Therefore, there is a god

[Cheerful Charlie]

Let's cancel out the double negative in the first statement and work from there. Others have done this I think, but it seems to me the clearest way to show the disconnect between premises and conclusion.

Premise 1: If there is {a prayer-answering} god, then it is true that if Speakpigeon prayed, then Speakpigeon's prayers would be answered.
Premise 2: Speakpigeon does not pray.
Conclusion: There is a god.

Obviously this tells us nothing, because the premise under examination (existence of a prayer-answering god) is not tested if Pigeon doesn't pray, and thereby perform an experiment to check out the truth of the initial premise.

No doubt Pigeon will insist the double negative is in some way vital to his point, but I just don't see it.

If God answer prayers, and I pray, God will answer my prayer. Proof that God answers prayers.

If God answers prayers, but I do not pray, God will not answer my lack of prayer. In and of itself no evidence. God tat answers prayers may exist of may not.

If God answers prayers, we should see that going by the success of those who do pray i getting their prayers answered.
But things like children's cancer wards where prayer does not save children seems to indicate God does not answer prayers. Christians do not work bigger miracles than Jesus as per John 14:12-14 and never did.

John 14:12-14
¹² Verily, verily, I say unto you, He that believeth on me, the works that I do shall he do also; and greater works than these shall he do; because I go unto my Father.

¹³ And whatsoever ye shall ask in my name, that will I do, that the Father may be glorified in the Son.

¹⁴ If ye shall ask any thing in my name, I will do it.

 

[Speakpigeon]

You seem to be aware of this, because that's the only reason to plug a non-testable variable like "god" into the argument as opposed to the functionally infinite set of testable variables which would work just as well and show how pointless it is.

Well, except, me, I don't don't how the argument about the jerrycans would go. Jerrycans don't usually answer prayers even when they exist.

Well, it's a long thread, so here it is again:

"If there is no gasoline in the gas can, then it is not true that if I fill my car's tank with it, my car will be able to drive. I don’t fill my car's tank with it; therefore, there is gasoline in the gas can".

It's the exact sentence you posted in the OP, with different values plugged in where you put the variables. Put that through how you've parsed out your example and tell me - have you just proven that there's gasoline in the gas can?

If you have proven that, you have an internally consistent logical analysis with a testable prediction which can be checked against reality and shown to be false. If you have not proven that, what is the difference between that sentence and the sentence you provided in the OP about God?

Yes, I broadly agree that you can plug different terms in the argument and get the same absurd result:

- If there is no alternative, then it is not the case that if I try, I’ll be able to do things differently. I don’t try; therefore, there is an alternative.

- If there is no biscuit, then it is not the case that if I eat something, I will eat a biscuit. I don’t eat; therefore, there is a biscuit.

You can't plug anything, though. You need the statement to make sense. Prayers and god, eating and biscuit, gas can and gasoline. And that's the crucial point. This thing makes sense and that's why the result is annoying.

This also shows there never was a need to use a gas can example. The one with god works just fine. If you can't explain the god one, you won't be able to explain the gas can one.

It never was me trying to prove god exists and therefore the question of the gas can was irrelevant all along. Some people seem to be so annoyed by the absurdity of the argument they seem unable to take the OP at face value and focus on what is asked. It's just a waste of time but there's nothing I can do about it.

For the rest, I won't repeat my last post. Seems there would be no use.
EB

 

[Speakpigeon]

How can I ignore this thread? The "thread tools" menu doesn't have the ignore option that it had in the past.

Yeah, it's already very unfortunate that there should be a god but it's just unfair you can't ignore it.

That said, you can put me on ignore. Be aware, though, that I may keep commenting on your posts and you'll have to watch powerless as other people reply to those comments and you won't be able to ignore those. One delusional dude tried it but gave up.
EB

 

[Speakpigeon]

Let's cancel out the double negative in the first statement and work from there. Others have done this I think, but it seems to me the clearest way to show the disconnect between premises and conclusion.

Premise 1: If there is {a prayer-answering} god, then it is true that if Speakpigeon prayed, then Speakpigeon's prayers would be answered.
Premise 2: Speakpigeon does not pray.
Conclusion: There is a god.

