Indian Logic Forum

Avi Sion · Posted: Tue Nov 08, 2005 6:53 pm Post subject: Arranging VV

Wow! Thank you very much Androsov.
That should be very helpful.

Avi Sion · Posted: Mon Nov 14, 2005 10:56 am Post subject: Verse 29 - the clincher

Just for the record, I would like to add here my latest comments on verse 29, which have been added to Ruminations chapter 5 in my website and will appear in the next hardcopy edition:

Mary

Dear friends - I have been looking at Prof. Androsov's suggestion for matching opposing postiions with Nagarjuna's responses, particularly in reference to v. 29, which Androsov matches with v.4.

Thus we have (not reduced, per Streng):

If [your statement] were that: "This is a denial of a denial," that is not true;
Thus your thesis, as to a defining mark (laksanata) - not mine - is in error.

If I would make any proposition whatever, then by that I would have a logical error;
But I do not make a proposition; therefore I am not in error.

OR:

OPPONENT: Your proposition is that my (previous) conclusion is a denial of a denial, but it is not. Since your proposition is false, you do not establish a defining mark and are therefore in error.

NAGARJUNA: If had any proposition, then by that I would have a logical error; But I do not make a proposition; therefore I am not in error.

I am combining this with Avi's observation that 'enlightenment' is relevant to interpretation. In thinking about this, it seems that Nagarjuna's own enlightenment is less important than Nagarjuna's faith that Buddha attained enlightenment.

Others here may be familiar with the work of R.D. Gunaratne (Department of Philosophy and Psychology at the University of Peradeniya, Sri Lanka). I was not. I have just found two papers (dated 1980 and 1986 respectively) that address Buddha's use of catuskoti and Nagarjuna's later use of catuskoti.* For Gunaratne, this issue seems critical to interpretation of Nagarjuna, as well (1986: pp. 230-1):

Avi Sion · Posted: Tue Nov 22, 2005 11:21 am Post subject: VV 29-30

Hello, Mary:

Thanks for this. I get the gist of it. But could you translate for me (and others) the foreign terms into English, please?

What is: catuskoti, Kaarikaa, paramaartha, sa.mv.rti, etc.? (I have not yet followed the link you give, however.)

Plamen:

Concerning your last post here, again:

Mary · Posted: Wed Nov 23, 2005 12:36 am Post subject: Best attempt at translation

Avi, et al.

I am not an expert in this area by any means! But, I will give my best attempt at translation. Catuskoti is a negative tetralemma, of sorts. First attributed to Buddha in some of the transcribed discourses. Actually, to explain catuskoti, I will qoute Plamen from another forum:

"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..."

"Kaarikaa" is a collection of verses - like a 'volumn'. Plamen or someone else may give you the literal translation, that is how I understand it. The same with the other terms. "Paramaartha" is the ordinary, everyday view of the world. "Samvrti" would be the view from 'internal empirical' observation, e.g. in meditative contemplation.

Hope this helps. Anyone better versed in Sanskrit, please correct me.

Regards, M.Lee

Mary · Posted: Wed Nov 23, 2005 12:37 am Post subject: Best attempt at translation

Avi, et al.

I am not an expert in this area by any means! But, I will give my best attempt at translation. Catuskoti is a negative tetralemma, of sorts. First attributed to Buddha in some of the transcribed discourses. Actually, to explain catuskoti, I will qoute Plamen from another forum:

"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..."

"Kaarikaa" is a collection of verses - like a 'volumn'. Plamen or someone else may give you the literal translation, that is how I understand it. The same with the other terms. "Paramaartha" is the ordinary, everyday view of the world. "Samvrti" would be the view from 'internal empirical' observation, e.g. in meditative contemplation.

Hope this helps. Anyone better versed in Sanskrit, please correct me.

