Buddhist Logic

[Thomas Knierim]

The concept of truth has great significance not only to philosophy and mathematics, but to human existence in general. While the average person may be content with the everyday notion of truth as something factual, or something in accordance with common experience and reason, philosophers and mathematicians tackle the concept of truth more systematically.

We generally think of a truth as bivalent, which means that an assertion or a truth variable can take on only two possible values, “true” or “false”. The bivalent notion of truth goes back to antiquity, more precisely to the Greeks, who investigated the relations of propositions in view of their form rather than their content. Aristoteles was the first Western philosopher who laid out a formal method of logical analysis. According to Aristotle, we can make valid (=true) conclusions by applying deductive reasoning to statements. Such statements come in the form of syllogisms, which consist of premises and conclusions. An example of a valid syllogism is: “All human beings are mortal ( = premise 1), I am a human being (= premise 2), therefore, I am mortal, ( = conclusion). This form of reasoning presupposes classical bivalent logic.

The principle of bivalence is that for any proposition P, either P is true or P is false. This is closely related to, though distinct from, the law of excluded middle and the law of non-contradiction. The law of excluded middle says that that for any proposition, either it or its contradiction is true; for any proposition P, either P or not P. The law of non-contradiction states that for any proposition P, it is not both the case that P and not-P. The difference between the law of excluded middle and the law of non-contradiction is fairly subtle. This comparison should make the distinction clear:

Law of the excluded middle: P or (not P) is true
Law of non-contradiction: Not (P and (not P)) is true

Obviously, both laws hold for any bivalent truth system. If we remove the law of excluded middle from a formal logical system, the result will be a system called intuitionistic logic. In logical calculus it is allowed to argue P or not P without knowing which one specifically is true, but intuitionistic bivalent logic doesn’t allow that. The introduction of (P or ~P) is considered a logical flaw.

The question that is perhaps of most interest is whether the classical system is adequate for ontological questions. Can a bivalent truth system succeed in describing reality? Its usefulness in mathematics, digital circuits, and ordinary language is certainly undoubted, but can it lighten the path to wisdom? In my opinion, it can’t. Classical logic is too limited. We need something different. Fortunately, we can draw on a choice of existing logical systems, including three-valued logic (true, false, and one indeterminate state), fuzzy logic (probabilistic, i.e. truth values representing the continuum between 0 and 1 expressed by a fraction 1/x), as well as a number of other more exotic systems.

The Buddhist logic is multivalent. If you have read some of the longer sutras, you will probably be familiar with it. Buddhist logic rises above the common bivalent notion by adding two more relations, resulting in a set of four possible relations between two given proposition in the form of “either…or…both…neither”.

In an example from the Aggi-Vacchagotta Sutta (Majjhima Nikaya 72), the wanderer Vacchagotta asks the Buddha whether the cosmos, the soul, and the Buddha are eternal. The Buddha answers:

“Even so, Vaccha, any physical form by which one describing the Tathagata would describe him: That the Tathagata has abandoned, its root destroyed, like an uprooted palm tree, deprived of the conditions of existence, not destined for future arising. Freed from the classification of form, Vaccha, the Tathagata is deep, boundless, hard-to-fathom, like the sea. Reappears doesn't apply. Does not reappear doesn't apply. Both does & does not reappear doesn't apply. Neither reappears nor does not reappear doesn't apply.”

Similar arguments appear throughout the Pali canon. We can formalize this easily. Let’s assume that X is a truth placeholder and that P and Q are contradictive propositions with Q = not P and P = not Q. Buddhist logic allows four possible equivalences:

(a1) X = P
(a2) X = Q
(a3) X = P and Q
(a4) X = neither P nor Q,

or respectively their negation, as phrased in the argument with Vacchagotta:

(b1) X = not (P)
(b2) X = not (Q)
(b3) X = not (P and Q)
(b4) X = not (neither P nor Q),

By replacing Q with Not (P) in (a1-4), we get:

(c1) X = P
(c2) X = ~P
(c3) X = P & ~P
(c4) X = ~P & ~(~P)

According to the existing rules of inference (double negation, commutative and associative laws), (c4) can be reduced to (c3). However, it is obvious that (c3) contradicts conventional logic, because it states the opposite of the law of non-contradiction. In other words, contradictions are allowed. We must realize that this defines a whole new system of logic with three elements {P, ~P, P & ~P}. It is obvious that the rules of inference need to be modified in order to accommodate for P & ~P.

