Predicate logic
Posted: Mon Jul 24, 2017 2:25 am
Let's discuss interpretations (yours and mine) of predicate logic, aka quantificational logic. It is the familiar logical language which includes
quantifiers (for all x, there exists an x such that - i.e. (x) and E(x)); the logical connectives of sentence logic (not, and, if..then, or); and then the atomic sentences of the form Fa where F is a predicate and a is a constant.
That's it, that's all predicate logic consists of. But here's the interesting part. It cannot function without the following meta-logical apparatus to support it. It is assumed in predicate logic, that there exists a domain of objects - an ontology in philosophical terms, a domain in mathematical terms. Each object has a unique name. These are usually represented by lower case letters from the beginning of the alphabet - a,b,c, d. Of course we can generate as many as we want by means of something like a', b', c' ... and then a'', b'', c'''... etc..
Each unique name (denoting an individual object of the domain) then can be joined with a predicate symbol, represented by upper case letters F, G, H, etc. to form atomic sentences of the subject-predicate form, Fa. The predicates, as with the objects and names of the domain, are given - that is, they are assumed and stipulated to at the beginning, as part of the formal language.
I am asking, in this thread (if anyone has read this far), for an interpretation of this logical apparatus. For instance, are the objects of the domain predicate-less simples that exist prior to the formation of atomic sentences? How are the predicates of a particular system chosen? Aren't they chosen specifically to apply to a preconceived domain of predicated objects? In which case, isn't this whole apparatus just a bit of contrived smoke and mirrors?
quantifiers (for all x, there exists an x such that - i.e. (x) and E(x)); the logical connectives of sentence logic (not, and, if..then, or); and then the atomic sentences of the form Fa where F is a predicate and a is a constant.
That's it, that's all predicate logic consists of. But here's the interesting part. It cannot function without the following meta-logical apparatus to support it. It is assumed in predicate logic, that there exists a domain of objects - an ontology in philosophical terms, a domain in mathematical terms. Each object has a unique name. These are usually represented by lower case letters from the beginning of the alphabet - a,b,c, d. Of course we can generate as many as we want by means of something like a', b', c' ... and then a'', b'', c'''... etc..
Each unique name (denoting an individual object of the domain) then can be joined with a predicate symbol, represented by upper case letters F, G, H, etc. to form atomic sentences of the subject-predicate form, Fa. The predicates, as with the objects and names of the domain, are given - that is, they are assumed and stipulated to at the beginning, as part of the formal language.
I am asking, in this thread (if anyone has read this far), for an interpretation of this logical apparatus. For instance, are the objects of the domain predicate-less simples that exist prior to the formation of atomic sentences? How are the predicates of a particular system chosen? Aren't they chosen specifically to apply to a preconceived domain of predicated objects? In which case, isn't this whole apparatus just a bit of contrived smoke and mirrors?