Dharmakīrti and liar paradox

Hello again, this is Szymon, a PhD student working on Buddhist logic. In my last post, I talked about the methodological background of my project. Today, I will tell you what Dharmakīrti says about liar-like sentences and how we can turn it into a novel approach to the liar paradox. In next posts, I will discuss some goods and bads of this approach and what it tells us about logical knowledge.

What is the liar paradox? Let’s look at the so-called liar sentence: ‘this sentence is false.’ You can reason from it to a paradoxical conclusion that the liar sentence is both true and false. Here’s how this reasoning goes. Consider the first case: the liar sentence is true. Then, what is said—that the liar sentence is false—is the case. So, if the liar sentence is true, then it is false. Now consider a different case and say that the liar sentence is false. Then it is true because that’s what it says. So, if the liar sentence is false, then it is true. When these two cases are put together, we see that the liar is true if and only if it is false. If every sentence is true or false, then the liar sentence is both true and false and this is paradoxical.

The liar paradox tells us something important about truth and logic. We cannot consistently believe that truth is simply what is the case, that every sentence is either true or false, and that no sentence is both true and false. Because of the paradox, we need to revise one of these otherwise attractive ideas.

The Buddhist epistemologists I study didn’t talk about the liar paradox explicitly. However, they talked about something similar: contradictions with one’s own words (svavacanavirodha). Classic examples of such a contradiction include ‘my mother is barren’ and ‘all sentences are false.’

In the rest of this post, I will tell you what Dharmakīrti says about contradictions with one’s own words in his Commentary on Epistemology (Pramānavārttika), chapter 4, verses 93-101. This fragment was translated into English by Tom Tillemans in his Dharmakīrti’s Pramānavārttika: an annotated translation of the fourth chapter (Parārthānumāna), pages 138-142. 

Dharmakīrti says, roughly and in between the lines, that contradictions with one’s own words are ambiguous. On the one hand, when you say that ‘my mother is barren’, you imply that a person you talk about cannot have children. This is what ‘barren’ conventionally means. On the other hand, you imply that the same person has a child. This is what ‘mother’ means. 

However, you cannot think that one person can and cannot have children at once. For Dharmakīrti, it is impossible to believe contradictions because contradictory beliefs impede with each other. It means that one belief prevents another from arsing in a similar way to which a drought prevents wheat from ripping. For him, the two beliefs implied by the sentence ‘my mother is barren’ are exactly like this: they impede with each other. Moreover, things in the world cannot have contradictory properties, so even if you were able to believe a contradiction, your belief couldn’t be supported by anything real.

The above reasoning has a few gaps. For example, you could argue that not all mothers are biological mothers or that your mother wasn’t barren in the past even though she is now. Leaving these immediate problems aside, there is something interesting about the Dharmakīrtian analysis of contradictions. 

For Buddhist epistemologists, knowledge is a belief produced in a justified way. If there’s no belief that your mother is barren, then there is no warranted belief. Consequently, it’s impossible to know that ‘my mother is barren’ is true. Moreover, it is impossible to know that ‘my mother is baren’ is false for the same reason. There is no belief expressed by this sentence and so there’s no way of showing that this sentence is actually false. 

Why is it interesting? Let’s think about the liar paradox again. The Dharmakīrtian analysis of the liar sentence—not something Dharmakīrti did but something I think can be successfully done—starts with the observation that the liar sentence implies two impeding beliefs. Firstly, ‘this sentence is false’ implies that it is false, and, secondly, it implies that it is true. This follows from how we conventionally understand what ‘false’ and ‘true’ mean. Consequently, the liar sentence is ambiguous between two interpretations. You can either think that it is true or that it is false but not that it is both true and false. Consequently, the liar sentence doesn’t express any belief and so it cannot be known to be true or false.

What’s the philosophical upshot of this approach to the liar paradox? There are a few but I will give you just one. Recall that that liar paradox arises because of an argument assuming that the liar sentence is true and that it is false. However, if the liar sentence is unbelievable, then we are unable to make these assumptions. If we cannot assume that, how can we reach the paradoxical conclusion that the liar sentence is both true and false? Maybe, the paradoxical nature of the liar sentence has more to do with what is possible to believe rather than what truth is, as the dominant approaches to the liar paradox assume. If that were the case, we would have a new approach to the liar paradox.

Sadly, it’s not all sunshine and roses. Whether the Dharmakīrtian approach to the liar paradox is plausible or not depends on several considerations. For example, it depends on whether it is actually impossible to have contradictory beliefs (I’m far from convinced that it is), whether only sentences expressing beliefs can be known to be true or false (this sounds right to me) and whether real things cannot have contradictory properties (I still don’t know!).

