Hi all, this is Szymon. In previous posts, I presented the Dharmakīrtian approach to the liar paradox and introduced the contemptible consequence problem. Today, I will give five answers to this problem and tell you what I plan to do next in my research.
My answers to the contemptible consequence problem will be sketchy. I want to give you a general picture of my project without boring you with too many details. I’m happy to tell more in comments. (It’s a good moment for a big shoutout to all great comments I get thus far, thank you!) I will end each answer with some questions I’m working on right now. As always, I’m very curious what you think.
Let’s start with recalling what’s the problem. I think that Dharmakīrtian philosophy gives us resources to devise an epistemic approach to the liar paradox. According to this approach, even though the liar sentence implies that it is false and that it is true, we cannot know that the liar sentence is true or that it is false.
However, there’s a logical problem with this view. If we reasoned following the contemptible consequence rules of classical logic ((A → ¬A) → ¬A), we could know that the liar sentence is false because it implies its negation and every sentence that implies its negation has to be false.
My first answer to the contemptible consequence problem is that the problem arises insofar as we represent the fact that the liar sentence implies its negation as a material implication from the liar sentence to its negation. However, there are reasons to be sceptical whether material implication adequately represents what we mean when we say that one sentence implies some other sentence. For example, when I say, ‘There are pistachios in the cupboard’, I imply that ‘You may have some’. We can represent this implication as a conditional expression ‘If there are pistachios in the cupboard, you may have some’ and interpret it as a material implication. Then, this conditional is false if ‘there are pistachios in the cupboard’ is true and ‘You may have some’ is false, and otherwise it is true. For example, it is true if there are no pistachios in the cupboard and you cannot have them. However, this is not what I meant.
Consequently, why to think that material implication adequately represents the fact the liar sentence implies its negation? Dharmakīrti and his commentators say that a contradiction with own words expresses (abhidhāya, vācinā) two opposing sentences or a contradictory state of affairs. What it means? What, if anything, Buddhist epistemology has to say about meaning of conditional expressions?
Here’s my second and my third answer. The contemptible consequence problem arises insofar as deference to logical rules generates knowledge. For Dharmakīrti, there are only two ways in which knowledge can be generated: through perception and through valid inference. We clearly don’t perceive that the liar sentence is false because it implies its own negation.
Is there a valid inference establishing that the liar sentence is false? This is how this inference could look like:
- The liar sentence is false because it implies its negation, and whatever implies its negation is false.
I have two problems with this inference. Firstly, I have a problem with its subject: the liar sentence. If the liar sentence is unthinkable and is a contradiction with own words, then it cannot be a subject of a valid inference. However, if that’s the case, how can we reason with the liar sentence at all? Especially, how do we know that if it is false, then it is true and vice versa?
Secondly, how to establish that whatever implies its negation is false? Buddhist epistemology offers us some tools to answer this question. Firstly, 1. could be valid if its inferential mark had the so-called triple characteristic. It means that a property designated in the middle part of the inference—the property that the liar sentence implies its negation—is present in the subject of the inference—in the liar sentence—and in similar cases, but it is absent in dissimilar cases. Does the property ‘implies its negation’ has the triple characteristic?
Alternatively, we can ask what’s the relationship between the reason and the property designated in the first part of the inference, that is, falsity. To use Dharmakīrtian terminology, is 1. true in virtue of the force of real entities (vastubalapravṛtta)? What that could mean in our context? Does the fact that the liar sentence implies its negation cause that the liar sentence is false in the same way as fire causes smoke? Are these two facts identical like the fact that some plant is an Indian rosewood is identical with the fact that it is a tree?
Two more brief points. Fourthly, what about an inference deferring to the admirable consequence rule ((¬A → A) → A)? Could it establish that the lair sentence is true because whatever is implied by its negation has to be true? Does it make us know that the liar sentence is both true and false?
Fifthly, maybe, what establishes the conclusion of the contemptible consequence argument is not a valid inference (anumāna) but a hypothetical reasoning (tarka, prasaṅga)? If so, how this reasoning looks like? Does it produce knowledge?
These five sketchy answers to the contemptible consequence problem invite further research. They span over a host of topics within the history of Buddhist philosophy, philosophy of language, philosophy of mind, epistemology, and logic. This is where my research is going next.
In my first post I said that I aim at providing my own philosophical arguments originating from Buddhists views. Dharmakīrti’s ideas about contradictions with own words gave me an opportunity to look at the old paradox from a new angle. Now, I take up this opportunity and develop my own philosophical position. I learn a lot from studying Buddhist epistemology, but I’m not interested in it as a thing of the past. I’m interested in it as a promising and fruitful avenue for philosophical research here-and-now.
Thank you so much for reading up to this point and I hope you had some fun along the way. I want to thank the Indian Philosophy blog team again. It was a pleasure writing for you. Last but not least, thanks to my supervisors Bronwyn Finnigan, Al Hájek, Koji Tanaka and Tom Tillemans for all their continuous help.
