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.