Categorical has added ingredients, the logic represented by the square of opposition. Take away ingredients and the square collapses to just contradictories.

This could be a lot longer and even more unclear, but I think if you look at the square and grok the collapse, you'll have got it. I'm betting on you!

Categorical has added ingredients, the logic represented by the square of opposition. Take away ingredients and the square collapses to just contradictories.

This could be a lot longer and even more unclear, but I think if you look at the square and grok the collapse, you'll have got it. I'm betting on you! — tim wood

I'm afraid your confidence in me is misplaced.

I can say that,

Predicate logic

Where Dx = x is God,

9. G = God exists = Ex(Dx)
10. ~G = God doesn't exist = ~Ex(Dx)

Now, Ex(Dx) is the contradictory of ~Ex(Dx) just as in sentential logic G is the contradictory of ~G.

In categorical logic it's different:

5. God exists (G) = All things identical to God are existent things = A
6. God doesn't exist (~G) = No things identical to God are existent things = B

A and B are contraries and not contradictories.

:confused:

You're tangled in language.

5) All S are P. (This assuming existence is a legitimate predicate. I don't think it is, being just All S is is.)
The negation of this is not No S are P. You see that, yes?
The negation is Not All S are P. That is, Some S are not P.

But this is quantitative. All, some, none, some not.

With universals, like God or George or Pegasus, it's qualitative, just either-or. Either-or is all you got, and it's contradictory.

Illustration: suppose many gods, of varying height. Then all these would make sense and the relations between them would make sense.
All G are T
Some G are T
No G are T
Some G are not T.

But if all you have is G is, then either
G is
G isn't.

You're using interchangeably a quantitative G and a universal G.

5. God exists (G) = All things identical to God are existent things = A
6. God doesn't exist (~G) = No things identical to God are existent things = B — TheMadFool

It's where you place the negation. It makes a difference from
1. G = God exist.
2. ~G = God doesn't exist.

You're tangled in language. — tim wood

I thought as much. I needed someone to tell me that. :up:

This assuming existence is a legitimate predicate — tim wood

Methinks therein lies the rub.

Existence isn't a legitimate predicate. So, in predicate logic where Dx = x is God,

God exists = (Ex)(Dx)

God doesn't exist = ~(Ex)(Gx)

(Ex)(Gx) and ~(Ex)(Gx) are contradictories. Nothing to fret about.

---

Let me give you some background info. I was engaged in a discussion on the law of karma (buddhism) with some folk. I claimed that karma doesn't have room for chance in our lives and my interlocutor disagreed saying that there's an element of chance.

I tried to formulate a sentential/categorical logic statement for this situation. My attempt vide infra:

1. Everything is determined (karma) = D

Negating statement 1, as the person I was discussing this with did, we get (please note, this is where I think I get tangled in language),

2. Everything is not determined = ~D

Let's now, translate 1 and 2 in categorical logic

3. All things are determined things (from 1)

4. No things are determined things (from 2) ?! (chess notation: dubious move)

The negation of 2 isn't 4, it's actually

5. Some things are not determined.

There I cleared up my confusion. Thanks a million for your help. Much appreciated.

It's where you place the negation. It makes a difference from
1. G = God exist.
2. ~G = God doesn't exist — Caldwell

Thanks.

Update

There seems to be a problem with existence as a predicate.

Sentential Logic

1. Apples exist = A
2. Apples don't exist = ~A

A is the contradictory of ~A

No issues.

Predicate Logic

where Px = x is an apple,

3. Apples exist = (Ex)(Px)
4. Apples don't exist = ~(Ex)(Px)

(Ex)(Px) is the contradictory of ~(Ex)(Px)

No problem here too.

Categorical Logic

5. Apples exist = All apples are existent things. = S
6. Apples don't exist = No apples are existent things. = T


The problem:

There's no conflict between the sentential logic and predicate logic translations: A, ~A and (Ex)(Px), ~(Ex)(Px) are contradictories.

However, in categorical logic, S and T aren't contradictories. They should be because they're translations of the same two contradictory statements [A and ~A or (Ex)(Px) and ~(Ex)(Px)]. Instead they're contraries.

