(I know you're not stupid but...)

[Stallin]

I'm assuming most know this already. But to put an end to further skepticism on the subject of logic here is a quick rundown:

There is only one way to prove a proposition, and that's through an arguement.

Example arguement:
1. Pain and suffering are real
2. if pain and suffering are real, then god does not exist
3 Threrefor god does not exist

proposition 1 and 2 are used to prove 3. 1 and 2 are premises, or the reasone to accept the conclusion of 3. Usually in an arguement normally encountered would start with just:

Pain and suffering are real, so there is no god.

When an arguement is started premis 2 is usually so obvious it isnt really stated, just assumed. It is however the same arguement. Logic is mostly concerned with whether the premises of a given argument warrant acceptance of the conclusion.

It is impossible for the conclusions of most arguement to be false if the premises are true. If this is the case the arguement is a deductive arguement, and if this is true then you have a sound arguement. If however your arguement is to prove the conclusion improbable to be false, then its an inductive arguement.

Deductive arguement examples:
(x and y are propositions)
If x then y.
x.
therefore y.
ALSO
if x then y.
not x.
therefore not y.

Not valid deductive arguement:
If x then y.
y.
therefore x.

Im not a college professor so i cant dive too deep into logic, but theres a few basic layouts for sound arguements that i use often. I know you guys arent stupid but incase anyone DIDNT know i just wanted to make sure you did.  

[Fogwolf]

Quote:

Deductive arguement examples:

...

if x then y.
not x.
therefore not y.

I'm not sure about this one.

An example argument of that structure is this:
If Tim stays awake all night, then he'll sleep well tomorrow.
It's not the case that Tim stayed awake all night.
Therefore, it's not the case that he'll sleep well tomorrow.

But it's still possible that Tim might sleep well tomorrow, even though he didn't stay awake all night. In fact, I think that's exactly what makes your next example, of an invalid argument, invalid - it accepts the possibility of y without x.

So I don't think not x, in conjunction with "if x then y", always excludes the possibility of y. If you said "if and only if x then y", then yes, not x would entail not y.  

[MegaTherion777]

i disagree. i dont think there is even ONE way to prove a proposition. i dont think any person can prove beyond reasonable doubt any one thing to another person.

taking your example

1 pain and suffering are real
2 if pain and suffering are real, there is no god
3 there is no god

you havent proven part two, so i can disagree. but no matter how you try to prove part two, i'll still be able to find something to disagree with if i really want to, and you wont be able to prove anything. the same goes for any argument you try to prove. nothing can be proven to someone who wishes not to believe.  

[Fogwolf]

If an argument is such that, if its premises are true then its conclusion cannot be false, then the argument is valid. This is the logical component.

However, an argument is only sound if it is both valid and it has true premises.

Two ways to attack an argument are to show that the conclusion does not follow (does not necessarily follow) from the premises, or to attack the premises and argue a case for one of them being false.

Validity alone does not prove anything (all people are cats, Tim is a person; therefore Tim is a cat - valid, but this isn't going to convince anyone), but if you can structure an argument such that a given person accepts all of the premises and the argument is valid, then unless they're willing to reject one of the premises that previously they might have accepted, it would be irrational of them to deny the conclusion.  

[MegaTherion777]

true. but descartes said (and i dont have the exact quote but it was something to this effect) that at some point in a persons life s/he must doubt/question EVERYTHING in order to discover what is true/what they believe. so if you find someone willing to do that, they will throw out one of the premises and you still wont be able to prove a thing.

i like doubting things. biggrin  

[Fogwolf]

MegaTherion777

true. but descartes said (and i dont have the exact quote but it was something to this effect) that at some point in a persons life s/he must doubt/question EVERYTHING in order to discover what is true/what they believe. so if you find someone willing to do that, they will throw out one of the premises and you still wont be able to prove a thing.

i like doubting things. biggrin

Yes, of course you can follow a sceptical line of reasoning as Descartes did - but Descartes did so because he was looking for exaclty what we are justified in believing in. And, Descartes himself ended up counting quite a few things among these: 1) the self, 2) God, and, once he figured he'd extablished these, he thought he could argue for 3) the rest of the material world, although not quite as we think it is (he basically thought that material bodies have extension and shape as we think they do, but that colour and some other properties were secondary and not real). My point here, though, is that even Descartes used argument - one had roughly this form:

p1: We (the self; you, "I") exist
p2: We think that material bodies exist
p3: God exists (he argues for this separately)
p4: God is is not a deciever; does not deceive us
p5: God has given us no way to establish that material bodies don't exist. (If they did not exist and God did not provide us the means to work this out, he would be deceiving us)
c: Therefore, material bodies exist.