Hi Syzmon, your problem with how the liar paradox gets defined by contemptible consequence reminds me of Patanjali placing asmitA (self-definition) among the kles’As (stresses) that make existence painful – Yoga-sUtra 2.3. And right here we have Boram saying that logic gives him a headache. That recovers something essential of the Buddhist wisdom, reframing the problem in terms of beliefs and conjectures, how we try out possibilities in the range of belief. I like that because I’m intent on recovering the ancient wisdom of Patanjali, which is really rather Chaldean or Indo-Hittite, for he worked on Mt. Sumeru, as if in Sumerian. Today, Jews are flowing into Dubai in search of this heritage.
Patanjali is now regularly placed in dispute with Buddhists, and Larson attributes the text and commentary to Vindhysvasin, mistaken for Vedavyasa. French neoplatonists have long highlighted terms shared with Buddhist discourse, and I’ve mapped them into both Vyasa’s commentary and Patanjali’s sUtras, and they miss the core arguments by a mile!
BUT Patanjali was a real scientist, and stated clearly that to grasp a phenomenon reliably you must place it against the void: yes, sunya, which has *not been flagged as a Buddhist term! All we get offered are more painful pre-definitions to patch the poor translations, and make for painful logicist wrangling.
Vyasa explicitly addresses Bauddha, a much older term related to Baudhyanana and buddhi, glossed as “intellectual”. And picks on their definitions! So the background is real and relevant, and what we are dealing with is properly theory of mind, or no-mind / void, which then marks a new departure. So to my question: was it not this painful difficulty which set the scene for Nagarjuna? Did DharmakIrti have a good answer, or did the debate pass down to the Mahayana?
Hey Orwin,
Thanks for you comment!
I’m not entirely sure what do you mean when you say that logic is painful. Do you mean that it has to lead to suffering because it uses concepts and concepts lead to volitions, volitions to craving, craving to suffering etc.?
For Dharmakīrti, the role of conceptual knowledge is to correct erroneous concepts and employ these corrected concepts to act in the right way and achieve human ends (puruṣārtha). Consequently, logic can be instrumental in counteracting pain and doesn’t need to amass it. Dharmakīrti develops his theory of valid means of cognition to establish the four noble truths.
Also, I don’t think that the liar paradox is defined by the contemptible consequence. I think that Dharmakīrtian approach to the paradox is prone to the contemptible consequence problem and I think that the problem can be resisted.
What Patañjali means when he says that self-definition makes existence painful? What is self-definition?
Syzmon, self-definition is itself a problem in definition: just where Patanjali (1.17) gave examples. you find “form (rupa)” written into some manuscripts! These readers wanted a handle for talking about the asmitA usages. And it’s not here the psychological there of cravings: rather the pragmatic concern shared by DharmakIrti. The pain arises from defining yourself into doing things that don’t work. So it’s what you believe you can or should do. And there I share your interest in epistemic logic, which is just emerging as a field of research, as at the Formal Epistemology Project at Leuwen in Belgium.
Most modern science is in fact presented in plausible form, a fact highlighted by Kurt Vaihinger in his philosophy of As If, which also brings in the hypothetical option. He was an influential editor and interpreter of Kant, and I’ve been tracking his impact, scratching out some most interesting but difficult passages in Kant’s archaic German. His editors were mostly Hegelians in pedagogy, and their relentless simplifications of Kant flowed on into ‘dumbing down” higher education, from which we now struggle to recover, painfully at times.
So I find your work very relevant and interesting. Vastu and Bala are also terms Patanjali uses to get a grip on the difficulties, asking after khyati – what is to be known. or discovered. So perhaps that was enough for DharmakIrti. But the traditional language is not enough for me now with Patanjali and Kant: logical predication does not give you Kant’s synthetic statements, or Patanjali’s as-ya, “which are”. There I now distinguish from the logical *is a pragmatic *as, defining a measure or criterion by which a question can be decided. Heinrich Riekert was onto that, following Kant.
Hi Szymon, all the great questions you raise here indicate what a rich and complicated problem this is. Not sure where to begin, so I will just raise two questions that leap to my mind.
(1) According to your presentation of the Dharmakirtian approach, a svavacanaviroddha case is unknowable because it implies two contradictory beliefs that impede each other. But I wonder if this description aptly or fully describes the liar sentence case, for two reasons. In the first place, it does not seem to me that each of the contradictory beliefs about the truth or falsity of the sentence can be formed at all , given the self-referential nature of the sentence. And if each of the two contradictory beliefs cannot be formed, they cannot be there to even contradict one another. Secondly, suppose that we work with conditional beliefs of the form “if A then not-A” and “if not-A then A”. Then, it seems to me (prima facie) that the two beliefs do not impede one another, but give rise to endless vacillation. Like so: I assume A. Thus, not-A according to the first conditional belief and modus ponens. But then A according to the second conditional belief and modus ponens. But then not-A…, and so on.