These are not the only questions I’m thinking about. In the next post, I will introduce yet another problem with the Dharmakīrtian approach to the liar paradox. It comes from Tom Tillemans and says that we could know that the liar sentence is actually false if we reasoned according to a logical rule that if a sentence implies its negation, then it has to be false ((A → ¬A) → ¬A). Discussing this idea will give us a chance to look into the relationship between Dharmakīrtian epistemology and contemporary logic a bit closer. Stay tuned!

7 Replies to “Dharmakīrti and liar paradox”

  1. Interesting post, Szymon. Thank you. Dharmakīrti’s approach as you describe it seems to hinge entirely on the concept of belief: we resolve the liar paradox by saying (eg) “All statements are false” is not a belief. This makes me wonder the next question: what is a belief, for Dharmakīrti? The simple question here is “which Sanskrit word are you translating as belief?”, but the more interesting question is what work that word does. It sounds like, for Dharmakīrti, the only entities that can be true or false are beliefs? Why is that – what is Dharmakīrti claiming about the nature of beliefs, or the nature of truth and falsity, that makes that the case? (Put a different way, one could ask Dharmakīrti: would “the cause of suffering is craving” still be a truth if nobody had ever believed it or thought about it?)

    • Hey Amod, thanks, these are all very interesting questions. I agree that this approach hinges on what beliefs are. Let me first say a few words about the context of Dharmakīrti’s claim that contradictions with own words are unbelievable and then I will answer your questions directly.

      Dharmakīrit says that contradictions with own words impede (pratibandhaka)—and I take it to mean that they are unbelievable/don’t express any beliefs—while commenting on Dignāga’s claim from the Pramāṇasamuccaya III.2cd that an argument has a fallacious subject (pakṣābhāsa) if it is opposed (anirākṛta) by authority (āpta). Dharmakīrit says that the words of authority and its opposing thesis (pratijña) impede and cannot invalidate (bādha) because neither the words of authority nor the opposing thesis can be supported by a valid means of cognition, just like contradictions with own words.

      If a speech is a product of warranted inference, then it expresses a cognition (jñāna) that has the triple characteristic. When someone says something false, they express erroneous cognition (mithyopalabdhi) that hasn’t been produced in a warranting way. When they state a contradiction with own word, then, I think, they are not expressing any cognition whatsoever. Why? Because, for Dharmakīrti, cognition—erroneous or not—is a unitary judgment (ekapratyavamarśa) and “My mother is barren” doesn’t express a unitary judgment because it expresses (abhidhāya, vācinā) a contrary state of affairs (viruddhārtha).

      With this picture in the background, I call ‘a belief’ any cognition that expresses a unitary judgment. This is my answer to your question what work ‘belief’ does in my post and how it relates to Dharmakīrti’s philosophical project. I’m aware that’s only a partial answer and I’m happy to say more.

      Answering your simple question, “which Sanskrit word are you translating as belief?”, there’s no single Sanskrit word I have in mind when I say that, for Dharmakīrti, contradictions with own words are unbelievable. I don’t think about my work as translating Dharmakīrti but rather making sense of what he says using contemporary terminology.

      Answering you comment that ‘the only entities that can be true or false are beliefs’, I think that only beliefs can be warranted by valid means of cognition and so only beliefs can be known to be true. On the other hand, only beliefs can be shown to be fallacious and so known to be false. I don’t think there’s anything interesting to say about true and false things that cannot be known to be true or false in the above sense. Consequently, I don’t know whether “the cause of suffering is craving” would still be a truth if nobody had ever believed it or thought about it. I know that if someone said that to me, then I would need to go through an inference to establish whether it’s true or not.

      Hope that helps! I’m very keen to say more, so feel free to keep asking.

      • Thanks, Szymon. I’m interested in trying to get at Dharmakīrti’s perspective here. It seems to me that as a Buddhist he would likely be committed to saying the four āryasatyas are in fact satyas, and that they would still have been such before the Buddha thought of them. Do you think that’s not the case?

        • No worries, Amod! That’s an interesting question. I’m not aware of any fragments of Dharmakīrti’s works where he talks about this problem explicitly (it doesn’t mean that there are none!) so my answer will be a bit speculative.

          Firstly, āryasatyas are true because they are supported by valid inferences and an inference is valid only if you went through it yourself. So, as long as you haven’t inferred that, for example, ‘Everything is suffering’ for yourself—possibly guided by the words of others—you have no reason to think it’s true.

          Secondly, ‘Everything is suffering’ was warranted for someone in the past, before you warranted it for yourself. It was warranted by Buddha, for Buddha. Then, through an uninterrupted tradition, his words reached you and, relying on Buddhists arguments establishing that ‘Everything is suffering’, you are now in position to infer that for yourself. However, words of Buddha are not a source of knowledge. Only inference is a source of knowledge and Buddha’s words, and Dharmakīrti’s argument, can only assist your own inferences.

