http://www.spittoon.org/archives/4267

Obviously, a bit of self-publicity.

Boring.

And the last word goes to…

Glad to see you back. Got any other half-baked, barely understood concepts in formal logic you would care to share?

For the record, I’m not M.S. (whoever he is).

This all started by you raising an objection to my comment and I responded by trying to show that your understanding of my comment was incorrect, and by accepting blame for the lack of clarity in my wording. You may choose to see this as an ad hominem attack but no offence was intended, so chillax. On the other hand, it was you who accused me, after my insistence that you still have not understood my comment, of being a “big tit” and I can only assume that this was intended as an insult (though personally I have always failed to see how comparison with highly sought after female organs constitutes an insult).

Be that as it may, far from “repeatedly demonstrating that my position is incorrect”, the truth of the matter is that you have only demonstrated that my position is actually enirely correct, as I shall explain:

I defined R.A. as a way to refute a proposition by showing that it necessarily leads to a logically inconsistent position. You objected by saying this was an “improper grasp” of R.A., which you defined as “a method of proving the necessary truth of a statement”. In a subsequent post you went on to show that a statement can be proved true by first negating it (“let us assume that the statement is false”) and then by showing that the negated statement necessarily leads to a logically inconsistent or absurd position, whereby the original statement is proved to be a tautology, ie., it cannot but be true. To which I responded that you are wrong to maintain that this is an exclusive definition of R.A. and that it is not opposed to mine, but is actually only an application of it. (Ie., negate the original statement and then apply my version of R.A.).

I could go into notational first order predicate calculus to describe this exchange, but – with respect – I think that would be out of place here.

Instead, I’ll stick to the point of the original article and explain it in those terms:

I said that it is logically inconsisent (and by my version R.A., incorrect) of a person to maintain the two following positions at the same time: i) that an action A is wrong only because it is prejudicial, and ii) another action B, which is also prejuducial, is correct.

In other words, a person is wrong to say that it is okay to ban Ahmeddiyya mosques and not okay to ban minarets, if their sole objection to the banning of minarets is that it is an act of prejudice, since the banning of Ahmediyya mosques is also a prejudicial act. And, for exactly the same reasons, a person is logically wrong to say that it is okay to ban minarets but not okay to ban Ahmediyya mosque.

This conclusion is straightfoward enough, but you said that it was incorrect (or to be precise, you said I do not have a clue of what I write) because of your objection that my understanding of R.A. is wrong.

Now, since your version of R.A. is the same as mine only with a negation appended to the front, it’s a trivial matter to prove the exact same conclusion using your version of R.A. by:

i. first starting with the conclusion itself, ie, “A person cannot maintain both of the following at the same time: i) Muslims are wrong to ban Ahmediyya mosques because its an act of prejudice, and ii) the Swiss are correct to ban minarets even though its an act of prejudice”

ii. and then negating the conclusion: “A person can maintain both of the following at the same time: i) Muslims are wrong to ban Ahmediyya mosques because its an act of prejudice, and ii) the Swiss are correct to ban minarets even though its an act of prejudice”

iii. By showing that the negation of my conclusion is internally logically inconsistent (ie., an act of prejudice cannot be both correct and incorrect), my conclusion is proved to be correct.

QED

If it makes you feel any better, I’m not “trying it on” or trying to “attack” you, but just trying to explain my (not particularly earth-shattering) comment in the face of your questions – degrees and qualifications notwithstanding.

I am really not very interested in continuing this argument with you. I have demonstrated repeatedly why your position is mistaken. You continue to illustrate your total disregard for common sense. In the end, you are reduced to ramping series of ad hominem attacks. That speaks volumes. I would stick to your last – you know, that thing Socrates suggested was the essence of justice.

Goodbye.

I’m surprised that you are insisting on this. As an expert in logic, you should know that Reductio ad Absurdam is primarily a form of refutation (not proof) that works by showing the the necessarily contradictory or absurd consequences of a given premise. Even the latin terms translate to “reduction to absurdity”.

It is very likely that you are, as you keep trying to prove, more intelligent me. Which only makes your pyrotechnic display of logical misunderstanding all the more confusing.