Regards, M.Lee

Avi Sion · Posted: Thu Nov 24, 2005 1:15 pm Post subject: catuskoti

Mary: - thank you for these translations. Looking at the Buddhist вЂњcatuskotiвЂќ as a logician, I have the following two comments:

a) The first sentence is not symmetrical with the next three. It should read: вЂњIt is not true that there exists an X such that characteristic y applies but z does not applyвЂќ вЂ“ for without this added clause, sentence (1) would include (3), so that the latter would be redundant.
b) Granting this modification, we have four premises вЂ“ but so far no conclusion. However, these four sentences do not constitute an illogical combination вЂ“ they are logically compatible. For they do formally allow for a conclusion, namely that вЂњX does not existвЂќ.

What this conclusion means is that these four sentences taken together are not really comparable to the вЂњtetralemmaвЂќ вЂ“ which is an inextricable self-contradiction (as in double paradox). They allow for a consistent way out (as in single paradox). These four alternatives simply form a normal вЂњfour-horned dilemmaвЂќ, whose conclusion is the denial of their antecedent (i.e. of вЂњX existsвЂќ).

Mary · Posted: Thu Nov 24, 2005 11:13 pm Post subject: Lemma?

Avi,

It would seem that your post supports Plamen's (qouted) position that " the Negative Buddhist Tetralemma [is] not lemma because it does not follow from any theorem."

Question: What if the theorem is already proposed by one's 'opponent' in a debate setting?

This would make the 'catuskoti' a misnomer, would it not? If the 'theorem' is 'assumed' as stated by a debate opponent, then would the form not be a five-fold logic rather than four-fold?

A quote from Gunaratne's 1980 artcile, cited above: " The catu.sko.ti is not a 'Buddhist logic'; Buddhists are only its critics, and they reject it. It ... makes use of the fact that four positions are possible in regard to any statement."

Just a passing thought. Apologies if this is not clear.

Regards, M.Lee

Avi Sion · Posted: Tue Nov 29, 2005 12:54 pm Post subject: catuskoti

Mary: the argument you have described to me is fully valid deduction, as I said. Here it is more clearly. It is a вЂ?simple destructive dilemmaвЂ™, or (by merging) an apodosis, as follows:

Major premise:

If X, then either вЂ?Y and ZвЂ™ or вЂ?Y and notZвЂ™ or вЂ?notY and ZвЂ™ or вЂ?notY and notZвЂ™

Minor premise:

But neither вЂ?Y and ZвЂ™ nor вЂ?Y and notZвЂ™ nor вЂ?notY and ZвЂ™ nor вЂ?notY and notZвЂ™

Conclusion:

Therefore, notX.

The major premise is a universal truth, given by the laws of thought, for any values of X, Y, Z. Why? Because (by matricial analysis):

For any value of X, only two mutually exclusive outcomes are consistent:
X, or notX.

For any value of X, Y, only four such alternatives are possible, viz.
X and Y, or X and not Y, or notX and Y, or notX and notY.

For any value of X, Y, Z, only eight such alternatives are possible:
X + Y + Z
X + Y + notZ
X + notY + Z
X + notY + notZ
notX + Y + Z
notX + Y + notZ
notX + notY + Z
notX + notY + notZ

and so forth (for more than three terms).

As can be seen in this list, granting X, there are only four combinations of Y and Z and their negations logically possible. If none of these combinations occur, then it must be one of the other four combinations that is true. The latter four all imply вЂ?notXвЂ™ true. So, that is our minimal and necessary conclusion.

The minor premise (the catuskoti) is supposedly given in a particular case of X, Y, Z. It is not a universal truth, but together with the universal major premise, it gives an undeniable formal conclusion, viz. the negation X. I donвЂ™t care what the Buddhists say pro or con.

The tetralemma, by the way, is a claim that, for any two terms X, Y, the four alternatives
вЂњX and Y, X and not Y, notX and Y, notX and notYвЂќ
are NOT mutually exclusive or exhaustive, contrary to the laws of thought.

