Indian Logic Forum

Mary · Posted: Fri Dec 02, 2005 10:55 pm Post subject: Thank you, Avi

Avi,

Thank you for your thorough work on this. I've not had time to fully consider your previous response, and now need to consider your latest reponse.

Just wanted to let you know I've not forgotten this discussion. I hope to be able to give more attention to it soon, but perhaps not the attention needed until after the first of the year. However, if I come upon thoughts worthy of discussion in the meantime, I will post them here.

Highest regards, M.Lee

Avi Sion · Posted: Mon Dec 05, 2005 3:10 pm Post subject: catuskoti

Actually, upon reflection, it is possible to represent the вЂњcatuskotiвЂќ argument more briefly, in hypothetical form (apodosis), by casting it as the major premise (rather than as the minor premise, as I earlier tried).

We are told (and can infer вЂњ=вЂќ from what we are told) the following:
not(X + Y + Z) = if X, then not(Y + Z) = if (Y + Z), then notX
not(X + Y + notZ) = if X, then not(Y + notZ) = if (Y + notZ), then notX
not(X + notY + Z) = if X, then not(notY + Z) = if (notY + Z), then notX
not(X + notY + notZ) = if X, then not(notY + notZ) = if (notY + notZ), then notX

These four statements may thus be summarized as:
вЂњif X, then not(Y + Z) and not(Y + notZ) and not(notY + Z) and not(notY + notZ)вЂќ;
taking this as the major premise of a modus tollens, whose minor premise is:
вЂњbut (Y + Z) or (Y + notZ) or (notY + Z) or (notY + notZ)вЂќ (by the law of the excluded middle),
our conclusion is вЂњnotXвЂќ categorically.

Alternative, using the contraposite form of the major premise:
вЂњWhether (Y + Z) or (Y + notZ) or (notY + Z) or (notY + notZ), then notXвЂќ;
together with the same minor premise:
вЂњbut (Y + Z) or (Y + notZ) or (notY + Z) or (notY + notZ)вЂќ (by the law of the excluded middle),
we have a modus ponens whose conclusion is again вЂњnotXвЂќ.

It should be added that the above apodoses may also be construed as simple dilemma, the modus tollens as a destructive one and the modus ponens as a constructive one.

Mary, no response needed. Enjoy life!

Plamen · Posted: Mon Dec 05, 2005 5:31 pm Post subject:

Jaina (quodammodo catuskoti):
1. Somehow A
2. Somehow not-A
3. Somehow (A and not-A)
4. Somehow not (A and not-A)

Buddha (negative catuskoti)
1. Not A
2. Not not-A
3. Not (A and not-A)
4. Not not-(A and not-A)

To all these four (catur) horns (koti), Nagarjuna adds a prasangAt (because the opposite leads to absurdum).

Avi Sion · Posted: Mon Dec 05, 2005 7:10 pm Post subject: Plamen last post

Plamen: I do not understand what you mean to say in your last post.
Are these other forms of catuskoti?
If so, they do not look as clear and legit as the one Mary taught me. Under logic based on the laws of thought:

The вЂњJainaвЂќ version: Something might be both вЂњsomehow AвЂќ and вЂњsomehow notAвЂќ. But nothing can be вЂњsomehow both A and notAвЂќ. And everything is more than вЂњsomehowвЂќ, i.e. always, вЂњnot(A and notA)вЂќ Also, what do you mean by the word вЂњsomehowвЂќ? Maybe (i.e. under some cognitive conditions)? or Somewhat (i.e. to some degree or in some respects)?

The вЂњBuddhaвЂќ version: вЂњNot AвЂќ and вЂњNot not AвЂќ can be affirmed separately but not together. вЂњNot (A and notA)вЂќ is universally true for all values of A. And, a contrario, вЂњNot not(A and notA)вЂќ is universally false for all values of A.

Additional note: I take вЂњAвЂќ to mean вЂњA to some degree or under some condition or in some respectвЂќ, so that вЂњnotAвЂќ means вЂњnot at all AвЂќ. If, however, we take a wider view, and say that something is вЂњpartly A, partly notAвЂќ (e.g. has a round head but a tubular body), then we have what might be called a вЂњtrilemmaвЂќ, viz. вЂњall A, all notA, or partly A and partly notAвЂќ. This is not against the laws of thought, if properly understood. However, it remains true that the three theses are mutually exclusive and exhaustive.

