## If the existence of God cannot be proved, why not?

Is there a God? If so, what is She like?

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surreptitious57
Posts: 4217
Joined: Fri Oct 25, 2013 6:09 am

### Re: If the existence of God cannot be proved, why not?

Hugh Nose wrote:
In order to be sound a deductive argument must be valid
A valid argument is one that is only true within itself and so is not objectively true
A sound argument is one that is both true within itself and is also objectively true
Logik
Posts: 4041
Joined: Tue Dec 04, 2018 12:48 pm

### Re: If the existence of God cannot be proved, why not?

The logical form of "Either nothing exists or God exists." is A ⊻ B ( https://en.wikipedia.org/wiki/Exclusive_or )

The truth table for XOR is as follows:

A | B | A⊻B
0 ⊻ 0 ⇒ 0
1 ⊻ 0 ⇒ 1
0 ⊻ 1 ⇒ 1
1 ⊻ 1 ⇒ 0

You insist (a priori) that A⊻B is true so you are discarding two possibilities (50% of the decision-space) without justifying why:
0⊻0 ⇒ 0 (Nothing exists and God doesn't exist)
1⊻1 ⇒ 0 (Something exists and God exists)

By inexplicably discarding the other possibilities you have left us with:

A | B | A⊻B
1 ⊻ 0 ⇒ 1
0 ⊻ 1 ⇒ 1

This, in turn can be reduced to A ⇔ ¬B which is the same form as A ⇔ ¬A. The law of excluded middle.

It's a truism.
Hugh Nose
Posts: 31
Joined: Fri Dec 25, 2009 10:28 am

### Re: If the existence of God cannot be proved, why not?

Logik wrote: Thu Jan 10, 2019 11:26 am The logical form of "Either nothing exists or God exists." is A ⊻ B ( https://en.wikipedia.org/wiki/Exclusive_or )

The truth table for XOR is as follows:

A | B | A⊻B
0 ⊻ 0 ⇒ 0
1 ⊻ 0 ⇒ 1
0 ⊻ 1 ⇒ 1
1 ⊻ 1 ⇒ 0

You insist (a priori) that A⊻B is true so you are discarding two possibilities (50% of the decision-space) without justifying why:
0⊻0 ⇒ 0 (Nothing exists and God doesn't exist)
1⊻1 ⇒ 0 (Something exists and God exists)

By inexplicably discarding the other possibilities you have left us with:

A | B | A⊻B
1 ⊻ 0 ⇒ 1
0 ⊻ 1 ⇒ 1

This, in turn can be reduced to A ⇔ ¬B which is the same form as A ⇔ ¬A. The law of excluded middle.

It's a truism.
You really should take another look at some of the things you have said here. Some are just plain false!

Everyone,

In an earlier post, either here or in another thread, I said that one should not rely on Logik for logic facts. I feel obligated to repeat that here. Again and again, including here in this post, Logic has made false claims. For example, A ⇔ ¬A is not the law of the excluded middle. In fact, A ⇔ ¬A is logically false.

Don't believe Logik and don't believe me... just check any decent site on the web that discusses propositional logic or check any introductory logic text.
Logik
Posts: 4041
Joined: Tue Dec 04, 2018 12:48 pm

### Re: If the existence of God cannot be proved, why not?

Hugh Nose wrote: Thu Jan 10, 2019 1:30 pm You really should take another look at some of the things you have said here. Some are just plain false!
Either there is a falsity you can point out, or you are a liar.

Hugh Nose wrote: Thu Jan 10, 2019 1:30 pm Don't believe Logik and don't believe me... just check any decent site on the web that discusses propositional logic or check any introductory logic text.
Don't do that. All introductions to logic teach Aristotelian (classical) logic. It's broken because the law of excluded middle is a mistake.

Classical logic is of no value in 2019.
Hugh Nose wrote: Thu Jan 10, 2019 1:30 pm For example, A ⇔ ¬A is not the law of the excluded middle. In fact, A ⇔ ¬A is logically false.
You are correct. I made an error. A ⇔ ¬A is not the law of excluded middle.

A | B | A⊻B
1 ⊻ 0 ⇒ 1
0 ⊻ 1 ⇒ 1

A ⇔ ¬B is the same as A ∧ B ⇒ 1.
Which is the same as A ∧ ¬A ⇒ 1.

That is the law of excluded middle.
Hugh Nose
Posts: 31
Joined: Fri Dec 25, 2009 10:28 am

### Re: If the existence of God cannot be proved, why not?

You are correct. I made an error. A ⇔ ¬A is not the law of excluded middle.