The development of paraconsistent logic was initiated in order to challenge the logical principle that anything follows from contradictory premises, ex contradictione quodlibet (ECQ). Let => be a relation of logical consequence, defined either semantically or proof-theoretically. Let us say that => is explosive if for every formula A and B, {A , ~A} => B. Classical logic, intuitionistic logic, and most other standard logics are explosive. A logic is said to be paraconsistent if its relation of logical consequence is not explosive.

Vacchagotta: “How is it, Master Gotama, when Master Gotama is asked if he holds the view the cosmos is eternal... after death a Tathagata neither exists nor does not exist: only this is true, anything otherwise is worthless, he says ...no... in each case. Seeing what drawback, then, is Master Gotama thus entirely dissociated from each of these ten positions?”

Buddha: “Vaccha, the position that the cosmos is eternal is a thicket of views, a wilderness of views, a contortion of views, a writhing of views, a fetter of views. It is accompanied by suffering, distress, despair, & fever, and it does not lead to disenchantment, dispassion, cessation; to calm, direct knowledge, full Awakening, Unbinding.”

Cheers, Thomas

[sylph]

Hmm, Thomas, I'm still not convinced regarding the usefulness of multivalent logic...

Simply: If X = P and X = ~P, then ~X.

(P & ~P) can be expressed in modern logic; however, it evaluates to FALSE.

I can see that some expressions of thought are outside (bivalent) logic, but I don't think it's useful to translate them into symbolic logic. As well, I have heard of fuzzy logic, but it seems that fuzzy logic is only applicable to certain domains.

The four equivalences of 'Buddhist logic' seem superfluous. I still think those 4 equivalences can be expressed by bivalent logic, as long as we have AND, OR, and NOT operators.

[Thomas Knierim]

Sylph,

I should perhaps mention that the four basic propositions (a1) to (a4) -sometimes called tetralemma- are not really a unique feature of Budhist philosophy. They appear in ancient Indian philosophy and it may be supposed that they have been taught to the Buddha by his early teachers. You are right in saying that the tetralemma may be stated in terms of propositional logic. That is what I did in the previous post. It is important to keep in mind that P and Q are antithetic, i.e. P = ~Q. It follows that only the first two propositions (X=Q or X=P) concur with Aristotelian logic, wheras the latter two (X=P & X=Q), (X=~P & X=~Q) are contradictory in bivalent logic.

I suggested that by replacing Q with ~P and applying the rules of inference of classical logic, it is possible to reduce the tetralemma to three statements, although I must confess that I doubt whether the replacement of the variable is a permissible operation, since we are dealing with a paraconsistent logic.

Sylph: Hmm, Thomas, I'm still not convinced regarding the usefulness of multivalent logic...

You are certainly not alone. Most people don't see too many real-life applications for multivalent logic, since day-to-day problems can usually be be solved with conventional logic. Multivalent logic, however, has quite a number of applications in science and engineering. For example, computer scientists should be familiar with fuzzy logic, linear logic, Belnap's 4-valued system, and Gödel's logic. But let's distinguish between multivalent and paraconsistent. I think the important property of Buddhist logic is paraconsistency, not multivalence. Paraconsistent logics are a fairly new topic in mathematics. The systematic investigation of paraconsistent systems has only begun recently in the 20th century, so it can be expected that there are not too many applications yet, since research is still in its infancy. Perhaps one day we will have machines that do not only distinguish between 0 and 1, but that will be capable of internal states that are neither 0 nor 1, or both 0 and 1.

Cheers, Thomas

[rich]

Thomas,

Quite accidentally and coincidently, in the Religion Forum under topic of Mia Culpa on Thebigview , I posted something similar to what you are saying.
At least similar, by offering four options. Here is what I posted:

Also, when two opposing mindsets/set minds oppose one another,
a neutral observer has a minimum of 4 choices.
1. Agree with mindset [A].
2. Agree with mindset [B].
3.Come up with their own[C].
4.If none of the above, resort to [D] or & :lol:

--------------------
Rich

[dog goddess]

why do you want everything to be mechanical thomas?

perhaps one day we will have all these great machines and computers that you want. maybe then you'll be able to figure out what ever it is you want to know.


in the mean time i'll be satisfied to sit on the beach and watch the sunset and be glad that i have the ability to figure out for myself just how beautiful it is.

and be glad i can be content with the grains of sand running through my fingers.

ah, how nice it is to be simple.

you search too hard thomas.
it really isn't all so difficult as you make it.