(2) I think you can provide a perfectly good response to the above. Namely, contrary to my prima facie impression, you can point out that the conditional beliefs “if A then not-A” and “if not-A then A” are contradictory. The conjunction of these two conditionals is necessarily false. Then you can apply the Dharmakirtian analysis of contradictory beliefs impeding each other to these two conditional beliefs. Once I fully realize that the two conditionals are contradictory, I would not be able to believe them conjointly, and my vacillation will be brought to a standstill by two opposing forces in counterpoise.
Similarly, I suggest that it could help (and not hurt) your Dharmakirtian analysis to accept both the contemptible and admirable consequence rules, because you can derive the contradiction A and not-A from them, beliefs about which would impede each other. Then you do not need to replace the material conditional with something else?
Hi Boram, thanks for your comments. They are very helpful!
(1) Firstly, it’s a good question whether ‘The liar sentence is true’ and ‘The liar sentence is false’ are believable if the liar sentence is unbelievable. The way I was thinking about it is that these two sentences disambiguate the liar sentence’s meaning. They each express a single belief that the liar sentence is true (only) and that the liar sentence is false (only). These two sentences, if they are believable, would contradict each other. Now, it all depends on how disambiguation works.
However, I see why one could think that these two sentences inherit the liar sentence’s unbelievability. The reason to think that is that (i) unbelievability is a semantic property and (ii) meaning is compositional. Let me briefly explain. On (i), the liar sentence is unbelievable because of its meaning: it means that it is true and that it is false and you cannot warrantably believe that a single entity (the liar sentence) has two opposing properties (truth and falsity). On (ii), meanings of complex expressions are products of meanings their constituents. So, every complex expression containing the liar sentence–for example, ‘the liar sentence is false’–will inherit the liar sentence’s meaning and will, at least partially, mean what the liar sentence means. Consequently, if the liar sentence is unbelievable, then every sentence containing the liar sentence is unbelievable as well.
I agree with (i) but disagree with (ii). Bob Hale argued that Dharmakīrti’s apoha is non-compositional and I’m convinced. I also have some independent reasons to think that a Dharmakīrtian meaning is not compositional based on his discussions about how meanings are fixed. Thirdly, independently of whatever Dharmakīrti thinks, I think that compositional analysis of meaning is more limited than we think.
Secondly, I really like the idea to work with “if A then not-A” and “if not-A then A”. I agree that they don’t impede. I’m a bit sceptical whether we can know that they are true or false even though they are believable. This scepticism doesn’t come from Dharmakīrti but from my independent interests in conditional semanticism. I really like Moritz Schulz’s work. I’m not aware on anything about conditionals in Buddhism/Sanskrit. Any ideas where to look? I like the vacillation idea as well and I think that the reason why we cannot decide whether A or not-A is because we cannot know whether A or not-A.
(2) I see how “‘if A then not-A’ and ‘if not-A then A’” is false under very evaluation in the classical logic. However, I’m not sure whether it makes us know that this sentence is necessarily false. Is this right that whenever a sentence is false under very evaluation in classical logic, it is necessarily false? How about other logical systems? These are open questions, but I try to get as much philosophical millage out of the Dharmakīrtian epistemicism without committing myself to a particular logical system. Nevertheless, I fully agree that’s a feasible and exciting line of research.
It’s also a good point that I would not need to change the material interpretation of the fact that the liar sentence implies its negation if I were to conjoin ‘if A then not-A’ and ‘if not-A then A’. And as much as it would make my work (somewhat) easier, I don’t think that the material implication adequately represents the fact that the liar sentence implies its negation. Btw, not that I know what represents it and I will report back the moment I’ll learn. Thanks for the suggestion, maybe I will end up doing just that.
Also, I have a small problem finding your email address. Maybe you could send me a message?
Szymon, thanks for your detailed responses, raising further interesting issues. I will need to reflect on them further. I will just say in passing that I never had the opportunity to understand the apoha theory properly, and it may be an interesting future blog post for you to share with us.
I’ve emailed you my address. All the best on your continuing research!
P.S. From an essay written by Timothy Williamson (linked by Brian Leiter on his blog):
“In 1993, Stephen Yablo published a paradox of truth which seems to involve no self-reference, direct or indirect. Instead, it has an infinite sequence of sentences, each saying that none of its successors is true. The problem is not so much self-reference as ungroundedness, where the buck of truth gets passed forever, either round and round in a circle or along an infinite chain.”
I’ve heard something like this before as well, and it sounds right to me.
Source:
https://iai.tv/articles/politics-truth-and-self-reference-auid-1758?_auid=2020