In other words, even if a person takes a sceptical line of reasoning, as Descartes did, they may still use logic (indeed, if like Descartes you want to establish what is real, then you will have to use logic to get beyond your most basic truth, in Descartes' case, "I am").

And, ultimately, yes - if you find someone who doesn't believe anything, who may believe that there is no knowledge/that it is impossible for humans to have knowledge and so on, then a deductive argument might not be terribly convincing for them. However, it could be said that it's impossible to hold no beliefs (after all, is "I believe nothing" not a belief?). And even if it is possible to have no beliefs, the majority of people are not like this, and deductive proofs might still convince the rest of us of the truth of a proposition.

Logic may not be perfect, but it's a useful philosophical tool to keep in mind.  

[MegaTherion777]

oh yes its useful. i dont argue that. i just dont think logic is the be all and end all of a philosophical argument.

i have only a limited knowledge of descartes' actual work - i dont have the $$ to go buy any of his books right now - so forgive me if i make an otherwise avoidable eroor in my argument but...

first, i have an issue with "i think therefore i am." the logic would seem to be

p1 i think
p2 all thinking things exist
c i exist

but do we know this is true? it sounds rational, but would we know it if something was capable of thought but didnt exist as we know it? i mean, thoughts don't exist as we know it - none of the senses can identify a thought. and part of "thought" is an electrochemical reaction in the brain, but that doesn't explain all of it. so if we start with something that doesnt exist as we know it, how can we use it to prove our existence?

then there's the whole god issue. i personally am an atheist, but i don't believe that we can dis/prove the existence of god(s), so that right there is another problem with his philosophy.

and even if there was a god, how can you prove that he wouldn't deceive us?

etc.

so yes, logic is useful. but i'm just making the point that logic isnt everything.  

[Fogwolf]

That is one interpretation of Daescartes' cogito argument, and there are people who believe that this was his intention. However, others hold that it isn't really an argument, but rather, a self-evident truth - If I doubt I exist, I must exist because there must be something to do the doubting. If at any time the proposition I exist is formed, it must at that time necessarily be true. Also, cogito, which is translated as I think, doesn't have to translate directly to 'think' in the sense we mean it - the word incorporates basically all mental experience - sensory awareness and so on as well as active thought.

This is important, though, because in order to develop an argument, we need premises, and by Descartes' system of doubt, there is nothing at first we can have as a premiss - he needs something which doesn't need to be argued for, and 'I exist' is supposed to be that thing. He can then use that base in arguments for other conclusions which we will not doubt, because we accept that premiss and because the arguments are supposedly logically valid.

As for 'can there be things which think but which do not exist' - because Descartes' reasoning at this point is through scepticism, he isn't interested in any argument from the physical (thoughts being networks in the brain), and he would argue that if it is thinking in the sense of cogito - having mental awareness - then it exists (it's a little more complicated than this, though, since the cogito 'proves' the existence of the self to the arguer, but not the existence of other minds). But Descartes has no problem at all with existing intangibly as opposed to physically - this is how he characterises the mind anyway.

The God issue - yes, I won't go into Descartes' argument for God now, since it's a bit long, it involves philosophical assumptions common to his time, and it isn't really convincing to people today. Plus, he didn't need to argue for the existence of God to achieve his ends - he only needed to argue that if God existed, he would not be a deciever, so the actual existence of God isn't really necessary to his ultimate cause.

Logic's usefulness, though, is in that it is convincing. I don't know what you believe, so I can't phrase an argument with premises that you accept, but try it out for yourself - build an argument with premises you don't doubt, and make it valid, and see if you can consistently reject the conclusion. Or, look at something you believe, and ask yourself why you believe it - you might even uncover an argument you didn't know about - your belief might be justified validly by a series of other premises.  