[Thomas Knierim]

Richie:
1. Agree with mindset [A].
2. Agree with mindset [B].
3.Come up with their own[C].

Yes, Richie, I can see the similarity. The first three lines roughly coincide with the Buddhist tetralemma. If mindset A and B are antithetic then the solution of the conflict is provided by C, a higher-order mindset or idea. The German philosopher Friedrich Hegel formulated the very same thing at the beginning of the 19th century:

"Hegel accomplished what Kant had declared impossible. According to Hegel, mind is capable of arriving at full knowledge about things in themselves. He formulated a dialectical method, according to which knowledge pushes forwards to greater certainty, and ultimately towards knowledge of the noumenal world. He said that ultimate reality is absolute mind, reason, or spirit, which manifests itself in history and in the universe. Hegel set forth the proposition, "what is real is rational and what is rational is real," and from this he concluded that everything that is, is knowable. The world mind (Weltgeist) is universal; the rational activities of individuals are therefore instances of the Absolute. The self-development of mind is the result of evolving idea systems, a process that he called the dialectical processes of thesis and antithesis. According to Hegel, an idea, a thesis, always contains incompleteness, and thus, yields a conflicting idea, an antithesis. In a higher-level theory, a third point of view, the synthesis, arises that provides the solution. The synthesis overcomes the conflict between thesis and antithesis by reconciling the truth contained in both at a higher level of insight. The synthesis then becomes a new thesis that is subsequently confronted by another antithesis, and so forth. By this dialectical method, the collective mind, namely that of a group, society, nation and ultimately the world, advances towards the perfection of its knowledge." (thebigview.com)

So, it seems that the third proposition of the Buddhist tetralemma (a3) X = P and Q is indeed the Hegelian synthesis. What is the fourth proposition?

dog goddess: why do you want everything to be mechanical thomas?

Funny, I don't recall myself uttering preference for a mechanical world. - Must have been the language I used. - I work in information technology, so I have an interest in mathematics, but I prefer my environment jungly, just like here in Thailand. About being content with the grains of sand running through my fingers... you may get bored with this, believe me.

Cheers, Thomas

[rich]

Thomas posted:
So, it seems that the third proposition of the Buddhist tetralemma (a3) X = P and Q is indeed the Hegelian synthesis. What is the fourth proposition? :rolleyes:





Thomas, I thought you would have surmised my silliness in what I posted. Was trying to be funny, by expressing proposition D; I intentionally enclosed the D in these brackets, [ D ], translating into this, :D .

Oh oh, What I meant to do, was precede each proposition by a colon, then, it should have read,
:A : B :C : D (note, I have to cheat a bit, with the : B & : D, or they would have translated into,
:B & :D). Of course, the following substitutions could be used for prop D, i.e.; :wacko: :angry: ,
contingent on your frame of mind. Perhaps, now there are too many options/propositions.

However,[ B ] =bold, and tab must be closed.

Best Wishes,

[dog goddess]

my misunderstanding thomas.



i agree with the jungle preference.
there's nothing like being a wild woodlands creature.

[sylph]

Sorry, Thomas. I put 'Buddhist logic' in quotes only because I assumed that type of logic was not unique to Buddhism and I didn't know what else to refer to it by. I wasn't trying to sound sarcastic.

Hmm, I guess multivalence and paraconsistency would open up new doors in terms of technology... Neural networks use fuzzy logic, right? I'm actually amazed at what is accomplished by only zeroes and ones. This beautiful website, these smilies :huh: ... how versatile only bivalent logic seems to be.

[Thomas Knierim]

Sylph: Sorry, Thomas. I put 'Buddhist logic' in quotes only because I assumed that type of logic was not unique to Buddhism and I didn't know what else to refer to it by. I wasn't trying to sound sarcastic.

No offence taken, Sylph. I did not even notice. Besides, you may be right. Because the tetralemma predates Buddhism, it should perhaps be called Hindu logic, or Indian logic. However, there is a difference in how it is applied by Hindu philosophers and Buddhist philosophers. The ancient Indian logicians treated each proposition as a valid alternative worthy of consideration, whereas the Buddha uses the tetralemma as a whole to create paraconsistency. You see that in the Vachagotta example the negation of each proposition is used to deny all alternatives. The intention of this argument is to reject all possible views. The psychological method is to frustrate the architect, the thinker, the builder of views, because all views are incomplete, all views contain falsities, and all views divide and create delusion. That is of course... only as long as the holder of the view believes him/herself to be in the sole possession of truth. In other words, the paraconsistent treatment of logic is used by the Buddha to ward off grasping ideas, views, and beliefs. The Buddha encourages the acceptance of antithetic views. He wants us to permit contradictive views, and most importantly he wants us to avoid attachment to these views.

