Therefore, there is a god

[Speakpigeon]

These rules are not entirely arbitrary in that mathematicians have considered the various possibilities open to them given a certain assumption and dismissed all but one. Good job. Now, look at the assumption... Oops, it's arbitrary. Oh, well, that's too bad but there's nothing we can do about that... So, in effect the rules are arbitrary. And I don't know of any mathematician, logician or philosopher who managed to justify this assumption with respect to logic itself or acknowledged that they couldn't do it, although some have suggested as much.
EB

If the rules used by mathematicians are arbitrary, how come math is so effective when applied to predicting what's going to happen in the world around us? Take a look at physics, and the technology around us. If you came up with any arbitrary rules you might want to make up, do you think they are likely to work?

I've been trying for quite some time to assess how much formal logic, as opposed to just our intuitive logical sense, is necessary to maths, computing sciences and physics. I drew a blank. Maybe if you have information on that...

The law is an example of arbitrary rules and it works fine. Chess has arbitrary rules and it works fine. So, you'll have to be more specific about what your argument is here.
EB

 

[Wiploc]

I won't talk to you; please don't talk to me.

If you can't live with my comments, just ignore me. That's easy enough to do.

Now it's up to you to explain yourself. If you can't bother to do that, then please abstain altogether.

She wants me to quit posting about her, but doesn't want to quit posting about me. Surely that's fair.

She wants me to ignore her and explain myself. That's just funny.

 

[Angra Mainyu]

These rules are not entirely arbitrary in that mathematicians have considered the various possibilities open to them given a certain assumption and dismissed all but one. Good job. Now, look at the assumption... Oops, it's arbitrary. Oh, well, that's too bad but there's nothing we can do about that... So, in effect the rules are arbitrary. And I don't know of any mathematician, logician or philosopher who managed to justify this assumption with respect to logic itself or acknowledged that they couldn't do it, although some have suggested as much.
EB

If the rules used by mathematicians are arbitrary, how come math is so effective when applied to predicting what's going to happen in the world around us? Take a look at physics, and the technology around us. If you came up with any arbitrary rules you might want to make up, do you think they are likely to work?

I've been trying for quite some time to assess how much formal logic, as opposed to just our intuitive logical sense, is necessary to maths, computing sciences and physics. I drew a blank. Maybe if you have information on that...

The law is an example of arbitrary rules and it works fine. Chess has arbitrary rules and it works fine. So, you'll have to be more specific about what your argument is here.
EB

Chess is not in the business of predicting outcomes. Neither is the law (which isn't entirely arbitrary, but regardless). Now, if we came up with completely arbitrary rules, one would expect that the universe would not oblige and behave in accordance to models developed through extensive usage of arbitrary rules. It would be hugely surprising.

Physics, on the other hand, is meant to be able to (at least) predict phenomena, on the basis of some amount of information. It does that through a mathematical model. And it is extremely good at it. The question of how much formal logic is required is not relevant in this context, because mathematics also uses our intuitive logical sense (what else do you think formal logic is based on?), and math does not use the interpretation of 'if' in the ordinary sense, in which your first premise would be intuitive - but the argument invalid -, and because math does use the sense of 'if' in which the argument would be valid (and you have no good reason to even suspect that the first premise is true) is pretty common.

 

[Speakpigeon]

Now it's up to you to explain yourself. If you can't bother to do that, then please abstain altogether.

She wants me to quit posting about her, but doesn't want to quit posting about me. Surely that's fair.

She wants me to ignore her and explain myself. That's just funny.

Good. At least now we know enough about you to feel that we won't loose anything by ignoring you.
EB

 

[Speakpigeon]

I've been trying for quite some time to assess how much formal logic, as opposed to just our intuitive logical sense, is necessary to maths, computing sciences and physics. I drew a blank. Maybe if you have information on that...

The law is an example of arbitrary rules and it works fine. Chess has arbitrary rules and it works fine. So, you'll have to be more specific about what your argument is here.
EB

Chess is not in the business of predicting outcomes. Neither is the law (which isn't entirely arbitrary, but regardless). Now, if we came up with completely arbitrary rules, one would expect that the universe would not oblige and behave in accordance to models developed through extensive usage of arbitrary rules. It would be hugely surprising.