[MegaTherion777]

oh yes, i know that logic is convincing. it was just that the guy who started this thread said it was the only way to prove something, and i just wanted to point out that even then it doesnt necessarily prove anything  

[MegaTherion777]

as for that the self exists, i do not deny that...but i would have a very difficult time trying to prove it, logically or not. as for different interpretations of "cogito," i will say that i was only familiar with the one and not the others. i guess using an alternate interpretation could make the logic valid. like i said, i have just begun to be interested in this subject and have not read much by descartes, nor much by his existentialist opponents on this topic (though i have read quite a few existentialist pieces on other topics)  

[MegaTherion777]

okay so i was having some trouble expressing what i meant, so i talked to my dad and i think i have a better way of explaining. yes, logic is very useful. but it is only useful if you start with a conclusion and premises that both parties agree is true. if the parties are in disagreement, logic is useless. while i agree with the conclusion that the self exists, i disagree that the premises used support the conclusion. i also disagree with descartes proof (as you have summarized) that the outside world exists. thus, until you can prove to me, using premises that i agree with, the existence of anything outside of myself (not to sound self-centered, just speaking hypothetically) you cant debate with me using logic. so logic's usefulness is limited.  

[Smartteaser192]

Stallin

Example arguement:
1. Pain and suffering are real
2. if pain and suffering are real, then god does not exist
3 Threrefor god does not exist


Deductive arguement examples:
(x and y are propositions)
If x then y.
x.
therefore y.
ALSO
if x then y.
not x.
therefore not y.

Let us take into the context of hypothetical conditional syllogisms.


Example argument:

If pain and suffering are real, then God does not exist
but, Pain and suffering are real
Threrefore God does not exist

"If pain and suffering are real, then God does not exist" - How would you be able to prove that God does not exist if pain and suffering are real? The presence of pain and suffering does not mean that God does not exist. It is not a good foundation because it is based on emotions. And this is what you call Argumentum ad Misericordiam.

Quote:

If x then y.
x.
therefore y.
ALSO
if x then y.
not x.
therefore not y.

Example.

If Wagne has cancer, then he is terminally ill.
But, he has Cancer.
Therefore he is terminally ill.

That's what you call the MODUS PONENS (Affirmative Way)
The opposite is the MODUS TOLLENS (Negative Way)

A violation of the modus ponens is called the fallacy of affirming the consequent where no valid conclusion can be inferred.

If X then Y
but Y+
Therefore,____ (No conclusion)

A violation of the modus tollens is called the fallacy of rejecting the antecedent , where no logical conclusion can be arrived at.

If X, then Y
but X-
Therefore,_____ (No Conclusion)

NOTA BENE:
The Fallacy of rejecting the antecedent is not a violation if the major premise involves "Sequential correlation". Here, even if the antecedent is denied in the minor premise, the conclusion remains to be valid.

e.g. If today is Monday, then tomorrow is Tuesday.
But today is not Monday.
Therefore, tomorrow is not Tuesday.  

[Tautological Tautology]

Smartteaser192

NOTA BENE:
The Fallacy of rejecting the antecedent is not a violation if the major premise involves "Sequential correlation". Here, even if the antecedent is denied in the minor premise, the conclusion remains to be valid.

e.g. If today is Monday, then tomorrow is Tuesday.
But today is not Monday.
Therefore, tomorrow is not Tuesday.

I don't know much about sequential correlation, but it seems to me that this is true because "tomorrow is Tuesday" implies that today is Monday. Would you say that the argument essentially says "p→ p"  

[Niniva]

Tautological Tautology

Smartteaser192

NOTA BENE:
The Fallacy of rejecting the antecedent is not a violation if the major premise involves "Sequential correlation". Here, even if the antecedent is denied in the minor premise, the conclusion remains to be valid.

e.g. If today is Monday, then tomorrow is Tuesday.
But today is not Monday.
Therefore, tomorrow is not Tuesday.

I don't know much about sequential correlation, but it seems to me that this is true because "tomorrow is Tuesday" implies that today is Monday. Would you say that the argument essentially says "p→ p"

Unfortunately what you are pointing out here is a troublesome spot in logic. Simply because on the truth table of (If P then Q) has a line in which Q is true, and P is false and yet the statement is still true simply because we cannot call it false if the anticedent is false but the consequent is true. Therefore just because today is not monday.....that does not necessarily imply that tomorrow is not tuesday.