Richie: Thomas, I thought you would have surmised my silliness in what I posted.

I know you were joking, Richie, but your observation was quite to the point. B)

Cheers, Thomas

[sahyo]

not even neither exists nor does not exist ;)

[a random hack]

I can see how this would work on a menu;

Would you prefer chicken?
Would you prefer fish?
Would you prefer chicken and fish?
Would you prefer neither chicken nor fish?

Seems we use this logic without realising, just because we don't consider / enunciate all the options.

[rich]

A Random Hack posted:
I can see how this would work on a menu;

Would you prefer chicken?
Would you prefer fish?
Would you prefer chicken and fish?
Would you prefer neither chicken nor fish?

Seems we use this logic without realising, just because we don't consider / enunciate all the options.

What about the option of leaving, since the menu ignores my preferences ? :unsure:

[a random hack]

RT, that would be option 'd';

Neither chicken nor fish :)

[rich]

Need to see a menu to see if what is being offered is to my liking. Many choices may be offered, but if I do not like any,
will go elsewhere. What other offerings are there? :unsure: :lol:

[a random hack]

RT,

Well, you could 'grow your own'.

[rich]

A fine way to treat a customer. :blink: :wacko:

[a random hack]

And you think I'M a disciple? LOL

[rich]

Random,

My definition of a disciple of Vicente's is a person who will not give credit to an Intelligence as being responsible for the creation of the entire universe, and still does not have an answer.

Even the Dahli Lama speaks and writes about God.

Many on this forum, agree with Vicente's opinion. Those in that camp, I labeled as, disciple's of Vicente.

I think that asheera, fu, ., ... and A Random Hack are his disciples for you agree with him. I'm not angry with any of you for agreeing with V, as i said before, when one looks over the menu, and finds what is offered not pleasing, there is another option to follow. :ph34r: :o

[...]

Check out the difference rich: My definition of a disciple of Vicente's is a person who will not give credit to a separate Intelligence as being responsible for the creation of the entire universe...,

[Polaris]

Even the Dahli Lama speaks and writes about God.


It is my impression that the Dalai Lama is aware that he has in international audience when he speaks publically. He is also aware and he respects that there are many different religions out there which include a God in their worship. I think that when he speaks to the world he tries very hard to speak in terms that will be accepted by the majority of people while still successfully conveying his message. Not that I've read everything or heard everything he has wirtten but from what I have read of his I'd have to say that what he says is extremely generic from a spiritual aspect. He speaks common sense stuff that is easily digested by any religion. That's why he is such a great statesman and respected world leader.
It is not in the Buddhist philosophy to flat out deny the existence of God and certainly not to deny the existence of people who believe in God. I am prefectly fine when I hear the Dalai Lama speak of God because in my personal understanding he is simply trying to relate an idea which is acceptable to everyone regardless of their spiritual beliefs.

Just my opinion, of course. :)

[rich]

Originally posted by ...@Jul 3 2003, 06:05 PM
Check out the difference rich: My definition of a disciple of Vicente's is a person who will not give credit to a separate Intelligence as being responsible for the creation of the entire universe...,
... posted:My definition of a disciple of Vicente's is a person who will not give credit to an Intelligence as being responsible for the creation of the entire universe, and still does not have an answer.


I see the difference, you added the word separate.
Not sure of how the meaning would change by adding the word, separate?

As I see it, all of us have built in to our person, an unobvious linkof awareness to this Intelligence. A disciple of Vicente's
will deny having any awareness, for they would regard this Intelligence as being a myth.

..., are you a dov? :unsure: :)

[...]

Not sure of how the meaning would change by adding the word, separate?

The "Intelligence" is not separate from us.

As I see it, all of us have built in to our person, an unobvious linkof awareness to this Intelligence.

What is unobvious to most is the being of intelligence.

..will deny having any awareness, for they would regard this Intelligence as being a myth.

You haven't been paying attention, have you?

..., are you a dov?

No...

[rich]

..., Guess I was not paying attention too closely, and reading a different meaning into separate, than what you intended. I should correct my own self, before criticizing anyone else, for having fixations. Sorry, :huh:

[a random hack]

rich,
So let me see, if I say I agree with something you say, I'm your disciple, am I?