A | B | A⊻B
1 ⊻ 0 ⇒ 1
0 ⊻ 1 ⇒ 1

A ⇔ ¬B is the same as A ∧ B ⇒ 1.
Which is the same as A ∧ ¬A ⇒ 1.

That is the law of excluded middle.
"A ⇔ ¬B is the same as A ∧ B" is False!
"Which is the same as A ∧ ¬A" is False!

It is true that A ∧ ¬A is the law of the excluded middle.

Cheers,

Hugh
Logik
Posts: 4041
Joined: Tue Dec 04, 2018 12:48 pm

### Re: If the existence of God cannot be proved, why not?

Hugh Nose wrote: Thu Jan 10, 2019 2:05 pm "A ⇔ ¬B is the same as A ∧ B" is False!
"Which is the same as A ∧ ¬A" is False!

It is true that A ∧ ¬A is the law of the excluded middle.

Cheers,

Hugh
So, you fail the nitpicker test.

∧ is AND
∨ is OR

A ∧ ¬A => False is the law of non-contradiction.
A ∨ ¬A => True is the law of excluded middle.
Hugh Nose
Posts: 31
Joined: Fri Dec 25, 2009 10:28 am

### Re: If the existence of God cannot be proved, why not?

Hugh Nose wrote: ↑Thu Jan 10, 2019 7:30 am
Don't believe Logik and don't believe me... just check any decent site on the web that discusses propositional logic or check any introductory logic text.
Don't do that. All introductions to logic teach Aristotelian (classical) logic. It's broken because the law of excluded middle is a mistake.
Many contemporary college "intro to logic" texts do offer a section on Aristotelian logic, but the primary focus in courses in introductory logic at the college level is introduction of the propositional calculus and the predicate calculus. Go to any of the contemporary publishers of logic texts for higher education and see for yourself.

Cheers,

Hugh
Logik
Posts: 4041
Joined: Tue Dec 04, 2018 12:48 pm

### Re: If the existence of God cannot be proved, why not?

Then you should stop teaching people bullshit.

According to your argument the truth-table for "Either nothing exists or God exists" is as follows:

A B
1 0 True
0 1 True

Follows: A ⇔ ¬B (1)

LEM states: A ∨ -A ⇒ True
From (1) replacing A with ¬B into LEM follows: ¬B ∨ -A ⇒ True

Either God doesn't exist is true, or the negation of “nothing exists” is true.

Oops! Where do you stand on double negation?

If you are going to appeal to "Higher Education" perhaps you should consider High-order logics.
https://en.wikipedia.org/wiki/Higher-order_logic
Last edited by Logik on Thu Jan 10, 2019 2:40 pm, edited 1 time in total.
Hugh Nose
Posts: 31
Joined: Fri Dec 25, 2009 10:28 am

### Re: If the existence of God cannot be proved, why not?

Logik wrote: Thu Jan 10, 2019 2:12 pm
Hugh Nose wrote: Thu Jan 10, 2019 2:05 pm "A ⇔ ¬B is the same as A ∧ B" is False!
"Which is the same as A ∧ ¬A" is False!

It is true that A ∧ ¬A is the law of the excluded middle.

Cheers,

Hugh
So, you fail the nitpicker test.

∧ is AND
∨ is OR

A ∧ ¬A => False is the law of non-contradiction.
A ∨ ¬A => True is the law of excluded middle.
Only because I was using ∧ in the way that I thought you were using it, as "or", and that was my error. Nevertheless, if we use the "and" understanding for ∧, it is still the case that,

"A ⇔ ¬B is the same as A ∧ B" is False!
"Which is the same as A ∧ ¬A" is False!

Cheers,

Hugh
Logik
Posts: 4041
Joined: Tue Dec 04, 2018 12:48 pm

### Re: If the existence of God cannot be proved, why not?

Hugh Nose wrote: Thu Jan 10, 2019 2:40 pm Only because I was using ∧ in the way that I thought you were using it, as "or", and that was my error. Nevertheless, if we use the "and" understanding for ∧, it is still the case that,
I inverted them. Intentionally to see how far your nitpicking goes.

See my last post. The previous post was a test (you failed).
Logik
Posts: 4041
Joined: Tue Dec 04, 2018 12:48 pm

### Re: If the existence of God cannot be proved, why not?

Hugh Nose wrote: Thu Jan 10, 2019 2:40 pm Only because I was using ∧ in the way that I thought you were using it, as "or", and that was my error. Nevertheless, if we use the "and" understanding for ∧, it is still the case that,
And had you interpreted the AND as OR you still made an error.

Given your premise "Either nothing exists or God exists" we concluded that A ⇔ ¬B.