This is absurd however. In order for logic to account for this troublesome spot we are forced to say that you cannot translate the sentence "If today is monday then tomorrow is tuesday" into the form "If P then Q" because that is not what is meant, nor what is implied by what the person saying it meant.

We must then translate it into a more complicated form that accounts for the impossibility in the english language any other day is followed directly by tuesday.

So it becomes (If P then Q) AND (If Q then P) Which is essentially the same as Q if and only if P. So no....it isn't a case of If P then P....its a case of Q....If and only if....P.

What I have said here is that based on what you have written: In the case of If P then Q....denying P has NO AFFECT on the truth of Q and so therefore (based on the law of the excluded middle) the statement is true. Think of it like this, the entire statement is considered true until such a time in which we find an example of a time when P is not directly followed by Q. But that does not mean that Q cannot ALSO be preceded by something else (in the case of multiple causes).....however because tomorrow being tuesday implies that today is monday BY DEFINITION....If P then Q is not adequate but Q if and only if P is perfectly adequate since it makes it so that there is no time that Q occurs that is not preceeded first by P.

But I would dissagree that saying "Today is monday" and saying "Tomorrow is tuesday" are saying the same thing. It seems like today being monday is implied by saying "Tomorrow is tuesday" sure, but that does not mean that they are the same. The object of the senteces....for example....is very different. So is their reference to time passing, the "thing" pointed out by the two sentences is vastly different, and so are the attitudes presented by the speaker.

So no, this is not a tautology, but If P then Q is also not an adequate translation either. Q if and only if P is the only way to say this correctly in logical form.  

[Tautological Tautology]

Niniva

Tautological Tautology

Smartteaser192

NOTA BENE:
The Fallacy of rejecting the antecedent is not a violation if the major premise involves "Sequential correlation". Here, even if the antecedent is denied in the minor premise, the conclusion remains to be valid.

e.g. If today is Monday, then tomorrow is Tuesday.
But today is not Monday.
Therefore, tomorrow is not Tuesday.

I don't know much about sequential correlation, but it seems to me that this is true because "tomorrow is Tuesday" implies that today is Monday. Would you say that the argument essentially says "p→ p"

Unfortunately what you are pointing out here is a troublesome spot in logic. Simply because on the truth table of (If P then Q) has a line in which Q is true, and P is false and yet the statement is still true simply because we cannot call it false if the anticedent is false but the consequent is true. Therefore just because today is not monday.....that does not necessarily imply that tomorrow is not tuesday.

This is absurd however. In order for logic to account for this troublesome spot we are forced to say that you cannot translate the sentence "If today is monday then tomorrow is tuesday" into the form "If P then Q" because that is not what is meant, nor what is implied by what the person saying it meant.

We must then translate it into a more complicated form that accounts for the impossibility in the english language any other day is followed directly by tuesday.

So it becomes (If P then Q) AND (If Q then P) Which is essentially the same as Q if and only if P. So no....it isn't a case of If P then P....its a case of Q....If and only if....P.

What I have said here is that based on what you have written: In the case of If P then Q....denying P has NO AFFECT on the truth of Q and so therefore (based on the law of the excluded middle) the statement is true. Think of it like this, the entire statement is considered true until such a time in which we find an example of a time when P is not directly followed by Q. But that does not mean that Q cannot ALSO be preceded by something else (in the case of multiple causes).....however because tomorrow being tuesday implies that today is monday BY DEFINITION....If P then Q is not adequate but Q if and only if P is perfectly adequate since it makes it so that there is no time that Q occurs that is not preceeded first by P.

But I would dissagree that saying "Today is monday" and saying "Tomorrow is tuesday" are saying the same thing. It seems like today being monday is implied by saying "Tomorrow is tuesday" sure, but that does not mean that they are the same. The object of the senteces....for example....is very different. So is their reference to time passing, the "thing" pointed out by the two sentences is vastly different, and so are the attitudes presented by the speaker.

So no, this is not a tautology, but If P then Q is also not an adequate translation either. Q if and only if P is the only way to say this correctly in logical form.

You're right, it should have been a biconditional instead of a conditional.

Do you think that they are not equivalent due to the sense-reference distinction? In other words are "tomorrow is Tuesday" and "today is Monday" extensionally equivalent because they both refer to Monday and intensionally inequivalent because they have different senses, being that the former takes into account an anticipated passage of time while the former says nothing of it?