I can't see how else you possibly can come to the conclusion that I, or anyone else, are disciples of V...
But looking forward to the explanation :)
Personally, I can't see the relevance of who anyone agrees or disagrees with, except in terms of whether I can allow myself to feel OK when people disagree with me, and whether I allow it to go to my ego-complex when they agree.

when one looks over the menu, and finds what is offered not pleasing, there is another option to follow.

So why ask me for more options?

G(n/r)ow your own!!!

[rich]

Random,
I believe I got your message. B)

I'll take your advice. :(

[a random hack]

s'funny, I thought my 'message' might prompt a happy face, it sure does for me :)

[rich]

So Sorry
NO HAPPY FACE PROMPTED

think i will sulk for a while. :( :blink: <_< :unsure: Have to reflect on your what you said.I Should not ever reveal any of my thoughts, for i make myself vulnerable to criticism. I never seem to learn, do I ? That's ok, another day shot.

[...]

I Should not ever reveal any of my thoughts, for i make myself vulnerable to criticism.

An earlier question remained unanswered richie; can you see the motion of perception that brings/is emotion? Above quote is a excellent example of where to look...

[Polaris]

I Should not ever reveal any of my thoughts, for i make myself vulnerable to criticism. I never seem to learn, do I ?
Hey Rich :) There's nothing wrong with criticism. We can all learn a lot about ourselves through criticism. It's a potential catalyst for change and that can be a really good thing if you want it to be :)

[rich]

Polaris,

It is not so much being criticized, that I mind, but it is me writing/saying certain things which are stupid, and then seeing the idiot within me, for writing/saying. :angry:

Really, not mad at anyone but me. I am myself's own and worst enemy. Will probably kick my self later for posting this.

Thanks anyway. :)

[Polaris]

:D Rich, that's called 'The 20/20 Hindsight Syndrome' which laymen such as myself refer as

D'OH!!

http://frames.free.fr/Images/homer.jpg

:lol: :D :)

[rich]

Thank's Polaris B) =20/20 hindsight. Did you see his beer belly?
How did you know that I resemble tht guy? :unsure: well, at the waist anyway. :lol: ;)

[a random hack]

It is not so much being criticized, that I mind, but it is me writing/saying certain things which are stupid, and then seeing the idiot within me, for writing/saying.

RT,
I assume that when you say these certain things they don't appear stupid, but then later on they do.
How do you KNOW which attitude is the correct one (assuming that either one is correct)?

[rich]

A Random Hack posted:

RT,
I assume that when you say these certain things they don't appear stupid, but then later on they do.
How do you KNOW which attitude is the correct one (assuming that either one is correct)?


RH,
True, while saying and not thinking before you speak/write, or just rambling on, may appear stupid later on, after reflecting.

KNOWING which attitude or opinion is correct, is contingent on what you the person believes is the correct answer. If the person you are answering thinks or believes differenly than you, then who is to say,
who is correct? Each has to do, what appears correct for you :) .

[...]

..wooshhh...

[Polaris]

Originally posted by ...@Jul 7 2003, 03:38 PM
..wooshhh...
;)
....the sound of cars on the freeway?
....the sound of a hawk swooping in on a field mouse?
....the sound of waves breaking on a sandy beach?
....the sound of one hand clapping?
....the sound of air moving through an empty void such as a cavern, cave or cranium?
....the sound of something going right over your head?
;)

[rich]

Elbow of right hand bent and resting on a table, withi ndex finger touching and pointing on the right temple of head, asking self the abbreviation of mountain, sounds pouring out of mouth saying, mt, mt.

:wacko:

[...]

..exactly...

[rich]

a random thought: ( hack, stealing part of your name) to post this quip:


An archeologist after close examination of some bones

he dug up, cried out, "I'm enlightened, It's me, it's me!"

[Owen]

Thomas :

The Buddhist logic is multivalent. If you have read some of the longer sutras, you will probably be familiar with it. Buddhist logic rises above the common bivalent notion by adding two more relations, resulting in a set of four possible relations between two given proposition in the form of “either…or…both…neither”.

In an example from the Aggi-Vacchagotta Sutta (Majjhima Nikaya 72), the wanderer Vacchagotta asks the Buddha whether the cosmos, the soul, and the Buddha are eternal. The Buddha answers:

“Even so, Vaccha, any physical form by which one describing the Tathagata would describe him: That the Tathagata has abandoned, its root destroyed, like an uprooted palm tree, deprived of the conditions of existence, not destined for future arising. Freed from the classification of form, Vaccha, the Tathagata is deep, boundless, hard-to-fathom, like the sea. Reappears doesn't apply. Does not reappear doesn't apply. Both does & does not reappear doesn't apply. Neither reappears nor does not reappear doesn't apply.”