          Thirdly, was ‘Everything is suffering’ true before the Buddha sat under the Bodhi three? Buddha walked a long-forgotten path, and there were Buddhas before him, and they taught the true Dharma, so they taught that ‘Everything is suffering’. Because world has no beginning, and there were infinitely many Buddhas in the past and in infinitely many words—I’m doing some very advance Mahāyāna here—there probably was always some Buddha somewhere teaching that ‘Everything is suffering’. However, we cannot know that because the deep past and other worlds are so-called radically inaccessible objects (atyantaparokṣa) of inference.

          Generally, I think that the question of āryasatyas’ truth before someone thought them feels foreign to the Dharmakīrtian framework. What makes it foreign is the nature of Dharmakīrtian truth-bearers. The sentence ‘Everything is suffering’ doesn’t express a proposition: an object having defined semantic properties—truth, falsity, etc.—interpedently of agents and their cognitive lives. Rather, ‘Everything is suffering’ has semantic properties insofar as it inherits them from someone’s belief that everything is suffering. Otherwise, the sentence is just a sound. So, ‘Everything is suffering’ is true iff you can go through a process of establishing that it is the case. Would it be true if no one went through this process? Maybe, it depends on whether we could infer that. And being able to infer is not different from actually inferring. Consequently, everything boils down to the question to whether there is an inference supporting that ‘Everything is suffering’, no matter whether Buddha actually taught that.

          Let me know if that makes any sense, I wish I had a better answer. I will keep an eye on this question and report back as soon as I will come across anything interesting.

  2. Szymon,

    Can you process belief without possibility, and in contrast, unbelief and impossibility? Modern logic finds one formalism for these, in modal or deontic logic, and I thought the Buddhists took the truth-table a step beyond the intuitionism of the Jains, looking beyond uncertainty to ambiguity, or ambivalence, as inherent to our often wavering convictions. On Dharmakirti in particular, though, I couldn’t say.

    By the way, on you core research questions, there are crisp answers in Plato: Philebus 14c touches on “common and acknowledged paradoxes” of relative terms, and in Phaedo 102+, these are contrasted to what Socrates is “in himself” (svabhava). And Republic 3, in the middle, after mention of Apollo, gives “long and short” as definitely just metre (Chandas): thus cause and effect like waves on the ocean, as in modern wave mechanics, from Hermann Grassmann, who took it direct to . . . Sanskrit!!

    • Hey Orwin,

      That’s interesting but I’m not sure I follow everything.

      What do you mean when you ask whether I can process belief without possibility? Do you mean whether I can believe something impossible or whether I can have a belief that’s impossible to have? I’m okay with believing something impossible.

      What’s the formalism you mean? Buddhists philosophers I’m studying didn’t use truth tables, neither did Jains as far as I know. That would be a surprise if they did! Could you say more? Also, what do you mean that Buddhists looked beyond uncertainty and ambiguity? What Buddhists?

      I know very little Plato but I’ve just looked into Philebus 14c and it says that “the assertions that one is many and many are one are marvellous, and it is easy to dispute with anyone who makes either of them”. Is this the fragment you have in mind? It’s interesting but I don’t know how it relates with my project.

      I don’t think Socrates has svabhāva because only dharmas have svabhāva and Socrates is not a dharma. I know nothing about wave mechanics and I don’t know who Herman Grassmann is, so I cannot help with that.

  3. With the Jains. it’s their mathematics, which was impressive, especially thru the Classical period: just as the impact from Ptolemy was felt, they took the lead in astronomy. with computational methods matching the Greek epicycles. So there you have an understated but genuine formalism: they were pointedly not engaging any ontological questions.

    That stance then sets a standard of comparison for Bhuddist logic, but not any way of engaging Buddhist texts. So there I may loose you. The Buddha’s own Nyeti Nyeti just gives you neither true nor false, the skeptic position that has been traced thru Pyrrho back to Greece. An inclusive option does surface later as bedha-abedha: doesn’t that have a background in the Abidharmakhosa? Or am I mistaken there?

    It is worth noticing that correlations work equally positive or negative, and that matters for all phenomenal accounts of causality, and Hume’s kind of skepticism.

    As for Socrates, he was saying something like his *idea of great *was dharma, as the true kind of standard or cause behind all appearances. That’s controversial of course: Platonism mostly denigrates the ideas. But Chrysippus the Stoic was noted saying ideas partake of the infinite, which gets me interested again.

    As for waves: at each point you can place vectors representing force and acceleration, as cause and effect: so if cause is not effect. you have the inclusive contradiction, *due to the continuum assumed, and points of representation, which come as infinite limits, or the ideal or spiritual ground discerned by Leibniz. I hope that all helps some way.

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