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!