WhatвЂ™s this about Nagarjuna? What is a вЂњprasangAtвЂќ вЂ“ can you give me the form or an example?

Plamen · Posted: Tue Dec 06, 2005 7:29 pm Post subject: Re: catuskoti

Avi Sion · Posted: Wed Dec 07, 2005 11:01 am Post subject: catuskoti

Plamen:

Regarding your statement:

Plamen · Posted: Wed Dec 07, 2005 5:00 pm Post subject:

Avi:

This is my original post to which I would like to add only one clarification

The positive tetralemma (the catuskoti rejected by Buddha!!!) results from the possible combinations of two "quantifiers" - sva and para (para being the logical negation of sva, and conversely, sva being the logical negation of para, namely, apara). There are four of them:

1. Sva (itself, oneself is atma)
2. Para (other, something else)
3. Sva and para
4. Neither sva nor para

If translated in this perspective, the above-cited text should first contain the positive tetralemma (it could be Jainist, Lokayatika, or even Vedic), followed by its negation which constitutes the propositional element of the negative Buddhist tetralemma. So we would have:

7 'Now then, Master Gotama, is suffereing inflicted by itself?' [Positive Lemma]
'Not so verily, Kassapa', said the Exalted One. [Negative Lemma]
8 'What then, Master Gotama, is one's suffering inflicted by something else?' [Positive Lemma]
'Not so verily, Kassapa', said the Exalted One. [Negative Lemma]
9 'What then Master Gotama, is suffering inflicted both by itself and something else?' [Positive Lemma]
'Not so verily, Kassapa', said the Exalted One. [Negative Lemma]
10 'What then, Master Gotama, has a suffering inflicted neither by itself nor by something else, befallen me by chance?' [Positive Lemma]
'Not so verily, Kassapa', said the Exalted One. [Negative Lemma]

Hence, the scheme from p. 21 of the book has nothing to do both with the positive catuskoti and the negative catuskoti. Moreover, the phrase, 'there exists an X such that chararacteristic y applies' is in no case a Buddhist proposition, because what the Buddhists really claim is that the Subject X does not exists. The proposed scheme mutatis mutandi applies to the Positive Jaina Tetralemma:

(1) there exists somehow an X such that chararacteristic y applies;
(2) there exists somehow an X such that y does not, but z does, apply;
(3) there exists somehow an X such that both y and z apply;
(4) there exists somehow an X such that neither y nor z apply.

Somehow (syad) is an existential modifier, and in point 3 there is no need for "in part", because z is a total negation of y.

The Buddhist catuskoti would be:

(1) It is not true that there exists an X such that chararacteristic y applies;
(2) It is not true that there exists an X such that y does not, but z does, apply;
(3) It is not true that there exists an X such that both y and z apply;
(4) It is not true that there exists an X such that neither y nor z apply.

Now you see clearly that the Negative Buddhist Tetralemma (BTW, coti is an alternative, not lemma because it does not follow from any theorem) is a logical expression of anatmavada.

To my knowledge, this is the first time that one is stating the anatta logical character of the Buddhist Catuskoti.

* * *

The clarification concerns the understanding of Z as not-Y. I am sorry I did not mention this important condition in my root post on the E-sangha forum. But it is clear from the explanation of sva and para - sva is Y, para is Z.

* * *

prsasngAt has been translated in my previous post - because of the absurdity, reductio ad absurdum. That's why a follower of Nagarjuna is called Prasangika.

Plamen · Posted: Wed Dec 07, 2005 5:08 pm Post subject:

The post above cited was in reply to this post of a member Plotinus

Avi Sion · Posted: Sun Dec 18, 2005 7:26 pm Post subject: catuskoti

Plamen: I have finally read your last two posts. My reading is that they confirm what Mary said, and the inference I drew from that. If you look again, maybe youвЂ™ll see that too.

You wrote:

Mary · Posted: Mon Dec 19, 2005 12:50 am Post subject: Excluding the Middle

Dear Avi,

You may not see this for some time, given that your schedule is busy, as is everyone's. Perhaps when you return, I too will have had more time to look at this issue.

I would like to point out that, once again, I think you have missed the point.