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How do I express this in FOL?

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I'm trying to express this in FOL:

Every word has at least one concept associated w/ it, and every concept has at least one word associated w/ it. Would it be:

For all (x)(Cx<->Wx)

or

(for all x(w(x) -> there exists y(c(y) & r(x,y)))) & (for all y(c(y) -> there exists x(w(x) & r(x,y)))), where r(x,y) denotes the concept associate w/ the word x. Anyway to make that clearer? What would this actually look like on paper?

Thanks!

@Protoman2050,

Protoman2050 wrote:

I'm trying to express this in FOL:

Every word has at least one concept associated w/ it, and every concept has at least one word associated w/ it. Would it be:

For all (x)(Cx<->Wx)

or

(for all x(w(x) -> there exists y(c(y) & r(x,y)))) & (for all y(c(y) -> there exists x(w(x) & r(x,y)))), where r(x,y) denotes the concept associate w/ the word x. Anyway to make that clearer? What would this actually look like on paper?

Thanks!

Even though I took a logic course and feel I am logical what the hell in FOL?

@Theaetetus,

First order logic; propostional logic w/ existential quantifiers; First-order logic - Wikipedia, the free encyclopedia

@Protoman2050,

Why do you want to express this in FOL? BTW why not UML? Isn't the expression you want to arrive at an app?

@Ron C de Weijze,

Ron C. de Weijze wrote:

Why do you want to express this in FOL? BTW why not UML? Isn't the expression you want to arrive at an app?

No, it's not for anything compsci related...just to condense my writing of a proof for God: http://www.philosophyforum.com/forum/philosophy-religion/1655-proof-god-s-self-evidence.html

@Protoman2050,

In quantificational logic, (x) (Cx<->Wx) translates as; For any (x), C(x) if and only if W(x). Your elaboration paints a different picture.

For FOL...you would need to assert something (i.e. universal or existential quantifier) to establish a categorical syntactical structure (unless you are assuming it).

Also, you would need to elaborate on the sentence constants (i.e. C and W) to show what exactly you are trying to prove.

Also, you may want to reconsider your notation with the bi-conditional and quantificational logic.

@VideCorSpoon,

VideCorSpoon wrote:

In quantificational logic, (x) (Cx<->Wx) translates as; For any (x), C(x) if and only if W(x). Your elaboration paints a different picture.

You would need to assert something (i.e. universal or existential quantifier) to establish a categorical syntactical structure (unless you are assuming it).

Also, you would need to elaborate on the sentence constants (i.e. C and W) to show what exactly you are trying to prove.

Also, you may want to reconsider your notation with the bi-conditional and quantificational logic.

So it would work better as --where C(x) means concept referred to by x, and W(x) means word linked to the concept of x; R(x,y) means the concept y associated w/ x--:
for all x(W(x) -> there exists y(C(y) & R(x,y))) & for all x(C(x) -> there exists y(W(y) & R(x,y)))

Can you show me how that would be read and what that would look like as symbols?

Thanks!

@Protoman2050,

You may be over complicating the process of quantificational logic. First and foremost, what is the literal argument for the existence of God you are trying to convey? It's difficult to interpret what you are trying to convey without a literal example. Also when you refer to the grammatical quantifier "linked,"

I'm assuming that you intend a conditional rather than a bi-conditional.

Take this for example? (x) (Cx --> Wx) (note: I substituted the bi-conditional for the conditional because of the lingual assumption.)

That formula translates as follows (in the universal affirmative); Every x such that x is C such that x is W.

Also, there are universal affirmatives here, but in your elaboration you use existential quantifications. This violates wff. You may want to revise that portion.

@VideCorSpoon,

I am trying to convey the idea that, for every word, there are one or more ideas associated w/ it, and for every idea, there are one or more words associated w/ it.

@Protoman2050,

Oh. You don't need to go into quantificational logic for that. You can stay within the realm of propositional logic and still accomplish your goal without predicative inferences.

All you need is a standard bi-conditional and a truth table to prove it.

@VideCorSpoon,

VideCorSpoon wrote:

Oh. You don't need to go into quantificational logic for that. You can stay within the realm of propositional logic and still accomplish your goal without predicative inferences.

All you need is a standard bi-conditional and a truth table to prove it.

But I'm trying to say for ALL words, and ALL concepts...there are NO meaningless words, and NO unnamed concepts.

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