Which is the same as:
A B
1 0 True
0 1 True

Ignoring the permutations 0,0 and 1,1 the truth-value is the same as A ∨ B.
FlashDangerpants
Posts: 2465
Joined: Mon Jan 04, 2016 11:54 pm

### Re: If the existence of God cannot be proved, why not?

Hugh Nose wrote: Wed Jan 09, 2019 3:42 pm
FlashDangerpants wrote: Mon Jan 07, 2019 11:47 pm
Hugh Nose wrote: Mon Jan 07, 2019 3:49 pm In order to know that one or the other, or both, are sound arguments, I would have to know if the first premise of each argument is true. In order to know that one or the other is not a sound argument, I would have to know that the first premise, or the second premise is false. If I don't know whether or not eh first premise is true or false, then I don't know if the arguments are sound arguments or not.
It makes no difference, they aren't valid for the same reason your argument isn't. I'm pretty sure that is his point. I really don't understand why you can't see the problem, it's been made clear enough for you.

You just have to look at the OR part in the first premise and anyone unburdened by severe head wounds can see that it doesn't work.

You used the grammatical form of a disjunctive syllogism, but you got it totally wrong, it isn't a syllogism at all. Please stop being silly.
Point 1: All three of the arguments, argument P, and the two arguments you have offered are valid, but I can see why you might think they aren't.
Those other two arguments weren't from me, you seem to have a habit of stripping the name of the person you quote for some reason. I can see why you think they are valid, but I'm afraid you are still confusing grammatical formations with logical ones. I'm going to try a different tack to see if we can get this explained for you.

I'm guessing that the book you learned this stuff from presented a few disjunctive syllogisms all in the same format...
Either my eyes deceive me, or that cat is wearing a wristwatch, the cat is not wearing a watch, therefore my eyes deceived me ... etc.
So let's start with a new one in a different grammatical form, I have foolishly strayed into a religion sub, so a parable seems appropriate:

Consider the sandwich shop which offers only two products. One is a bacon sandwich, the other is a cheese sandwich. The wise man walks into the sandwich shop whereupon the sandwich making guy asks him "would you like a bacon sandwich sir?". The wise man replies that he would not, so and the sandwich guy responds "coming right up", for he has arrived at the correct deduction that the wise man therefore would like a cheese sandwich.

This highly artificial scenario works on an all other things being equal basis because there are only two valid states of sandwich which can exist: cheese || bacon. Therefore if not bacon, then cheese. This is the sense in which it is a valid syllogism: the fact that it arrives at a true deduction. the definition of validity you are trotting out from your intro to logic book is only there to help you get to here.

Now consider applying this to a real sandwich shop that for unknown reasons still only stocks two fillings. In the real shop, there would be the possibility of Cheese AND Bacon as well as of cheese or bacon. Under that scenario, there are now three possible states of sandwich. With three states of sandwich, not bacon is no longer proof of cheese. This scenario cannot arrive at a true deduction, and that means it isn't valid, no matter what your opinion on the relationship between premises and conclusion may be. You can write it out as a bad syllogism if you want ... either Cheese or Bacon, not bacon, therefore cheese. But the assertion of the grammatical form does nothing to obscure the logical failings which result from just forgetting the cheese and bacon option.

So I guess we have to think about what is the actual purpose of this thread you started? On the one hand you seem to be testing a bad syllogism. On the other you seem to be trying to prove there is a god in the real world.

Your syllogism is valid only if you are asserting an artificial circumstance where the only two options on the table are that nothing exists, or God does. It then amounts to a description of an imaginary doll's house that only exists if the carpenter does, not a description of the universe.

If your purpose is to actually argue that god exists irl, and people should believe in him, then your syllogism is deductively invalid because you have ignored the third state of sandwich for no good reason. God might exist, and he might not, but this argument offers no additional light on the matter.
Age
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Joined: Sun Aug 05, 2018 8:17 am

### Re: If the existence of God cannot be proved, why not?

Hugh Nose wrote: Thu Jan 10, 2019 10:57 am
Logik wrote: Thu Jan 10, 2019 10:24 am
Hugh Nose wrote: Thu Jan 10, 2019 10:05 am Either Hugh Nose is a resident of Delaware or Hugh Nose is a resident of Pennsylvania.
Either Logik is a resident of New York, or Logik is a redisent of London.
Logik is not a resident of London.
Therefore Logik is a resident of New York.

The conclusion is false. How can I tell? Because I don't live in either of those cities. So..
A deductive argument is said to be valid if and only if it takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false. Otherwise, a deductive argument is said to be invalid.
The conclusion is false. How is that possible?
The explanation is that the premises are false.

