Middle Way Logic

[SanteriSatama]

Aristotle, Nagarjuna and the Law of Non-Contradiction in Buddhist Philosophy
Peter G Jones

https://philarchive.org/archive/JONANA-6

Short and sweet article about the illogic that metaphysical extremes, such as being vs. non-being, mind vs matter etc. form valid pairs of contradiction.

[Soul_of_Shu]

This is the Peter Jones who has contributed to this forum, and more so in its previous incarnation, albeit very rarely ever since this thread from 2017, wherein he and Scott (aka jse...@gmail.com), and others, could not come to terms on Nagarjuna, mumorphism, The Heart Sutra, Rupert Spira, or much else, resulting in PJ deciding to leave the forum. I wonder if it might now be anymore resolvable since then?

[Ben Iscatus]

Peter Jones is a great thinker and apparently a keen supporter of Aristotle's logic. But I wonder what he thinks of the intuitionist logic idea that the truth of any proposition must be proved by direct evidence.

[Soul_of_Shu]

I suppose I must step in here and point out that since this topic is in the 'FPD' section, it should remain focused on a discussion pertaining to the linked article—although mea culpa for posting another link diverting to that old thread that is not strictly about what the article is about.

So to get back on topic, can anyone point out why what PJ is getting at in the article must be deemed incompatible with the idea of mumorphism, since if indeed true words seem paradoxical, and when he states in conclusion that "They may seem less so if we take note of Aristotle’s rule for contradictory pairs and allow ourselves to abandon the absurd extremes for an exploration of the mean", then the idea of mumorphism seems to fit the bill.

[SanteriSatama]

Peter Jones is a great thinker and apparently a keen supporter of Aristotle's logic. But I wonder what he thinks of the intuitionist logic idea that the truth of any proposition must be proved by direct evidence.

Intuitionist logic does not allow applying LEM to infinities parts of which can't be named, ie. are not propositions. To state not-P, you need to be able to state P in the first place. And for infinites beyond finite constructibility, P can't be stated for all infinite members of a infinite set.

This seems closely with metaphysical infinite polarities that make claims about "all" without ability to state each and every particular, and hence can't form valid contradictory pairs.

[Eugene I]

Regarding non-Aristotelian logic, I already posted some useful links in another thread:
Non-classical logic
non-Aristotelian logic
I think most mathematicians and logicians have already accepted the fact that the Aristotelian logic is not the only one possible, and there is no reason to assume that the reality has to obey particularly and only the Aristotelian logic among other alternative ones, or obey any logic at all for that matter.

[ScottRoberts]

Aristotle, Nagarjuna and the Law of Non-Contradiction in Buddhist Philosophy
Peter G Jones

https://philarchive.org/archive/JONANA-6

Short and sweet article about the illogic that metaphysical extremes, such as being vs. non-being, mind vs matter etc. form valid pairs of contradiction.

While I am in agreement with Peter's main claim in this essay -- that Buddhism contains no contradictions, that is, is fully compatible with Aristotelian logic, I do have two big differences with him.

The first is that he includes as a pair of extremes to be shunned: idealism and materialism. Extremes should be shunned because affirming either of them leads to absurdity. But I see no absurdity in claiming that idealism is true and materialism false. The same goes for will/determinism. I see no absurdity in claiming that all that happens is willed to happen.

The second is his saying "From a logical perspective [Nagarjuna’s] famous proof states no more than that all positive or extreme metaphysical positions are logically absurd." I argued that mumorphism is a positive metaphysical position that is immune from Nagarjuna's arguments (since it incorporates them in its derivation -- see my Tetralemmic Polarity essay). I requested that he show how Nagarjuna's proof shows the absurdity of mumorphism, but he never did.

[AshvinP]

This is the Peter Jones who has contributed to this forum, and more so in its previous incarnation, albeit very rarely ever since this thread from 2017, wherein he and Scott (aka jse...@gmail.com), and others, could not come to terms on Nagarjuna, mumorphism, The Heart Sutra, Rupert Spira, or much else, resulting in PJ deciding to leave the forum. I wonder if it might now be anymore resolvable since then?

From Peter's paper, Samuel Butler says:

Life, they urge, would be intolerable if men were to be guided in all they did by reason and reason only. Reason betrays men into the drawing of hard and fast lines, and to the defining by language -- language being like the sun, which rears and then scorches. Extremes are alone logical, but they are always absurd; the mean is illogical, but an illogical mean is better than the sheer absurdity of an extreme.

- Samuel Butler, Erewhon

I am not sure of Butler's position without more context, but there is a very similar (and longer) passage in Dostoevsky via his "Underground Man", and Dostoevsky was famously critical of Utopian fantasies.