Similar arguments appear throughout the Pali canon. We can formalize this easily. Let’s assume that X is a truth placeholder and that P and Q are contradictive propositions with Q = not P and P = not Q. Buddhist logic allows four possible equivalences:

(a1) X = P
(a2) X = Q
(a3) X = P and Q
(a4) X = neither P nor Q,
--------------------------------


Yes, we can do this by establishing 't' as a truth value representing factual truth and 'f' represents '~t' that is, factual falsity.

(a1) X = t (factual truth)
(a2) X = f (factual falsity)
(a3) X = F (logical falsity) (contradiction)
(a4) X= T (logical truth) (tautology)

We can define each of these truths in terms of "t" alone, if we are also given the nand or the nor operator "|".

D1. ~t defined t|t, (not t) = (t nor t)
D2. f defined ~t, f = (not t)
D3. F defined t|f, F = (t nor f)
D4. T defined ~F T = ~(t nor f)

Factual falsity is not the same as contradiction.
For example: If my car is blue, then to say, My car is black .. is factually false.
But, My car is blue and My car is not blue, is logically false.
Also, My car is blue and My car is black .. is contradictory.
Tautology and contradiction are not factually (physically) determined.
There are no factual tautologies and there are no tautologous facts.

This multivalued logic includes all of the theorems of classical propositional logic and standard (S5) modal logic and intuitionist propositional logic.

Owen

[Thomas Knierim]

Owen: This multivalued logic includes all of the theorems of classical propositional logic and standard (S5) modal logic and intuitionist propositional logic.

Welcome to thebigview.com, Owen!

Okay, that is interesting. Given this logic, what is the truth value of for example (t & F) or (f -> F)? What does the truth table look like? Reference, or link would be great.

How do you think this relates to the Buddhist tetralemma? :think: Is it possible to evaluate all four equivalencies to 'true'?

Cheers, Thomas

Are you the same Owen who posts on Genius?

[Owen]

Thomas:
Welcome to thebigview.com, Owen!

Thanks and Hello again Thomas!

Thomas:
Okay, that is interesting. Given this logic, what is the truth value of for example (t & F) or (f -> F)? What does the truth table look like? Reference, or link would be great.

Not (~)
~t = f, ~f = t, ~F = T, ~T = F.

And (&)
t & t = t, t & f = F, t & F = F,
f & t = F, f & f = f, f & F = F, f & T = f,
F & t = F, F & f = F, F & F = F, F & T = F,
T & t = t, T & f = f, T & F = F, T & T = T.

Or (v)
t v t = t, t v f = T, t v F = t, t v T = T,
f v t = T, f v f = f, f v F = f, f v T = T,
F v t = t, F v f = f, F v F = F, F v T = T,
T v t = T, T v f = T, T v F = T, T v T = T.

Implies (->)
t -> t = T, t -> f = f, t -> F = f, t -> T = T,
f -> t = t, f -> f = T, f -> F = t, f -> T = T,
F -> t = T, F -> f, = T, F -> F = T, F -> T = T,
T -> t = t, T -> f = f, T -> F = F, T -> T = T.

Equivalence (<->)
t <-> t = T, t <-> f = F, t <-> F = f, t <-> T = t,
f <-> t = T, f <-> f = T, f <-> F = t, f <-> T = f,
F <-> t = f, F <-> t = f, F <-> F = T, F <-> T = F,
T <-> t = t, T <-> f = f, T <-> F = F, T <-> T = T.

Necessity ([])
[]t = F, []f = F, []F = F, []T = T.

Possibility (<>)
<>t = T, <>f = T, <>F = F, <>T = T.

Tautologies (theorems) are those expressions that have T for every logical calculation of its truth values, e.g. p v ~p.

C. I. Lewis, Symbolic Logic (1932), considers 5 different groups which all require that both t and T are designated values.

My method only needs T as the designated value.

See: Contemporary Philosophical Logic (1978), Copi & Gould, pp 241-249.

Due to the isomorphism between modal propositional logic and monadic predicate logic these calculations apply there too.

Note: The above tables apply to any function of one predicate variable or one propositional variable. To apply the method to two or more variables, an extension of the basic four values is required.
16 values are needed for two predicate variables.
64 values are needed for three predicate values etc..

Computers make the calculations easy.