Physics, on the other hand, is meant to be able to (at least) predict phenomena, on the basis of some amount of information. It does that through a mathematical model. And it is extremely good at it. The question of how much formal logic is required is not relevant in this context, because mathematics also uses our intuitive logical sense (what else do you think formal logic is based on?), and math does not use the interpretation of 'if' in the ordinary sense, in which your first premise would be intuitive - but the argument invalid -, and because math does use the sense of 'if' in which the argument would be valid (and you have no good reason to even suspect that the first premise is true) is pretty common.

Thanks. I think we're all running out of things to say here.
EB

 

[Wiploc]

At least now we know enough about you to feel that we won't loose anything by ignoring you.

She told me that I should have no trouble ignoring her, so she should find it easy to ignore me.

 

[Cheerful Charlie]

These rules are not entirely arbitrary in that mathematicians have considered the various possibilities open to them given a certain assumption and dismissed all but one. Good job. Now, look at the assumption... Oops, it's arbitrary. Oh, well, that's too bad but there's nothing we can do about that... So, in effect the rules are arbitrary. And I don't know of any mathematician, logician or philosopher who managed to justify this assumption with respect to logic itself or acknowledged that they couldn't do it, although some have suggested as much.
EB

If the rules used by mathematicians are arbitrary, how come math is so effective when applied to predicting what's going to happen in the world around us? Take a look at physics, and the technology around us. If you came up with any arbitrary rules you might want to make up, do you think they are likely to work?

I've been trying for quite some time to assess how much formal logic, as opposed to just our intuitive logical sense, is necessary to maths, computing sciences and physics. I drew a blank. Maybe if you have information on that...

The law is an example of arbitrary rules and it works fine. Chess has arbitrary rules and it works fine. So, you'll have to be more specific about what your argument is here.
EB

Whitehead and Russell, Frege, Peano, Cantor, and others. There is a large and technical corpus of works on the subject of the logical foundations of math. You will need to do a little homework to really have some understanding about logic and it's connection to mathematics. An online forum is unlikely to be able to supply you with a royal road to understanding the subject I am afraid.

 

[Bomb#20]

Thanks. I think we're all running out of things to say here.
EB

Well, you have at least one more thing to say here. In your reply to post #157, you didn't answer my question. Once again:

Do you believe "(My prayers will not be answered and I pray) or (there is a god)."?

 

[Angra Mainyu]

Chess is not in the business of predicting outcomes. Neither is the law (which isn't entirely arbitrary, but regardless). Now, if we came up with completely arbitrary rules, one would expect that the universe would not oblige and behave in accordance to models developed through extensive usage of arbitrary rules. It would be hugely surprising.

Physics, on the other hand, is meant to be able to (at least) predict phenomena, on the basis of some amount of information. It does that through a mathematical model. And it is extremely good at it. The question of how much formal logic is required is not relevant in this context, because mathematics also uses our intuitive logical sense (what else do you think formal logic is based on?), and math does not use the interpretation of 'if' in the ordinary sense, in which your first premise would be intuitive - but the argument invalid -, and because math does use the sense of 'if' in which the argument would be valid (and you have no good reason to even suspect that the first premise is true) is pretty common.

Addition: More precisely, people who make laws tend to make predictions about how other people will respond to them, based on the information available to them, but that is not arbitrary, either, as (generally) our expectations about the behavior of people we interact with aren't arbitrary.

 

[Speakpigeon]

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.​

That's obviously true. So, yes, to answer your question, I believe that is true. I also think most people would agree with me on this.

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)."?

OK, yes, I think this expression is necessarily true. Not exactly so readily intuitive as the original formulation but still clear enough.

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".

Very good, I think it's indeed a good summary of the situation. So you did have something interesting to say after all. You should have said that straight away. That would have saved us a lot of time.
Maybe you learnt something there. And of course, I take this as a vindication of my OP. Other readers of this thread should have learnt something judging by the abysmal inadequacy of their posts.