But in any case, all this has little to do with with my original comment. But I suppose a postgraduate degree in philosophy does not preclude one from barking up the wrong tree.

I suppose it comes from dealing with joint honours “anthropology and psychology” (or such like) bods… *sigh* to borrow your deeply patronising tone… I suppose I should have known.

Now, do crawl away before you make an even bigger tit of yourself.

Fine, MS. See you.

Thanks for the information.

To be honest, I’m not surprised your students are in a tangled mess if you’re trying to teach them Reductio ad Absurdam from it’s slightly more advanced applications instead of from first principles, and if you’re telling them that to think Reductio ad Absurdam is a method to refute a proposition is “not a proper grasp” of it. Quod absit.

Now I have work to do untangling the mess other students leave in their wake. Goodbye.

My particular favourite is the largely unexplored, incomplete system KHLem{0} (following Cresswell and Hughes labels for systems of normal modal logics). I can tell you its frames are connected.

Deontic logics are generally built on the axiom D (again Cresswell and Hughes) – with, of course, the axiom of normal systems, K.

verification proofs of normal modal logical axioms

Actually, it is a common enough method to discover the validity of any sentence in a propositional logic.

Consider the conditional if p (is true) then p (is true) then p (is true). This is a trivial tautology, as I hope you understand and agree; but it serves as a demonstration of the method of RA.

We can write this as p then [p then p]. {apologies, I cannot seem to access a more convenient means of expressing “if… then” graphically}

The validity of this can be tested by RA (in other words, RA is a method, as I commented):

Let us assume that the statement is false, where V is the truth-value of the sentence:

(i) V (p then [p then p]) = 0

You should know the truth table of a conditional statement. It will only be false if the antecedent is true and the consequent is false. Thus we can derive from (i) the following:

(ii) V (p) = 1 – this is the antecedent.

(iii) V (p then p) = 0 – this is the consequent.

Look at the consequent. Again, by application of the known truth table for conditionality, we arrive at the result that (iii)’s antecedent must be true and its consequent must be false. But this means

(iv) V (p) = 1; and V (p) = 0.

Thus the value of the propositional variable, p, is simultaneously both true and false. This is, of course, impossible – indeed absurd.

Thus, the statement is a tautology. It is true and cannot be otherwise.

This is a validity proof by RA.

Thanks for your attention.

For example, you might find it enlightening to look at the way Saul Kripke exploited RA to deliver verification proofs of normal modal logical axioms, for example. The approach is to show that if the axiom were false it would lead to a contradiction amongst its propositional variables. That is, of course, exactly my point – and would suggest that Saul Kriple, comme moi, is also mistaken in his understanding of RA. Mais, tant pis, Abu Yusuf has spoken.

One gets the title by studying the subject at degree and post graduate level. I was unaware one could qualify in Hoover technology; however, given that one may take courses in “Golf Studies”, or “Byzantine Studies and Wood Technology” (my favourite – it actually exists) at a” University of Polytechnic” these days, nothing would surprise me.

Contrary to what you may think, the only thing which changed between my first post and the second was my wording, and consequently your understanding. The points I were making were exactly the same.

You’re right, I’m not a “logician” and I don’t claim to be one. Logic is tool. I don’t claim to be a “hooverologist” either, but I keep my house clean.

By the way, how does one earn the title of “logician” these days? Do you need to learn about, for example, “reductio ad absurdum”, because of your definition of it was hopelessly wrong.

[I was hoping it wouldn't come to this, but c'est la vie.]

You have been caught misapplying a systematic form of argumentation (logic) and then attempting to recant the same.

You are now being disingenuous and playing hurt when no offence has been done, other than to disagree with you and point out that you do not have a clue of what you write.

As it happens, I am a logician. You, clearly, are not.

Those are the conclusions you want to draw. If that makes you happy, so be it.

I’m aware that most of your fellow contributors to Spittoon are not so openly obtuse and unnecessarily belligerent, and they will clearly see that:

i. My use of logic did not change from the first post to the second
ii. I meant exactly the same thing in both posts.
iii. What I’m trying to say is actually very simple