Obviously this tells us nothing, because the premise under examination (existence of a prayer-answering god) is not tested if Pigeon doesn't pray, and thereby perform an experiment to check out the truth of the initial premise.

No doubt Pigeon will insist the double negative is in some way vital to his point, but I just don't see it.

Yeah, I have to insist not on the double negative but certainly on you addressing the OP as it is and this means taking the argument as it is. Anything else is just irrelevant and so a waste of your life.

Also, the argument works for each one of us who doesn't pray. Or even for people who pray but not now, or who don't pray at some point in time. This thing is really absurd and you don't need to change the terms to see it as it is.

We all agree this thing is absurd. This is not the debate. The question is whether you can explain why it is absurd.
EB

 

[Speakpigeon]

Your expression of disbelief and your rather dismissive reply is strong evidence that by "if there is no god, it is not true that if you pray then your prayers will be answered", you meant "If there is no god, it is not true that if you prayed, your prayers would be answered." That one would be true if "god" has a meaning and only a god possibly answers prayers (as you seem to believe). But of course, the modified argument

Premise 1: If there is no god, then it is not true that if Speakpigeon prayed, then Speakpigeon's prayers would be answered.
Premise 2: Speakpigeon does not pray.
Conclusion: There is a god.
​

is not valid.

Sure but again there's no room for a counterfactual interpretation. All you have are three propositions, G, P and A: If not G, then not if P then A; Not P; therefore G. The only equivocation is that we need the three propositions to make sense together otherwise we may not be so annoyed by the argument. But even if they don't make sense, we still have an absurd result because we can use the argument to prove just about anything. I take your point that if P then A is true because P is false but that seems to be how truth tables work. So, unless you can produce some rule to the contrary, one coming from textbook logic, I'm afraid you should too accept that's it's just the way truth table logic works.

And the two premises are true at least for appropriate interpretations of G, P and A, which is good enough. If there is no god, it's not true that if I pray my prayers will be answered (by a god). I can pray if you like. I can do that, I guess. I can assure you my prayers won't be answered. And it's true I don't pray. What you seem to interpret as a counterfactual seems to be part and parcel of the way truth tables work. Any implication is assessed on the basis of logical cases which are de facto counterfactual to each other: if one is true then the others are false. Again, maybe there are some textbook restrictions on this, but that's what you'd need to show.

And, your point is excellent, anyway. So, you could say I'm halfway to being convinced, if you like. I think I would rather prefer if there was some explicit and official rule making this argument unsound. I'll try to investigate further on that.

Now, I don't think this is working, so I would like to ask you again: Why do you not believe that there is a god?

You don't need reasons to believe. You do or you don't, as most posters on this thread have shown themselves to be rather pathetic examples of. Still, you're right. I don't believe there is a god and I don't buy this logical argument that there is one but it's all intuitive. The first time I came across it, I knew the argument was wrong even before I possibly have realised what it meant exactly. That's a split second intuition and I still don't buy it. So, I would say that the most likely explanation is that there must be some textbook rule that makes this argument unsound. So, you see, there's always wriggle room enough to discount a good logical argument if you put your heart to it. The problem is, nobody here seems to know whether this rule exists or not.

If there is no rule, it is not true that if I try I'll be able to rule out that this argument is sound; I don't try; Therefore there is a rule. (therefore this argument would be unsound if only I tried).

I also want to use this later, to try to persuade you by different arguments.

I think there should be just one reason this argument doesn't work. This argument is either sound or unsound and if it is unsound it should be because of one reason. You may be a little bit too creative, here, possibly.
EB

 

[Bobinius]

Okay, let me see if I can work thru this Angra's way.

We start with this:
P1: If there is no god, then it is not true that if I pray, my prayers will be answered.
P2: I don’t pray (stipulated)
C: Therefore, there is a god

P2 is stipulated true, which makes the "I pray" in P1 false. Thus, we get:

P1: If there is no god, then it is not true that if FALSE, my prayers will be answered.
P2: I don’t pray (stipulated)
C: Therefore, there is a god

Angra says any conditional with a false antecedent is true.

Since, "if FALSE, my prayers will be answered," is a conditional with a false antecedent, we get this:

P1: If there is no god, then it is not true that TRUE.
P2: I don’t pray (stipulated)
C: Therefore, there is a god

"It is not true that TRUE," is false, thus:

P1: If there is no god, then FALSE.
P2: I don’t pray (stipulated)
C: Therefore, there is a god

That makes P1 a conditional with a false consequent.