Because I don't live in New York or London!
The first time you posted this message, you said that the argument was invalid. I assume you have backed away from that claim. Perhaps you went back and re-read the excerpt from IEP
It is important to stress that the premises of an argument do not have actually to be true in order for the argument to be valid.
The premise is a false dichotomy.
You can call it a false dichotomy if you like, but the mere fact that it is a disjunction that does not mention all of the possibilities is not what makes it false. What makes it false is the fact that you don't live in New York or London. The statement, "Either Hugh Nose lives in Delaware or Hugh Nose lives in Pennsylvania" is as much a false dichotomy as "Either Logik is a resident of New York, or Logik is a redisent of London", yet it is true- I do in fact live in Pennsylvania.

One of us does indeed need instruction and one of us does indeed need to read more carefully. The audience can decide who.

Cheers,

Hugh
I am glad that you brought this last sentence up. i, an audience participant, have decided that;
If you are going to say that what makes the premise Either Logik is a resident of New York, or Logik is a resident of London false, is the fact that logik is NOT a resident of either, then i will now ask you;

How is your premise Either nothing exists or God exists NOT false?

In fact are you even trying to suggest that that premise is true? Or, did you just write it for some other reason?

See, I can ask logik if they are a resident of either or none, and if I get an honest reply, then I will KNOW if the premise is true or false. However, how do you KNOW if the premise Either nothing exists or God exists is true or false?

Also, if we are to accept that your OWN logic of; "If I don't know whether or not eh first premise is true or false, then I don't know if the arguments are sound arguments or not." is correct, then to KNOW if God is proved, with an argument, then we would need to know if your premise Either nothing exists or God exists is true.

You asked, If argument P is not a proof that God exists, why not?
My response is, The reason argument P is NOT a proof that God exists, to me, is because I do NOT know if the premise; Either nothing exists or God exists is true, or false. Therefore, I do NOT know if argument P is a sound argument or not. If I do NOT know if an argument is sound or not, then I will NOT know if the argument is actually proving some thing or not.

Quite simple really.

And, as I am still on the same issue as I pointed out to you in my first response, to you, which you subsequently ignored, I will repeat it again; For YOUR argument to be a sound, valid argument you would have to first SHOW Who/What 'God' IS, AND, also prove that THAT/Thing HAS TO exist whenever something exists.

Now are you suggesting/stating that your first premise is true?
If yes, then define what 'God' is, and then prove that that definition of 'God' must ALWAYS exist whenever something exists. Until you do that, then your argument P is NOT proof that God exists. For the reasons I have given here above, and in my first response to you here in this thread.

If, however, your answer is no to this question here, then that is fine.
gaffo
Posts: 3488
Joined: Mon Nov 27, 2017 3:15 am

### Re: If the existence of God cannot be proved, why not?

If the existence of God cannot be proved, why not?

refer to Robert Sheckley's short story: "Ask a Foolish Question"

http://www.gutenberg.org/files/33854/33 ... 3854-h.htm
Hugh Nose
Posts: 31
Joined: Fri Dec 25, 2009 10:28 am

### Re: If the existence of God cannot be proved, why not?

Logik wrote: Thu Jan 10, 2019 2:24 pm Then you should stop teaching people bullshit.

According to your argument the truth-table for "Either nothing exists or God exists" is as follows:

A B
1 0 True
0 1 True

Follows: A ⇔ ¬B (1)

LEM states: A ∨ -A ⇒ True
From (1) replacing A with ¬B into LEM follows: ¬B ∨ -A ⇒ True

Either God doesn't exist is true, or the negation of “nothing exists” is true.

Oops! Where do you stand on double negation?

If you are going to appeal to "Higher Education" perhaps you should consider High-order logics.
https://en.wikipedia.org/wiki/Higher-order_logic
You say,

"LEM states: A ∨ -A ⇒ True"

If LEM stands for the law of excluded middle, OK. if the "⇒ True" means that the law of excluded middle is true, OK!

You say,

"From (1) replacing A with ¬B into LEM follows: ¬B ∨ -A ⇒ True"

If I understand this properly, it is further demonstration that when it comes to logic, you don't know what you are doing. The replacement of "A" in A v -A with ¬B is not a truth preserving replacement. SO, the claim that ¬B v -A is true as a result of such a replacement is just false. A simple truth table analysis will show that this 'inference' is invalid.

You say

"Either God doesn't exist is true, or the negation of “nothing exists” is true.

Oops! Where do you stand on double negation?"

There is no instance of double negation in the proposition [as the term "double negation" is used in propositional logic in college level intro to logic texts]. In a formula such as ¬¬B v ¬A, ¬¬B is an instance of double negation.

I don't know what to make of your comment about Higher-order logic. Nothing that you have mentioned draws on anything from higher order logics-- no appeal to higher order logics saves any of your false statements.