Philosophers have always been a big fan of solving problems by thinking of even weirder ones. They try to come up with the craziest and most extreme thought experiments to try and simplify finding the answer to their questions. We see this in Gettier’s “Ten Coins Case” or Descartes wax experiment. They’re both situations in which we wouldn’t find ourselves everyday; relating someone qualified for a job to the amount of coins he has in his pocket or putting our hand in the fire to see if it’s hot, are circumstances we wouldn’t consider parts of our daily activities.
In the medieval logic they came up with a thought experiment that was, and is till this day, a very famous one called “The Liar Paradox”. It consists of two propositions, one being “Everything I say is a lie” and the other “You are awful human beings”. The paradox hasn’t been solved yet, but people agreed there were two ways of interpreting the problem.
Some people say, if everything I say is a lie, then according to logic it naturally follows that the other proposition in relation to the first, must also be a lie, because we assume the principle of bivalence to be true, that something has to be true or false and can’t be both at the same time. Obviously in this thought experiment, the word ‘everything’ includes every single thing you say afterwards, therefore also including the second proposition, causing the statement “You are awful human beings” to be false, or at least a lie.
Others think you should not just apply the word ‘everything’ to the second proposition that follows afterwards, but use it in the first one already. If I am of the opinion that everything I say is a lie, then this sentence that I’ve just uttered, must also be a lie, it being a part of all the things I say therefore a part of ‘everything’ I say.
The problem is that these two perspectives are obviously equally possible and that no one, yet, has come up with an argument to dismiss one or the other, causing the paradox to remain unsolved. I, however, would like to try and look at it from a completely different view.
“The Liar Paradox” is considered to be a problem of medieval logic. Therefore, both attempts to solve the problem try this according to the rules of logic, such as necessary consequential relations and the principle of bivalence. But what if we try to dismiss these rules and take the problem out of it’s context? When we think of problems in logic and a number of propositions, we use the Principle of Deductive Closure to get to a conclusion. If A is the case and B is a logical deduction of A, then we assume B to also be the case. We use this principle everyday. For example, if I have to go outside and it’s raining, I make the logical deduction that this will necessarily end up in me getting soaked, which is among most people considered an uncomfortable event, and therefore why I will think to bring my umbrella or just renounce the whole idea of going outside.
Entirely giving up on this principle would seem a little radical to me, probably causing you daily problems fulfilling the most normal actions, but deciding not to use it in all cases might help us with certain difficulties as “The Liar Paradox”.
If we would for example rid ourselves in this case of the principle of deductive closure and we would look at the first interpretation of the problem, the necessary consequence of the second proposition to be included by the word ‘everything’, therefore causing the second proposition to be a lie, wouldn’t be the only rational possible outcome. Without the principle of deductive closure, the second proposition could exist separately and independently from the first proposition, which would make room for other interpretations. We could start looking at other relations between the two and not see them necessarily in the given order. Why would people be awful human beings? I wouldn’t say because of their nature, but because their actions made them that way. Obviously lying is regarded as a wrong action, which is why the association of awful human beings with lying would seem very logical. This way, both propositions could exist at the same time without one dismissing the other; “People that only tell lies are awful human beings” sounds correct and seems in line with our intuition.
However, when dismissing the principle of deductive closure and other rules of logic, lot’s of the outcomes will probably feel wrong and everything but in line with your intuition, but discarding some principles of logic in certain situations might sometimes enlarge our perspectives. Something to think about.
From Knights to computers 