What gives?

You're using interchangeably a quantitative G and a universal G. — tim wood

@TheMadFool change the negation of universal with an existential. Then try to see if a logical equivalence is equal to a logical translation.

Do you want to talk about the God of actual religions, or the God of philosophers?

If the former, then your analysis doesn't apply, because God is defined as the unique being, and as such, incomparable to any other being. God doesn't exist the way tables and chairs do, or as humans do, nor can he be known the way tables and chair can be known, or the way Tom and Jane can be known.

If the latter -- then ask yourself why bother.

Do you want to talk about the God of actual religions, or the God of philosophers?

If the former, then your analysis doesn't apply, because God is defined as the unique being, and as such, incomparable to any other being. God doesn't exist the way tables and chairs do, or as humans do, nor can he be known the way tables and chair can be known, or the way Tom and Jane can be known.

If the latter -- then ask yourself why bother. — baker

Not god, existence. Is it a valid predicate.

Sentential logic

1. Apples exist

2. Apples don't exist

1 is the contradictorg of 2

Categorical logic

3. All apples are existent things. (translation of 1)

4. No apples are existent things (translation of 2)

3 and 4 are not contradictories, they're contraries.

Not god, existence. — TheMadFool

When you're talking about the existence of God, what I said applies.

When you're talking about the existence of God, what I said applies. — baker

Not God, existence.

Your examples:

1. G = God exist.
2. ~G = God doesn't exist.
/.../
5. G = All things identical to God are existent things. = A
6. ~G = No things identical to God are existent things. = B — TheMadFool

It is interesting to see you putting the question of God's existence down to logical equations because recently I have been thinking it is a matter of semantics. My own recent thought has been that it comes down to how we name the underlying force behind existence, with some calling it 'God' and others preferring scientific frames of description. So, the underlying question may be how much the matter is about logic, language and causal explanations, and the complex mixture of these in our own descriptions and grasp for understanding and meaning.

Your examples — baker

I also wrote,

There seems to be a problem with existence as a predicate.

Sentential Logic

1. Apples exist = A
2. Apples don't exist = ~A

A is the contradictory of ~A

No issues.

Predicate Logic

where Px = x is an apple,

3. Apples exist = (Ex)(Px)
4. Apples don't exist = ~(Ex)(Px)

(Ex)(Px) is the contradictory of ~(Ex)(Px)

No problem here too.

Categorical Logic

5. Apples exist = All apples are existent things. = S
6. Apples don't exist = No apples are existent things. = T


The problem:

There's no conflict between the sentential logic and predicate logic translations: A, ~A and (Ex)(Px), ~(Ex)(Px) are contradictories.

However, in categorical logic, S and T aren't contradictories. They should be because they're translations of the same two contradictory statements [A and ~A or (Ex)(Px) and ~(Ex)(Px)]. Instead they're contraries.

What gives? — TheMadFool

It is interesting to see you putting the question of God's existence down to logical equations because recently I have been thinking it is a matter of semantics. My own recent thought has been that it comes down to how we name the underlying force behind existence, with some calling it 'God' and others preferring scientific frames of description. So, the underlying question may be how much the matter is about logic, language and causal explanations, and the complex mixture of these in our own descriptions and grasp for understanding and meaning. — Jack Cummins

Thanks to you and @baker for stressing on the God angle. I wonder if the issue I'm grappling with has anything to do with the ontological argument (St. Anselm Of Cabterbury)

Immanuel Kant's critique [of the ontological argument] was based on what he saw as the false premise that existence is a predicate, arguing that "existing" adds nothing (including perfection) to the essence of a being. — Wikipedia

TheMadFool change the negation of universal with an existential. Then try to see if a logical equivalence is equal to a logical translation. — Caldwell

Sorry, I didn't quite get that.

Here's how I see the issue.

1. Apples exist (A) = All apples are existent things. (S)

2. Apples don't exist (~A) = No apples are existent things. (T)

A and ~A are contradictories but their corresponding equivalents, S and T are contraries.