Angra says, A conditional with a false consequent is true if and only if the antecedent is false. Thus:

If P1 is true, then, "There is no god," is false!

Phrased differently:

If P1 is true, there is a god.

Thus, the only way to avoid the conclusion that god exists is to doubt the truth of P1.

Thank you Angra, that was quite a ride.

And my apologies to Speakpigeon.

---

What was P1 again?

P1: If there is no god, then it is not true that if I pray, my prayers will be answered.

If we're doubting P1, I become curious. In what ways can P1 be false?

First, P2 could be wrong; Speakpigeon could pray, thus the "I pray" in P1 could be true rather than false. I don't know what that would get us.

Second, things other than gods could answer prayers. Could we work our way around that, maybe change, "if I pray, my prayers will be answered," to, "If I pray to gods, my prayers will be answered by gods." Would that eliminate this second possible way for P1 to be wrong?

This is fun. I'm going to call it a night.

I think it is valid, but of course P1 is false. It is a particular set of conditionals and it can be made more intelligible by transforming it in equivalent constructions. Which will show that the argument does not prove anything. Some provisos.

1. Denying a conditional ¬(If P, then Q) = P AND ¬Q

So the consequent of the first conditional is transformed accordingly: ¬ (If I pray, then my prayers will be answered) = I pray AND my prayers are not answered.

2. The truth value of a conjunction

A conjunction P AND Q is true if and only if (IFF) both P and Q are true. It is false in all other cases. So a conjunction is actually indifferent to the truth value of what follows after 'AND' once the first member is false.

So the conjunction I pray AND my prayers are not answered is false if I pray is false. No matter what the truth value of the second operand or proposition is. So once I pray is false, I pray AND the weather is nice is false, I pray AND my dog is gay is false, I pray AND 2 is smaller than 3 is false, I pray AND Trump is not a chinese citizen is false etc.

3. Denying the consequent is a valid.

If not God, then I pray.
I don't pray.
Therefore not (not God).
Therefore God.

By now it should be clear that Speakpigeon's argument is actually equivalent to this:

1. IF NOT God exists, THEN (I pray AND my prayers are not answered).
2. I don't pray.
3. THEREFORE NOT NOT (God exists).
4. THEREFORE God exists.

Or

1. If God doesn't exist, then (I pray AND my prayers aren't answered).
2. I don't pray.
3. God exists.

Which can be transformed ad infinitum since all possible conjunctions containing a false operand are false:

1. If God doesn't exist, then (I pray AND Trump has big hands).
2. I don't pray.
3. God exists.

or

1. If God doesn't exist, then (I pray AND the Sun is cold).
2. I don't pray.
3. God exists.

This doesn't really prove anything of course, because P1 is false. People can and do pray to non-existing gods. And the crap with the term 'my prayers are answered' is pointless. You can replace it with anything you want. So finally I agree it is valid, but not an analytical or logical truth, it is not even sound.

Bobinius

 

[Speakpigeon]

And my apologies to Speakpigeon.

My pleasure.

I'm not entirely sure how you got there, though, except perhaps that Angra Mainyu somehow managed to convince you the OP was bona fide. So, I guess I'll need to have Angra Mainyu around to look after me each time I post a new thread and get abuse from all the uncouth of this forum. That's a hell of a job for a destructive spirit.
EB

 

[Speakpigeon]

So, all I have so far is that an argument is sound if it is valid and all its premises are true. Which, according to me at least, seems to fit the OP's argument.

Still, in light of Angra Mainyu and Bomb#20's reasoning, I'm open to any suggestion as to what the definition of soundness should be, if anyone has a suggestion, that is. Be aware that any such would need to be algorithmically operational and preserve logical laws such as the transitivity of the implication for example.
EB

 

[Angra Mainyu]

If there is no god, it's not true that if I pray my prayers will be answered (by a god).

I have no good reason to even suspect that that is true, because that - as I have explained in detail - that claim of yours is true if and only if there is a god, and as I already explained, I have no good reason to even suspect so.

I can pray if you like. I can do that, I guess. I can assure you my prayers won't be answered.