Thomas: How do you think this relates to the Buddhist tetralemma?

I am not familiar with this concept.

Thomas: Is it possible to evaluate all four equivalencies to 'true'?

I don't think so, e.g. F (contradiction) cannot be thought as 'true'.
Logic abhors contradictions ...Russell.

Thomas: Are you the same Owen who posts on Genius?

Yes.

Regards,

Owen

[Thomas Knierim]

Thomas: How do you think this relates to the Buddhist tetralemma?
Owen: I am not familiar with this concept.

Okay, it's basically the four statements contained in the above article. P and Q are supposed to be antithetic. IMO there is no logic inwhich X is always true.

(a1) X = P
(a2) X = Q
(a3) X = P and Q
(a4) X = neither P nor Q

Thomas: Is it possible to evaluate all four equivalencies to 'true'?
I don't think so, e.g. F (contradiction) cannot be thought as 'true'.
Logic abhors contradictions ...Russell.

So it seems. What's your take on paraconsistent logic then?

Thanks for posting the truth tables. I shall play around with them and see what new insights come from that... B)

Thomas

[Owen]

Thomas: Is it possible to evaluate all four equivalencies to 'true'?
I don't think so, e.g. F (contradiction) cannot be thought as 'true'.
Logic abhors contradictions ...Russell.

Thomas: So it seems. What's your take on paraconsistent logic then?

I have not read anything about it yet.
From what you have said, it seems very suspicious.

Thomas: Thanks for posting the truth tables. I shall play around with them and see what new insights come from that...

You are most welcome.
Note that there are many non-classical truth functional operators that are available in this system.
For example: physical necessity and physical possibility, synthetic and analytic, etc..

Owen

[Thomas Knierim]

Owen: Note that there are many non-classical truth functional operators that are available in this system.

Yes, that is fascinating.

Owen: For example: physical necessity and physical possibility, synthetic and analytic, etc..

I suppose the distinction between synthetic and analytic arises from the difference between factual and logical truth. Is that so? - Old Immanuel probably protest (but he doesn't have a vote, anyway :devilish:). The analytical part is isomorph to Boolean logic, I guess!?

Thomas

[Owen]

Owen: Note that there are many non-classical truth functional operators that are available in this system.

Thomas: Yes, that is fascinating.

I agree. Even the classical operators such as (not, and, or, implies, equivalence) have more than one interpretation.

The theorems of classical logic are duplicated by limiting our calculations to T and F only.
And, the same theorems result when we include all four values, and much much more.

When we deal with modal propositions or monadic predicate logic expressions we need to expand the number of truth values.

Within the contex of 'truth functions', the four values work for any number of propositional variables.

Owen: For example: physical necessity and physical possibility, synthetic and analytic, etc..

Thomas: I suppose the distinction between synthetic and analytic arises from the difference between factual and logical truth. Is that so?

Yes, an analytic proposition is either tautologous (T) or it is contradictory (F), and a synthetic proposition is either factually true (t) or it is factually false (f).

- Old Immanuel probably protest (but he doesn't have a vote, anyway ). The analytical part is isomorph to Boolean logic, I guess!?

Kant's 'synthetic apriori' makes no sense to me, how about you?

It's raining or It's not raining, is analytic even though 'It's raining' itself is synthetic.

Nothing is learned about the weather or the world, when we know that 'It's raining or It's not raining'.

Boolean logic (of classes) and Aristotle's Syllogistic logic are both reducible to (finite) truth value analysis.


Owen

[Thomas Knierim]

Owen: Kant's 'synthetic apriori' makes no sense to me, how about you?

It makes sense to me.

It's raining or It's not raining, is analytic even though 'It's raining' itself is synthetic. Nothing is learned about the weather or the world, when we know that 'It's raining or It's not raining'.

Certainly. But that is not what Kant meant with synthetic a priori. The 'analytic - synthetic' distinction in the British analytic tradition (Russell, Whitehead, Quine, et al) is somewhat different from the notions associated with the same words in continental philosophy (Kant, Hegel, and others, too many to enumerate). Husserl, for example, assigns to it the class of statements of ontological necessitation, such as "The Universe is the only natural system with no environment.", or "All things consist of atoms." Wittgenstein would probably dismiss these statements as grammatical circularities, but then there is another class of statements such as "The speed of light is constant," which are neither circular nor a posteriori. The nature of light had not yet been derived empirically (although the Michelson-Morley experiment went into this direction), when Einstein began to formulate Special Relativity. He started from intuitive insight and used 'c' as a premise. Planck's notion of a quantum is another example for a synthetic a priori. In fact, most axioms in the natural sciences fall into that class, just like most analytic a prioris are mathematical axioms.