I am not sure how useful St Anslem's arguments are for us because we live with such different perspectives of the world. I think that part of the problem which I see is that the idea of God is so complex because it can be seen from various angles ranging from the Christian and anthropomorphic pictures of a deity to much softer ones like the idea of the Tao. I am not saying that I don't think the question of God's existence, or lack of existence is important. However, it does depend on how we try to approach the idea of God, because the concept has so many varying connotations and associations.

I am not sure how useful St Anslem's arguments are for us because we live with such different perspectives of the world. I think that part of the problem which I see is that the idea of God is so complex because it can be seen from various angles ranging from the Christian and anthropomorphic pictures of a deity to much softer ones like the idea of the Tao. I am not saying that I don't think the question of God's existence, or lack of existence is important. However, it does depend on how we try to approach the idea of God, because the concept has so many varying connotations and associations. — Jack Cummins

:ok:

Good points. I suppose when someone claims God exists, he means to say so in the sense that, say, dogs exist (in the physical plane) and not in the same way as ideas exist (in the mental plane).

Is existence a property that can be ascribed to an object like mammalhood for example.

Mammalhood

1. Dogs are mammals = M = All dogs are mammals

The contradictory of M is,

2. Some dogs are not mammals = ~M

So far so good.

Existence

3. Dogs exist = D = All dogs are existent things

4. Dogs don't exist = ~D = No dogs exist = No dogs are existent things???

But, All dogs are existent things is not the contradictory of No dogs are existent things. They're contraries.

Perhaps I'm the only one, but I have no idea what any of this means.

Update

It appears that existence as a predicate results in a contradiction:

Sentential logic

1. Dogs exist = D

Categorical logic

D becomes,

2. All dogs are existent things = P

Sentential logic

3. Dogs don't exist = ~D

Categorical logic

~D becomes,

4. No dogs are existent things = Q

D and ~D are contradictories but P and Q are not contradictories (they're contraries). Contradiction because D = P and ~D = Q.

Let's refrain from making existence a predicate as below from using a universal claim to make an existential claim (only particular categorical statements have existential import)

Sentential logic

5. Dogs exist = D

Categorical logic

D becomes,

6. Some existent things are dogs = Some dogs are existent things = R

Sentential logic

7. Dogs don't exist = ~D

Categorical logic

~D becomes,

8. No existent things are dogs = No dogs are existent things = S

NOW,

D & ~D are contradictories and also R and S are contradictories.

As is patently clear, if existence is used as a predicate then it must be only in ways that the statement in question be amenable to conversion (E and I statements). In cases where this is not possible, existence can't be used as a predicate (A statement; please note, O statements seem to be ok).

Perhaps I'm the only one, but I have no idea what any of this means. — Tom Storm

If you're not pulling my chain, can you go study classical logics (sentential, categorical and predicate logics) and St. Anselm's ontological argument and give the issue I'm wrestling with here a second look. Thanks.

I was serious. I'm aware of St A's version of the argument but I have never studied any type of logic. It seems so tedious.

I have never studied any type of logic — Tom Storm

You might as well; after all you're a good philosopher, it should be a piece of cake.

:gasp: I'll try to make sense of this and see if I can handle it.

Update

Sentential logic

1. Dogs exist = D

Categorical logic

1 becomes,

2. Some dogs are existent things [particular categorical statements have existential import]

Predicate logic

2 becomes,

3. (Ex)(Dx) = Something is a dog, where Dx = x is a dog

Sentential logic

4. Unicorns don't exist

Categorical logic

4 becomes,

5. No unicorns are existent things

Predicate logic

5 becomes,

6. ~(Ex)(Uz) = (Ax)(~Ux) = Every thing is not a unicorn

Look at 6. The only way, "every thing is not a unicorn" is if every thing exists; if not, we can't say (Ax)(~Ux).

This suggests, to me, that if merely a thing then, existence is implied. Parmenidean!

A dilemma presents itself: Unicorns exist OR Unicorns are nothing!

St. Anselm of Canterbury...

God is a thing (cataphasis). Ergo, must exist OR God is nothing (apophasis)!