You still do not understand your own statement as long as we stipulate that you are not equivocating (i.e., of course you continue to equivocate, but I haven't found a way to make you realize that, so I'm going to try another approach).

The problem is, nobody here seems to know whether this rule exists or not.

That is not the problem. I understand the rules. The problem lies elsewhere (no offense ).

I think there should be just one reason this argument doesn't work. This argument is either sound or unsound and if it is unsound it should be because of one reason. You may be a little bit too creative, here, possibly.

No, I have explained the matter thoroughly. I haven't been creative enough to persuade you, though, so here I will try again, by addressing your reply to Tom Sawyer. You said:

If there is no biscuit, then it is not the case that if I eat something, I will eat a biscuit. I don’t eat; therefore, there is a biscuit.

Here, we have:

Premise 1': If there is no biscuit, then it is not the case that if Speakpigeon eats something, Speakpigeon will eat a biscuit.
Premise 2': Speakpigeon does not eat anything.
Conclusion: There is a biscuit.

That is clearly valid. But let me ask you about the statement whose negation constitutes the consequent of Premise 1', namely:

S1: If Speakpigeon eats something, Speakpigeon will eat a biscuit.

Suppose that Premise 2' is true. Could you please tell me whether S1 is true?

 

[Angra Mainyu]

So, all I have so far is that an argument is sound if it is valid and all its premises are true. Which, according to me at least, seems to fit the OP's argument.

Still, in light of Angra Mainyu and Bomb#20's reasoning, I'm open to any suggestion as to what the definition of soundness should be, if anyone has a suggestion, that is. Be aware that any such would need to be algorithmically operational and preserve logical laws such as the transitivity of the implication for example.
EB

The definition is fine. But you have no good reason whatsoever to even suspect that Premise 1 is true (assuming, of course, that you're not equivocating, which seems pretty clearly false to me, but I'm leaving that aside because you keep disputing that fact, and I'm trying to narrow things down).

In other words, I'm saying that you have no good reason at all to even suspect that "If there is no god, then it is not true that if Speakpigeon prays, then Speakpigeon's prayers will be answered. " is true. If you believe it is true, then either you are being irrational, or you do not understand the meaning of the statement 'If there is no god, then it is not true that if Speakpigeon prays, then Speakpigeon's prayers will be answered.'.

I believe, by the way, that you do not understand the meaning of the statement in question (in this context). But I hope you address the biscuit case. It might be helpful. Or not, in which case smurfs are coming next!

 

[Speakpigeon]

You said:

If there is no biscuit, then it is not the case that if I eat something, I will eat a biscuit. I don’t eat; therefore, there is a biscuit.

Here, we have:

Premise 1': If there is no biscuit, then it is not the case that if Speakpigeon eats something, Speakpigeon will eat a biscuit.
Premise 2': Speakpigeon does not eat anything.
Conclusion: There is a biscuit.

That is clearly valid. But let me ask you about the statement whose negation constitutes the consequent of Premise 1', namely:

S1: If Speakpigeon eats something, Speakpigeon will eat a biscuit.

Suppose that Premise 2' is true. Could you please tell me whether S1 is true?

No, obviously. I can eat something that's not a biscuit.

However, if I may, the converse is true: "If I don't eat something, then I don't eat a biscuit". And this is true whether I eat something or not. Maybe you could tell me if you agree with that as I would expect you to but now I'm not so sure so I have to ask just to clear the water. So, don't you agree with that? This may be relevant since we may have a clear case of what you and Bomb#20 appear to see as a case of equivocation through relying on counterfactuals. More generally, if the implication A → C is true, then it is true whether A is true or not. That point is fundamental but maybe I'm wrong in thinking that it's relevant to the case of answered prayers when I don't pray, at least as you see it.

Still, coming back to your question, the implication "if I eat something, then I eat a biscuit" is constrained in the complete argument by the antecedent "if there is no biscuit", so now, I can eat something but I cannot eat a biscuit and so the implication "if I eat something, I will eat a biscuit" is false not just because I can eat something else than a biscuit but also because I can't even eat a biscuit to begin with. So if this implication is false, its negation is true and therefore the implication "If there is no biscuit, then it is not the case that if I eat something, I will eat a biscuit" is necessarily true, i.e. irrespective of whether I eat something or not. I suspect you're somehow going to disagree with that... God, I wish I could pray to God.
EB

 

[Speakpigeon]

It might be helpful. Or not, in which case smurfs are coming next!