Thomas

[beesting42]

Logic is part of buddhism.... for sure. But try this...
Life is death and death is life. But life and death are not the same.

[zero2infinite]

Zero =emptyness=sunyata=openess can accomedate all.

(+infintie)+(-infinite) = zero.so it has all possiblities.

Empty set creates other sets

It is like a stem cell when divides- it create all other cells

[vicente]

An empty set may be the sum of all sets, that is, all negatives and positives equal nothing,....however, an empty set is not Zero, for it is a 'set', not Emptyness.

:)

[Spiny]

Originally posted by Thomas Knierim@Jun 30 2003, 09:23 AM
Sylph,

I should perhaps mention that the four basic propositions (a1) to (a4) -sometimes called tetralemma- are not really a unique feature of Budhist philosophy. They appear in ancient Indian philosophy and it may be supposed that they have been taught to the Buddha by his early teachers. You are right in saying that the tetralemma may be stated in terms of propositional logic. That is what I did in the previous post. It is important to keep in mind that P and Q are antithetic, i.e. P = ~Q. It follows that only the first two propositions (X=Q or X=P) concur with Aristotelian logic, wheras the latter two (X=P & X=Q), (X=~P & X=~Q) are contradictory in bivalent logic.

I suggested that by replacing Q with ~P and applying the rules of inference of classical logic, it is possible to reduce the tetralemma to three statements, although I must confess that I doubt whether the replacement of the variable is a permissible operation, since we are dealing with a paraconsistent logic.

Sylph: Hmm, Thomas, I'm still not convinced regarding the usefulness of multivalent logic...

You are certainly not alone. Most people don't see too many real-life applications for multivalent logic, since day-to-day problems can usually be be solved with conventional logic. Multivalent logic, however, has quite a number of applications in science and engineering. For example, computer scientists should be familiar with fuzzy logic, linear logic, Belnap's 4-valued system, and Gödel's logic. But let's distinguish between multivalent and paraconsistent. I think the important property of Buddhist logic is paraconsistency, not multivalence. Paraconsistent logics are a fairly new topic in mathematics. The systematic investigation of paraconsistent systems has only begun recently in the 20th century, so it can be expected that there are not too many applications yet, since research is still in its infancy. Perhaps one day we will have machines that do not only distinguish between 0 and 1, but that will be capable of internal states that are neither 0 nor 1, or both 0 and 1.

Cheers, Thomas
"Most people don't see too many real-life applications for multivalent logic, since day-to-day problems can usually be be solved with conventional logic. "

Buddhist logic can be viewed in the same way as a Zen koan, ie it's purpose is to challenge the way we usually think about things and it is deliberately counter-intuitive. It's a bit like quantum mechanics!

[VossistArts]

Originally posted by rich@Jul 7 2003, 12:34 AM
Polaris,

It is not so much being criticized, that I mind, but it is me writing/saying certain things which are stupid, and then seeing the idiot within me, for writing/saying. :angry:

Really, not mad at anyone but me. I am myself's own and worst enemy. Will probably kick my self later for posting this.

Thanks anyway. :)
Sometimes its hard to look at what weve said or done when it appears ignorant, but isnt it at the same time proof that we are enlightening by recognizing where we lack and where we need to improve? the teaching and the answer are of two as one.

And somehow, just from reading your posts I doubt youd kick any anyone else or call them idiot or stupid so why do it to yourself. If you can forgive others of being human then you can be cool to yourself too. Ultimately, if everyone in a sangha is aware of how to be kind to and understanding of others and what might seem like their faults then they can be kind to themselves knowing everyone knows how it is, what its for, and that its ok.

Besides, youre brilliant. Brilliant people who dont ever make mistakes are sort of hard to relate to heh.

That and the fact that negative reinforcement can lead to neurodysfunction and clinical depression. ugh **** that eh :) Be good to you.

[sahyo]

And somehow, just from reading your posts I doubt youd kick any anyone else or call them idiot or stupid



hehehe

yes happened
though he didn't exactly as was described

maybe vArts not assume?

[VossistArts]

Originally posted by asheera@May 17 2005, 02:28 AM

And somehow, just from reading your posts I doubt youd kick any anyone else or call them idiot or stupid



hehehe

yes happened
though he didn't exactly as was described

maybe vArts not assume?
hehe maybe not . but probably .