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On Argument

reason

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However, if not B, then one of either Premise 1 or Premise 2 is false. So it seems to me, among rationally thinking people, only those who would believe the Conclusion would also believe both Premise 1 and Premise 2.
That is basically my point, and there are many ways which the principle could be expressed. For example, take your simple argument,

A, A then B |= B

Now,

B |= A then B

Therefore,

A, B |= A, A then B

and,

A, A then B |= A, B

Therefore,

A, A then B =||= A, B

The premises 'A, A then B' and 'A, B' are semantically equivalent, both have precisely the same consequences, both say the same thing in a different way and so are also interchangable. In consequence, the original argument can be rewritten in the following form,

A, B |= B

In that form it is clear that the premises provide no good reason to accept the conclusion, and indeed one of the premises is entirely unecessary. Moreover, the same procedure can be applied to any valid argument to reveal its, whole or partial, circularity.
 

ygolo

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This is an idea that vexed me since high-school.

There is some "practical" meaning to "circular reasoning." If while designing a circuit, and running a simulation, I put in an operating voltage at the node as an input to the simulation, and it stays there, I have only proven that it is a valid operating region. If I force that node in the simulation to the desired voltage, the simulation shows little other than how the circuit responds to being forced to that voltage. If however, I don't set an operating point for that node at a different voltage, and it changes and goes to a different voltage, then that different voltage (assuming it settles) is likely a stable equilibrium.

There are analogous situations in digital circuits and computing. I wonder if the "stable equilibrium" idea can be transfered to logic in general.
 

Orangey

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Hey reason, would you mind explaining this process to me? I don't think I quite understand what you did :confused:.

A, A then B |= B

Now,

B |= A then B

Therefore,

A, B |= A, A then B

and,

A, A then B |= A, B

Therefore,

A, A then B =||= A, B

Edit: Nevermind, I think I see it now. Though couldn't you just say that A, A->B =||= B, which breaks down to B =||= B?
 

reason

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Edit: Nevermind, I think I see it now. Though couldn't you just say that A, A->B =||= B, which breaks down to B =||= B?
Now I am the one who doesn't understand.

A, A then B |= B

but,

B |!= A, A then B

Therefore,

A, A then B =!||= B

Moreover, I do not understand what you mean by 'breaks down to B =||= B'.
 

reason

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To explain more comprehensively for anyone who does not understand.

The letters 'A' and 'B' are propositional-variables. The relation 'A → B' can be read as 'if A is true then B is true'. The turnstile represents a valid inference, so 'A |= B' can be read as 'there is no consistent assignment of truth-values where "A" is true and "B" is false'. Finally, the comma is used to seperate premises and conclusions where there is more than one. For example, consider the following argument.

A, A → B |= B​

Here we have the two premises 'A' and 'A → B', from which we validly infer the conclusion 'B'. This simple deduction employs the rule known as modus ponens, which states: if the antecedent of a conditional is implied by any of the premises then its consequent can be validly inferred. In this case, 'A' is implied by 'A', which is the antecedent of the conditional 'A → B', and so according to modus ponens the consequent can be valdily derived, which is the conclusion 'B'. With this argument in mind it should be clear that the following argument is also valid.

A, A → B |= A, B​

In fact, this argument is the same as the previous one but with the addition of 'A' as a conclusion, and since 'A' is implied by the premise 'A' the argument is valid. However, the next argument I wish to present is somewhat less intuitive.

B |= A → B​

This argument states that the conditional 'A → B' can be validly derived from the premise 'B'. Now some people might look askew at that argument, but it is actually valid. To understand why we need do no more than reconsider the definition of the turnstile symbol: the argument 'B |= A → B' can be read as 'there is no consistent assignment of truth-values where "B" is true and "A → B" is false'. In other words, if 'A' is true then 'B' is true, but since 'B' is true anyway then it must be true that if 'A' is true then 'B' is true. From this we can obtain the following valid argument.

A, B |= A, A → B​

It should be clear that this argument is valid, since we have simply added 'A' into the premises and derived 'A' as a conclusion, while changing nothing else. Now this argument, combined with our previous result, can reveal our problem.

A, A → B |= A, B
A, B |= A, A → B​

The above arguments are identical except for the fact that the premises and conclusions have been swapped. In other words, the premises imply the conclusions and the conclusions imply the premises. This relation can be captured by rewriting the above argument using a double turnstile.

A, A → B =||= A, B​

This means that everything which can be derived from the premises can also be derived from the conclusion, and vice versa. In other words, the premises 'A, A → B' and 'A, B' are semantically equivalent i.e. their logical content is exactly the same. Therefore, 'A, A → B' and 'A, B' are synonymous, and so any instance of one can be swapped with the other and retain the semantic interpretation of the argument. In consequence, the original argument can be rewritten from.

A, A → B |= B​

To.