I suspect I know what you're going to do.

In any case, don't expect me to admit to eating smurfs.
EB

 

[Angra Mainyu]

It might be helpful. Or not, in which case smurfs are coming next!

I suspect I know what you're going to do.

In any case, don't expect me to admit to eating smurfs.
EB

I'm afraid it was something less fun, but now that you mention it...

Let's consider the following statement:

S11: If Speakpigeon eats every small, edible, living thing she encounters, then Speakpigeon will eat a smurf.

We stipulate that in S11, the words 'if' and 'then' have the same meaning as in 'if Speakpigeon prays, then Speakpigeon's prayers will be answered.', in the argument under discussion.
My question is: Is S11 true?

 

[Speakpigeon]

It might be helpful. Or not, in which case smurfs are coming next!

I suspect I know what you're going to do.

In any case, don't expect me to admit to eating smurfs.
EB

I'm afraid it was something less fun, but now that you mention it...

Let's consider the following statement:

S11: If Speakpigeon eats every small, edible, living thing she encounters, then Speakpigeon will eat a smurf.

We stipulate that in S11, the words 'if' and 'then' have the same meaning as in 'if Speakpigeon prays, then Speakpigeon's prayers will be answered.', in the argument under discussion.
My question is: Is S11 true?

I take it that by smurf you don't mean the Belgian comic's fictional character, which should be written "Smurf", not "smurf". If that's what you meant, then the conditional is false since Smurfs are not real and cannot be eaten, even by a real Speakpigeon.

I also assume you don't mean the verb, that would make an ungrammatical sentence.

That being said, if a smurf was indeed a "small, edible, living thing", that would still not make a true conditional since Speakpigeon would need first to encounter a smurf to get a chance to eat it and that would not be necessarily the case.

Anyway, I would assume that by now you would have clarified at least one issue here. So, could you explain for the benefit of all those who are still insisting on reading this thread?
EB

 

[Angra Mainyu]

I'm afraid it was something less fun, but now that you mention it...

Let's consider the following statement:

S11: If Speakpigeon eats every small, edible, living thing she encounters, then Speakpigeon will eat a smurf.

We stipulate that in S11, the words 'if' and 'then' have the same meaning as in 'if Speakpigeon prays, then Speakpigeon's prayers will be answered.', in the argument under discussion.
My question is: Is S11 true?

I take it that by smurf you don't mean the Belgian comic's fictional character, which should be written "Smurf", not "smurf". If that's what you meant, then the conditional is false since Smurfs are not real and cannot be eaten, even by a real Speakpigeon.

I also assume you don't mean the verb, that would make an ungrammatical sentence.

That being said, if a smurf was indeed a "small, edible, living thing", that would still not make a true conditional since Speakpigeon would need first to encounter a smurf to get a chance to eat it and that would not be necessarily the case.

Anyway, I would assume that by now you would have clarified at least one issue here. So, could you explain for the benefit of all those who are still insisting on reading this thread?
EB

Yes, I can explain that, though I already did that more than once and did not convince you, so there are no guarantees. Anyway, here's my next attempt:

First, you are correct in assuming I don't mean Smurf, etc. In fact, I meant the blue small funny looking people, etc., as described in the stories. But what I meant by it is pretty much irrelevant, at least as long as I meant something by it (more below), which I did.

Second, you haven't said clearly whether you think S11 is false, though it seems to me it's implicitly what you hold (unless you think it's neither true nor false?). But in any case, your assessment that in order for S11 to be true Speakpigeon would need first to encounter a smurf to get a chance to eat it and that would not be necessarily the case, is mistaken. In fact, S11 is true. But the smurfs were not relevant. For example, consider:

S12: If Speakpigeon eats every small, edible, living thing she encounters, then Speakpigeon will rule the Earth for 1 billion years.

We stipulate that in S12, the words 'if' and 'then' have the same meaning as in 'if Speakpigeon prays, then Speakpigeon's prayers will be answered.', in the argument under discussion. Is S12 true?