I therefore well believe Gunaratne's statement that the catuskoti may not be Buddhist logic, if by the latter term we consider the logic of Nagarjuna. For I daresay he would not be loathe to claim that X might well exist even though it is neither вЂ?Y and ZвЂ™ nor вЂ?Y and notZвЂ™ nor вЂ?notY and ZвЂ™ nor вЂ?notY and notZвЂ™, or some such contradiction.

Avi Sion · Posted: Fri Dec 02, 2005 9:45 am Post subject: catuskoti

Mary: my apologies! Upon awakening this morning, I realized that I had made an error in my last post to you, concerning the formal representation of the Buddhist вЂњcatuskotiвЂќ argument as a sort of modus tollens.

My error consisted in describing the minor premise of the argument as вЂњNeither (Y + Z) nor (Y + notZ) nor (notY + Z) nor (notY + notZ)вЂќ. This is of course an absurdity, since such an unconditional disjunctive proposition would by an antinomy, i.e. disobey the law of the excluded middle, which requires that one of these four alternatives be true! Clearly, implicit in the argumentвЂ™s minor premise is that the condition вЂњgranting XвЂќ, which is specified in the major premise. However, we cannot give the argument as a whole a standardized format, using this kind of condition. We have to completely review our interpretation of it.

So here is my revised explication of the catuskoti argument, for the record.

For any value of three items X, Y, Z, eight (i.e. 2x2x2) alternatives are logically possible, viz:
X + Y + Z
X + Y + notZ
X + notY + Z
X + notY + notZ
notX + Y + Z
notX + Y + notZ
notX + notY + Z
notX + notY + notZ
According to the law of non-contradiction, these combinations are mutually exclusive, because if you take any two (or more) of them together, you are bound to have a contradiction (or more than one). For example, taking the first two alternatives together, the conflict is between Z and notZ.
Also, according to the law of the excluded middle, these combinations are exhaustive, i.e. they cannot be all together denied in any given case. For in such case, we would find ourselves with neither X nor notX, neither Y nor notY, and neither Z nor notZ вЂ“ three breaches of the said law.

Thus, we can say, universally, i.e. for any values of X, Y, Z whatsoever, one and only one of these eight alternatives must be true, i.e. applicable to the case at hand. This disjunctive proposition with eight disjuncts is our argumentвЂ™s major premise, formally given by the laws of thought, independently of what specific content we apply to the items X, Y, Z.

The correct minor premise is a conjunction of the negations of the four first alternatives in a specific case. This is identical to the four вЂњcatuskotiвЂќ premises you gave me, quoting Plamen, modified slightly as earlier discussed.

The preliminary conclusion from these two premises is simply the disjunction of the remaining four alternatives, in the case concerned. That is, it is a statement that one and only one of these leftover alternatives must be true.

Now, using this preliminary conclusion as our major premise, we can infer the following from it. Since:
(notX + Y + Z) implies notX вЂ“ and
(notX + Y + notZ) implies notX вЂ“ and
(notX + notY + Z) implies notX вЂ“ and
(notX + notY + notZ) implies notX вЂ“
it follows that вЂњnotXвЂќ will be true whatever the outcome вЂ“ i.e. we can conclude вЂњnotXвЂќ already now, even before we know which of these four alternatives will turn out to be true. This is an ordinary dilemmatic argument (simple constructive). It says:
Whichever of the remaining four alternatives is true, X will be false;
but one of the four has to be true;
therefore, X must be false.
This (as earlier stated) is our final conclusion вЂ“ i.e. the valid formal conclusion possible from the given four вЂњcatuskotiвЂќ premises.

Note again, that when anti-logical Buddhists (like Nagarjuna, I presume) reject this argument, they do so because they refuse to admit the laws of thought. As far as they are concerned, the initial eight alternatives are not mutually exclusive and not exhaustive вЂ“ i.e. any two or more alternatives may be mixed together or all alternatives may be denied simultaneously, and too bad for contradictions or in-betweens that are bound to result. But of course, such a nihilist discourse is not an вЂњalternative logicвЂќ; although it can be said by stringing words together like this, is meaningless and worthless.