A, B |= B​

The final form presented here would surely do nothing to convince anyone that 'B' is true, and the addition of 'A' as a premise is entirely superfluous. The problem which arises for anyone who wants to argue for a conclusion is that the results of this procedure can be replicated for any valid or invalid argument.
 

Anja

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I agree with the original poster.

In fact I now avoid arguments of any type. From my perspective they are simply mental exercises and tend to create rifts rather than connections with others. I have little desire to connect with others in an adversarial manner. This was not always true.

I do experience any type of an argument as an effort to prevail over another human.

But I've learned that I like my life better when I am not wasting energy on trying to make others change.

And I often perceive arguments on the net as really just a way of playing or of releasing pent-up uncomfortable emotions. The latter a no-no in my book when it is done at the expense of another.

While logic is not my strong point I have a good brain and am well-informed on a number of issues. The zeal of youth often compelled me to argue with others about my perceivedly odd ideas and it was predictable that I would be the "odd" man out. Not a pleasant experience to pursue.

What's an argument about? Who's right, therefor implying that there is one who's wrong. Why would I want to force my viewpoint on someone else? Why would I want to point out flaws in others if I want to connect with them? What purpose would it serve other than an attempt to elevate my self-esteem through defeat of others. Ack.

I much prefer now to simply present my viewpoint for others to consider, listen to others' opinions and perhaps draw from them to change my viewpoint if I see a personal advantage in doing so.

And I did just that here! :)
 

ygolo

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In many circles the word "argument" means "reasoning presented for others." Confusing this for an other meaning of argument, a "verbal fight" may not always be good.

Arguments are used all the time in math, philosophy, and more "practical" things like making business and engineering decissions.
 

Orangey

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Now I am the one who doesn't understand.

A, A then B |= B

but,

B |!= A, A then B

Therefore,

A, A then B =!||= B

Moreover, I do not understand what you mean by 'breaks down to B =||= B'.

Okay, I understand what you did now (from your other post)...thanks for the explanation :). I was doing something different, so I will try to explain.

Here's what I was thinking (which is probably somehow wrong, I was tired when I thought of it):

When you state the premises (in this case A, A->B) it means the same thing as stating the conclusion (B). The conclusion is just another way of saying what the premises together already mean. So the conclusion B is implicit when stating A, A->B.

It's like...

All humans are mortal
Socrates is human
_________________
Socrates is mortal

which can essentially be restated (equivalently) as

Socrates is mortal
________________
Socrates is mortal

If an argument is valid, then there is no new information passing between the premises and conclusion...they are epistemologically equivalent. The premises of any valid argument are simply restated in a different form in the conclusion, making it essentially circular.

Where I went wrong when I thought of this is that a true circular argument assumes the conclusion to prove the conclusion...the difference being that in the above argument, I didn't really assume that Socrates was mortal in the premises in order to prove that he is mortal...they (premises) just restated it (conclusion) in a different form, sort of how 2+2=4 is the same thing (epistemologically speaking) as saying 4=4.

Anyway, that's my ramble...I hope it seems more coherent to you than it does to me at the moment.
 

Anja

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In many circles the word "argument" means "reasoning presented for others." Confusing this for an other meaning of argument, a "verbal fight" may not always be good.

Arguments are used all the time in math, philosophy, and more "practical" things like making business and engineering decissions.

Thanks for the reminder of a secondary definition of "argument," ygolo.

I've presented my experience of argument in a broader way, of course. And, still as an INFP, arguing in any form isn't appealing to me.

So there's the viewpoint of one INFP, for what it's worth. Now I'll sit back and watch you thinkers flex your brain power! It's fairly awesome to think that humans can do what you're doing here. Maybe those who "can't," watch.

Hey! What's your favorite color? ;)
 
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Shadowrose

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I figure I'll throw my 3 cents into the mix here.. the way I see it, is that Logic, in and of itself, is essentially infallible. The problem is when dealing with the premises. I'm not sure you can synthesize any new knowledge from known premises, so any time you present an argument you are, effectually, showing another facet of knowledge from the pieces you started with. In any situation where you generate 'new' knowledge, as it were, I think you have to start with a premise which you cannot know is entirely true.

One big reason why I argue, truthfully, is for the sake of clarity. It's a simple example but it demonstrates the point.. if Socrates is Human, and all Humans are Mortal, Socrates is Mortal. It may not have occurred to the person I am speaking to that Socrates is, in fact, a mortal human. Granted, this is a mildly silly example but in more complex situations it does frequently happen. Argument is one of the tools a person has for teaching, in that it forces a person to look at something in a, perhaps, unfamiliar light.

Another reason I tend to argue is related to clarification. When I talk to a person about something they hold to be a core belief, I will frequently attack their belief from many angles. The point of this is not to be cruel or aggravating, the point is to assist the person in building a stronger defense and understanding of why they hold such a belief. I've found that the deeper one's understanding runs, the more able one is to work within said understanding.