And again, the answer is: Yes, S12 is true. I hope you are getting the idea. Consider

S13: If Speakpigeon eats every small, edible, living thing she encounters, then the Earth is flat, the Moon Landing never happened, Elvis is alive, and the Rapture will happen before 2019.

We stipulate that in S13, the words 'if' and 'then' have the same meaning as in 'if Speakpigeon prays, then Speakpigeon's prayers will be answered.', in the argument under discussion. Is S13 true?

Easy enough: of course, S13 is true.

The reason all of those statements are true is that the antecedent 'Speakpigeon eats every small, edible, living thing she encounters' is false. As a matter of fact, you do not eat every small, edible, living thing that you encounter.
Now you might protest and say that in the ordinary sense of the words, those conditionals are false. Maybe, if the ordinary sense here is counterfactual, or some other colloquial usage, or at least one among those if there are more than one, etc. But the moment you choose to use the truth tables and claim the argument is valid, you are implying that you are using the conditional in a manner that renders S11 and S12 true. If you use different kinds of conditionals as if they were one - i.e., one kind of conditional to assess the truth of Premise 1, and then you switch to a different kind to use the truth table -, you equivocate, as Bomb#20 pointed out.

From a different perspective: if you say S11 is not true, then in that sense of 'if' and 'then', your argument to the conclusion that there is a god is invalid, and you may not use the truth tables as you did to prove otherwise. The truth tables are simply not for that.

I sincerely hope that this time I convince you. If this also fails, I'm not sure what else to do. I'm running out of approaches.

 

[Speakpigeon]

At least I can reassure you I understand what you say. But I was wrong, I thought you were going to go a different route (as you were announcing).

But your example doesn't work. Your example here is an implication which is true because the antecedent is false. However, this implication is not valid because if the antecedent was true, the consequent could be false (the substance of my answer in my previous post). And a true implication will be of no consequence if it is not valid. Your analogy is therefore wrong here because your example is that of an invalid implication when the implication in the argument about god is valid. If there is no god, then it is not true that if I pray, then my prayers will be answered by a god and since it is a premise of the argument, this premise is true, making the argument sound together we the other true premise that I don't pray.

And there is still an aspect of the problem you haven't addressed. I don't believe you will. Different posters have sort of alluded to it in the course of this thread without really realising. So, to be honest, we don't need you to try again the same line of reasoning. I can assure you I understand what you say. I understood the first time round. And I'm immune to it. The only avenue would be for you to try this other aspect. So I take it we're done here until such a time as you realise there's something else entirely to be said about this argument.

Thanks for your efforts. I probably won't be around so often but I'll try to have a look now and then just in case. Thanks also to Bomb#20, although I guess he must be rather pissed off.
EB

 

[Bomb#20]

Sorry, I tried to make sense of your argument but failed.

Fair enough -- there's an error in it. My bad.

I checked the logic of the OP's argument, again, and it's impeccable. I'm sure you can check for yourself that the premises imply the conclusion.

I never denied that the premises implied the conclusion. Of course your argument is valid. But it's unsound. The first premise is clearly false and you never offered a substantive reason to think it's true.

I also don't want to go into discussing another argument, namely the one you chose to discuss here, i.e. "if there is no god then it is true that if you pray, your prayers will be answered". I'm sure it's interesting but maybe you could start another thread.

That is not another argument. That's not an argument at all; it's simply a proposition. And don't blame me for it -- I brought it up because it's a logical consequence of your second premise. The error in my attempted proof was that I thought it conflicted with your first premise. Turns out that's because I made the same mistake you did -- I used natural language reasoning at a critical step, instead of sticking strictly to truth table reasoning. Going strictly by truth table reasoning, your premises are not contradictory. Rather, your two premises together amount to assuming the single premise "There is a god.".

So, my request is that you address the OP's argument as it is. Using standard logic. That's what I did and the implication is true in all logical cases. That's what I call a logical truth. There is no possible case where the argument would be false.

Also, if it was a piece of cake, I fail to see why you don't just produce the relevant proof.

I thought that's what I was doing. Sorry about the error.

My claim is that according to standard logic, the OP's argument is true in all logical cases. Can you prove otherwise?

Sure thing -- that's trivial. The OP's argument is not true, because it is an argument. Arguments are not true or false. (Deductive) arguments are valid or invalid, and sound or unsound, but never true or false. Calling an argument "true" is a category error.