Thanks for your good work here.
EB

 

[Speakpigeon]

I've been trying for quite some time to assess how much formal logic, as opposed to just our intuitive logical sense, is necessary to maths, computing sciences and physics. I drew a blank. Maybe if you have information on that...

The law is an example of arbitrary rules and it works fine. Chess has arbitrary rules and it works fine. So, you'll have to be more specific about what your argument is here.
EB

Chess is not in the business of predicting outcomes. Neither is the law (which isn't entirely arbitrary, but regardless). Now, if we came up with completely arbitrary rules, one would expect that the universe would not oblige and behave in accordance to models developed through extensive usage of arbitrary rules. It would be hugely surprising.

Physics, on the other hand, is meant to be able to (at least) predict phenomena, on the basis of some amount of information. It does that through a mathematical model. And it is extremely good at it. The question of how much formal logic is required is not relevant in this context, because mathematics also uses our intuitive logical sense (what else do you think formal logic is based on?), and math does not use the interpretation of 'if' in the ordinary sense, in which your first premise would be intuitive - but the argument invalid -, and because math does use the sense of 'if' in which the argument would be valid (and you have no good reason to even suspect that the first premise is true) is pretty common.

"mathematics also uses our intuitive logical sense (what else do you think formal logic is based on?), and math does not use the interpretation of 'if' in the ordinary sense, in which your first premise would be intuitive - but the argument invalid -, and because math does use the sense of 'if' in which the argument would be valid (and you have no good reason to even suspect that the first premise is true) is pretty common."

I'm a bit lost as to what you're trying to say. As I see it, there's just one logic and that's the logic that's done by our brain and essentially all our neurons individually, and that comes out as logical intuitions. Any reasoning that we do, right or wrong, relies on it. You can take any reasoning as a crude formalisation of logic. Aristotle went a step further but no one has improved on that since Aristotle. The mathematisation of logic done in the 19th and 20th centuries is obviously a progress but on form only, not on substance. So, as I see it, mathematicians can indeed only use their own intuitive and essentially Aristotelian sense of logic to do any maths but I fail to see where would be the difference with the kind of reasoning done routinely by ordinary people. People ordinarily do all sorts of reasoning, including with premises they think are false (counterfactuals) or that they just assume as true for the sake of the argument. I expect mathematicians to do exactly the same thing.

Of course, any such reasoning can be expressed through language, and so in effect formalised, but without going into the kind of formalisation using truth tables. So, my guess is that mathematicians don't need and and don't use truth table logic. You seem to agree at least with that last bit. This leaves open the question of the practical use of truth table logic, if any. I haven't found any example of that. Truth table logic seems to be just an object of study without any application whatsoever. Maybe I'm wrong on this but I haven't any example that I would be.
EB

 

[Speakpigeon]

I've been trying for quite some time to assess how much formal logic, as opposed to just our intuitive logical sense, is necessary to maths, computing sciences and physics. I drew a blank. Maybe if you have information on that...

The law is an example of arbitrary rules and it works fine. Chess has arbitrary rules and it works fine. So, you'll have to be more specific about what your argument is here.
EB

Whitehead and Russell, Frege, Peano, Cantor, and others. There is a large and technical corpus of works on the subject of the logical foundations of math. You will need to do a little homework to really have some understanding about logic and it's connection to mathematics. An online forum is unlikely to be able to supply you with a royal road to understanding the subject I am afraid.

Thanks for the advice and that's indeed what I'm doing. I have a good scientific library nearby where I live. It's fun to see how little these people understood of logic.

Please note that I make the distinction between logic and methods of logic. I take logic to be what our brain does and as such there's just one logic. I'd love to see any conclusive counterexample to that. I also believe Cro Magnon also had the same logic as us. Methods of logic on the other hands are multiple and at best efforts to find a way to calculate logical formulas. However, unfortunately, all existing methods seems either irrelevant or just plain wrong.

Forums have their limitations but they are definitely useful. I can't argue but Russell himself you know and all these people have been necessarily biased in their views. I think talking to ordinary people like here is necessary. That would be true whatever the subject.
EB