And my favorite colors are blue and red. ^_^
 

reason

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This is refined version of my original post:

The purpose of this essay is to discuss the limits of rationality. The focus of criticism will be the following presupposition:
The premises of a good argument provides a good reason to accept its conclusion​
The majority of rational debate is undertaken with the expectation that participants should advocate a position, rally support and mount defenses. The perennial debate between rationalists (empiricists, intellectualists, objectivists, etc.) and irrationalists (relativists, dogmatists, postmodernists, etc.) is conducted with this shared assumption, each asking the question ‘do good arguments exist?’, and coming away with a different answer. This presupposition forms a framwork in which problems are identified and solutions evaluated, a metacontext in which rational discussion is conducted, and does so with such authority that few ever question it.

There is an argumentative fallacy called petitio principii: the fallacy of assuming in the premises of an argument that which one wishes to justify in the conclusion; a begging of the question. That said, an argument which begs the question is not invalid. In logic an argument is valid when it has no consistent interpretation where the premises are true and the conclusion is false, and so an argument which assumes in the premises that which it is intended to justify in the conclusion must be valid. The fallacy of begging the question does not depend on the logical form of an argument, but on what the argument is expected to achieve. Therefore, if an argument is presented without the expectation that its premises can provide a good reason to accept its conclusion, then there can be no begging of the question.

Here arises the problem. Taken in conjunction with the prohibition against question begging arguments, the presupposition that the premises of a good argument provides a good reason to accept its conclusion implies that there do not exist any good arguments.

If someone places apples into an empty basket then they would not expect to take anything out of the basket except some of the apples they put in. This is not unlike how valid arguments function: the premises are placed in the basket and nothing can be taken out except some of the premises which were put in. What is taken out of the basket often appears different to what was put in, but this superficial change is only a trick of the transformational rules of logic. If an argument is valid then the conclusion will always repeat, either wholly or partially, what is already assumed, either implicitly or explicitly, in the premises. In other words, no valid argument can avoid the charge of petitio principii when it is offered with the expectation that its premises are a good reason to accept the conclusion.

On the question ‘do good argument exist?’ the irrationalists are correct: good arguments cannot exist by definition. However, irrationalists then jump to the conclusion that argument is futile, everything is relative, there is no truth etc. but there is no need to despair for rationality yet. There are other options: if the definition of a 'good argument' prevents its own existence then a more sensible response might be to reconsider that definition. For example, the nonexistence of "good arguments" does not imply that every argument is invalid nor that any argument is false. This problem may render the search for good reasons futile, but the search for truth can go in unimpeded. There is even some good that can come it, perhaps encouraging more humility regarding our ability to recognise the truth if it is discovered.

There may be some resilience to this idea and the question might be asked: if no argument can justify its conclusion then why should someone believe it? The correct answer is simply 'because it may be true'. The decision to accept an argument lies with each individual, as do the consequences of deciding to accept an incorrect argument.

If I were to stub my toe on the doorstep tomorrow then I would not hold the doorstep morally responsible for my pain, and nor would I hold it responsible for my good fortune if in my moment of pain I were to spot $100 which I would otherwise have not noticed. The doorstep is not a decision-making agent, and no punishment nor reward could have any consequence on its future behaviour. The doorstep will not move aside to prevent me stubbing my toe in the future, and nor will it leap into my path to draw my attention toward some item of worth. It seems to me that many people want to be my doorstep. The metaphors of coercion, compulsion, addiction and force seem to infuse ordinary rational discourse, betraying a peculiarly authoritarian attitude to rationality.

Whenever choice is mentioned it is with a ring of resignation, choosing is what is done when there is no decision-procedure, no authority giving orders. When there is no rule to decide for us, rules on which people so often unload their responsibility, reason has failed. The language of debate describes 'forceful points', 'compelling arguments', 'destructive criticism', 'powerful defence' and so on, a good argument should compel, by the force of reason. If the argument can be doubted, dismissed or deflected in some ad hoc manner, then the argument is at fault, it lacks sufficient force. A good argument cannot be denied, but compels all "right-thinking" people to accept it.

I think, however, that it is our choice to be rational, to care about logic, evidence, critical discussion, ethics, and our conduct with other men. It is not something which can be forced on us, but a free choice with all the responsibility that entails.

To insulate theories from criticism and refutation is the easiest thing, done simply by denying the applicability of all standards of criticism, allowing any theory, whether scientific, mathematical, ethical or whatever, to be immunised from refutation. If a theory is to be criticisable, then the responsibility lies with each individual to decide what kind of criticism they will accept. In other words, theories are refutable if people choose to make them refutable i.e. clarify the problem which the theory is an attempt to solve, and then specify what kind of argument or experiment could be deployed as a test. The rationalist ought to be someone who voluntarily enters into this arrangement, eschewing authority outright, with the intention of learning from his errors before acting on them.
 
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