're taking? Something you read? What got you thinking about this in the first place?
I was reading Delia Graff Fara's 'Descriptions as Predicates'. She distinguishes logical forms from truth conditions. What she said as truth conditions is the same as what I've been thinking as logical forms. So, I asked a question about it here.
Right. I didn't find where I can read the whole paper at the moment, but based on the abstract, the idea is probably something like this: that truth conditions aren't the same as logical form because the logical form can be a definite description while the truth conditions (in such a case) are simply predicative rather than definite-descriptive. In other words, in a particular case, the truth conditions can simply be a matter of predicating a property of a particular individual rather than having to be parsed in a definite description translation, despite the fact that logically, that is, in terms of the apparent from of the sentence, it is a definite description.
The "logical form" is a "form", a particular syntax. The "truth conditions" are facts of the world, not ways to shape a sentance. This is actually a huge difference.
When we talk about 'truth' of a sentence we are implying a meaning for it, which requires that there be a semantics. In the study of logic the relationship between syntax and semantics is covered by the study of semantics. A Theory T in a Language L is a bunch of syntactically valid sentences in L, with no assumed meaning. A Model M for T is a conceptual structure whose elements correspond to certain elements ('terms') of L via a mapping called an Interpretation. A sentence S in the Theory is 'true' in M if the relationship(s) in M that are implied by the Interpretation of S in M actually hold.
Logical forms are merely strings of symbols.
Truth conditions are what we are implying a meaning.
I understand.
For every x, if Fx, then Gx
The truth condition of "all dogs are animals" would be:
For every x, if x is a dog, then x is an animal.
Now I understand how they are different.