The OP argument is valid but unsound. The conclusion follows from the premises but the first premise is false. You only think it's true because you didn't stick to truth table reasoning.

The larger point here is that your argument and your intuition are based on an equivocation fallacy. You are equivocating on the word "if". You are using "if" to refer to both the "material conditional" and the "counterfactual conditional". The "if" used in truth tables and boolean algebra is the material conditional. You have an intuition that "If there is no god, then it is not true that if I pray, my prayers will be answered." because you are using the first "if" to refer to the material conditional and the second "if" to refer to the counterfactual conditional. When you derived "there is a god" from your premises you replaced the counterfactual conditional with a second material conditional.

Sorry, I just used truth tables. So, I'll take that as good enough unless you can explain why truth tables shouldn't be used in this case.

If that were the case then you would not believe your first premise.

In truth table reasoning, "if P then Q" is equivalent to "Q or not P". It's safest to rewrite all the statements in that form to avoid getting confused by the English-language meaning of "if" -- exactly what happened to both of us. Let us rewrite your first premise in "or" form:

If there is no god, then it is not true that if I pray, my prayers will be answered.

If there is no god, then (it is not true that (my prayers will be answered or I do not pray)).

If there is no god, then (my prayers will not be answered and I pray).

(My prayers will not be answered and I pray) or (there is a god).​

That is what your first premise means when "if" is interpreted using truth tables. Do you believe "(My prayers will not be answered and I pray) or (there is a god)."?

When you combine that premise with premise 2, "I do not pray", that implies (My prayers will not be answered and I pray) is false. "(False) or (there is a god)." is equivalent to "There is a god". It isn't surprising that you can deduce "There is a god" from "I don’t pray; and my prayers will not be answered and I pray or there is a god.", but it isn't a reason to think there's a god, or that truth table reasoning doesn't work. All it means is that truth table reasoning doesn't adequately capture the English language meaning of "if".

Anyway, thanks for trying. I guess we don't have the expert logician here who could clarify the issue.

We certainly do. Angra Mainyu hasn't made any logic errors so far.

It should be said that the truth table of the argument is quite simple and straightforward. Unfortunately, it says that there is a god. We have to live with that.

It doesn't say there's a god. Your premises say there's a god. Truth tables are a perfectly workable procedure for computing "Garbage in, garbage out."

 

[Angra Mainyu]

At least I can reassure you I understand what you say. But I was wrong, I thought you were going to go a different route (as you were announcing).

But I did go on a different route. I explained the problem with your argument in a way that was different from the previous ones.

But your example doesn't work. Your example here is an implication which is true because the antecedent is false. However, this implication is not valid because if the antecedent was true, the consequent could be false (the substance of my answer in my previous post). And a true implication will be of no consequence if it is not valid. Your analogy is therefore wrong here because your example is that of an invalid implication when the implication in the argument about god is valid. If there is no god, then it is not true that if I pray, then my prayers will be answered by a god and since it is a premise of the argument, this premise is true, making the argument sound together we the other true premise that I don't pray.

No, that is simply not true. No offense, but you very probably do not understand what I'm saying, though I know you are sure you do.

As I explained carefully and repeatedly, you do not have any good reasons whatsoever to even suspect that the statement 'If there is no god, then it is not true that if I pray, then my prayers will be answered by a god' is true, and that would almost certainly be obvious to you by now if you understood what I'm saying.

And there is still an aspect of the problem you haven't addressed. I don't believe you will. Different posters have sort of alluded to it in the course of this thread without really realising. So, to be honest, we don't need you to try again the same line of reasoning. I can assure you I understand what you say. I understood the first time round. And I'm immune to it. The only avenue would be for you to try this other aspect. So I take it we're done here until such a time as you realise there's something else entirely to be said about this argument.

Thanks for your efforts. I probably won't be around so often but I'll try to have a look now and then just in case. Thanks also to Bomb#20, although I guess he must be rather pissed off.

You're welcome. Given your replies, I reckon it's very probable that you do not understand what I'm saying. But I'm not planning to keep trying, as I have not been able to think of an alternative that might have a shot at convincing you.

