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1. Originally Posted by ygolo
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.

2. 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.

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

Originally Posted by reason
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?

4. Originally Posted by Orangey
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'.

5. 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.

6. 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!

7. 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.

8. Originally Posted by reason
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.

9. Originally Posted by ygolo
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.

10. 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. ^_^

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