Now I ask you: what can be expected of man since he is a being endowed with strange qualities? Shower upon him every earthly blessing, drown him in a sea of happiness, so that nothing but bubbles of bliss can be seen on the surface; give him economic prosperity, such that he should have nothing else to do but sleep, eat cakes and busy himself with the continuation of his species, and even then out of sheer ingratitude, sheer spite, man would play you some nasty trick. He would even risk his cakes and would deliberately desire the most fatal rubbish, the most uneconomical absurdity simply to introduce into all this positive good sense his fatal fantastic element. It is just his fantastic dreams, his vulgar folly that he will desire to retain, simply in order to prove to himself--as though that were so necessary--that men still are men and not the keys of a piano, which the laws of nature threaten to control so completely that soon one will be able to desire nothing but by the calendar.

And that is not all: even if man really were nothing but a piano-key, even if this were proved to him by natural science and mathematics, even then he would not become reasonable, but would purposely do something perverse out of simple ingratitude, simply to gain his point. And if he does not find means he will contrive destruction and chaos, will contrive sufferings of all sorts, only to gain his point! He will launch a curse upon the world, and as only man can curse (it is his privilege, the primary distinction between him and other animals), may be by his curse alone he will attain his object--that is, convince himself that he is a man and not a piano-key! If you say that all this, too, can be calculated and tabulated--chaos and darkness and curses, so that the mere possibility of calculating it all beforehand would stop it all, and reason would reassert itself, then man would purposely go mad in order to be rid of reason and gain his point!

I believe in it, I answer for it, for the whole work of man really seems to consist in nothing but proving to himself every minute that he is a man and not a piano-key! It may be at the cost of his skin, it may be by cannibalism! And this being so, can one help being tempted to rejoice that it has not yet come off, and that desire still depends on something we don't know?

- Dostoevsky, Notes from the Underground

These discussions can get tricky, because we are not exactly sure how "reason" is being used. I think it is safe to say, however, that it is being used more in the sense of "intellect" and "rationality" rather than pre-modern Scholastic sense of faculty of mind which can nearly reach the Divine. Even though Peter is trying to show how Nagarjuna analysis of Buddhism does not go against Aristotelian logic, it is being done in modern intellectual terms. That is the sort of "reason" Butler and Dostoevsky are critiquing, it seems to me. The modern, mechanical rational intellect, i.e. man as a "piano-key". And it is precisely the intellect's inability to recognize faculties of cognition beyond itself which leads to logical contradictions within spiritual traditions. Ancient thinkers such as Nagarjuna can hardly be blamed for that, because such faculties of cognition could not be consciously adopted or, relatedly, put into any coherent set of words in a systematic philosophy, but modern intellect no longer has that excuse. We have examples of people who put such things into words in a systematic way, i.e. Coleridge and Steiner. Also Jung to a somewhat lesser yet still remarkable extent.

Dana, you said before that these philosophical debates can get repetitive after many years of discussing it and that is exactly why it must remain repetitive - it thinks of man, and the entire world man perceives, as a piano-key. It is forever surprised when man acts, speaks, or thinks in ways that are unlike a piano-key; in ways which reveal there still much more unknown about man's true nature - the source of all his desires, motivations, feelings, and thoughts - than known within philosophy and science. The intellect then takes this unknown and tries to solve it by way of more piano-keys. We now have the language to express why that is and where we may start looking to get beyond mere intellect and rationality, but in the meantime we have lost the motivation and sense of responsibility needed to get underway. It's quite the predicament modern man finds himself in. Yet it is not nearly as bad as it would be if man was actually a piano-key, by way of matter or ideals. It is still infinitely more optimistic to know that our desires depend on something we don't yet know, but that we are entirely capable of knowing.

[Eugene I]

Short and sweet article about the illogic that metaphysical extremes, such as being vs. non-being, mind vs matter etc. form valid pairs of contradiction.

I wonder, at the very moment of making such statement, if Peter was at the same time aware and non-aware of making this statement

[SanteriSatama]

While I am in agreement with Peter's main claim in this essay -- that Buddhism contains no contradictions, that is, is fully compatible with Aristotelian logic, I do have two big differences with him.

The first is that he includes as a pair of extremes to be shunned: idealism and materialism. Extremes should be shunned because affirming either of them leads to absurdity. But I see no absurdity in claiming that idealism is true and materialism false. The same goes for will/determinism. I see no absurdity in claiming that all that happens is willed to happen.

The second is his saying "From a logical perspective [Nagarjuna’s] famous proof states no more than that all positive or extreme metaphysical positions are logically absurd." I argued that mumorphism is a positive metaphysical position that is immune from Nagarjuna's arguments (since it incorporates them in its derivation -- see my Tetralemmic Polarity essay). I requested that he show how Nagarjuna's proof shows the absurdity of mumorphism, but he never did.

Scott,

Is your position that idealism/materialism and will/determinism are Aristotelean genuine contradiction pairs, with no other possibilities? And that idealism and will are purely logical conclusions with 100% certainty, in the context of Classical logic?

Or are you making a scientific plausibility argument?