 

[Angra Mainyu]

Speakpigeon,

Just for the fun of it, why don't you take a look at the following parallels, and then reassess whether my smurf analogy works?

Premise 1': If there are no smurfs, then it is not true that if Speakpigeon eats every small, blue, moving thing she encounters, Speakpigeon will eat a smurf.
Premise 2': It is not the case that Speakpigeon eats every small, blue, moving thing she encounters.
Conclusion': There is at least one smurf.

The argument is valid, but obviously unsound. Premise 2 is true. Premise 1 is obviously false. Compare:

Premise 1'': If there is no god, then it is not true that if Speakpigeon prays, Speakpigeon's prayers will be answered by a god.
Premise 2'': It is not the case that Speakpigeon prays.
Conclusion'': There is at least one god.

The argument is valid, but it is sound if and only if there is a god, i.e. (your latest definition of "god") an omnipotent being. I'm inclined to say it's very probably unsound, and Premise 1 is very probably false. At any rate, neither you nor I has any good reasons to even suspect that Premise 1 might be true.

Now let's define "omnimax=omnipotent, omniscient, and morally perfect".

Premise 1''': If there is no omnimax agent, then it is not true that if Speakpigeon prays, Speakpigeon's prayers will be answered by an omnimax agent.
Premise 2''': It is not the case that Speakpigeon prays.
Conclusion''': There is at least one omnimax agent.

The argument is valid, but it is not sound. Premise 1 is false.

 

[Wiploc]

Now let's define "omnimax=omnipotent, omniscient, and morally perfect".

Premise 1''': If there is no omnimax agent, then it is not true that if Speakpigeon prays, Speakpigeon's prayers will be answered by an omnimax agent.
Premise 2''': It is not the case that Speakpigeon prays.
Conclusion''': There is at least one omnimax agent.

The argument is valid, but it is not sound. Premise 1 is false.

But P1''' looks true.

P1 always looked dodgy, but P1''', I don't see how it could fail to be true.

I'm not arguing with you--I've been wrong plenty already in this thread--I'm just reasoning aloud.

Is the following statement true?

• If Speakpigeon prays, Speakpigeon's prayers will be answered by an omnimax agent."

Is that true? If an omnimax agent exists, it could be true and it could be false. But if an omnimax agent does not exist, then it has to be false.

But ... you're saying I'm wrong about that. And at this point I have to trust you more than I trust me, which is really weird and frustrating. And P1''' still really looks like a true statement.

So, this is fun.

Can I replicate Bobinius's reasoning? Let me try.

• P1''': If there is no omnimax agent, then it is not true that if Speakpigeon prays, Speakpigeon's prayers will be answered by an omnimax agent.

I'm going to look at part of that, the consequent, right? and try to translate it:

• it is not true that if Speakpigeon prays, Speakpigeon's prayers will be answered by an omnimax agent.

That means the same as this:

• It is true that ...

Hmm. I don't know what it's the same as. Maybe I need a truth table. Let's have a truth table for this:

• If Speakpigeon prays, then Speakpigeon's prayers will be answered by an omnimax agent.

Angra says--if I understand--that I should plug in a T for every value where the antecedent is false, like this:

	Prays	Not Prays
Answered	T	T
Not Answered	F	T

To get the value FALSE, we have to have the prayer and have it not answered.

Therefore, the truth table for this statement ...

• It is true that if Speakpigeon prays, then Speakpigeon's prayers will be answered by an omnimax agent.

... has to look like this:

	Prays	Not Prays
Answered	F	F
Not Answered	T	F

I'm just feeling my way here. Somebody please correct me if I'm wrong.

So this statement ...

• It is not true that if Speakpigeon prays, then Speakpigeon's prayers will be answered by an omnimax agent.

... can be restated this way:

• Speakpigeon prays and the prayer is not answered by an omimax agent.

So now we plug that into P1''' to get this:

• If there is no omnimax agent, then Speakpigeon prays and the prayer is not answered by an omnimax agent.

If I haven't made a mistake, the meaning of this is same as the meaning of P1'''. But P1''' looks true and this doesn't.

Why does one version look true when the other doesn't? According to Bobinius--assuming I understand--the difference is that I have eliminated an ambiguous "if."

I don't understand what was ambiguous about it. Can somebody explain that to me?