Lesson 12

Lesson 12: Unsolved Problems & Paradoxes in Philosophy Introduction

 

There exist in the realm of philosophy from time to time, questions that are so complex or absurd that they have yet to find a definitive answer. Bordering more on thought problems or food for thought, these issues continue to confound and delight thinkers both young and old. This lesson delves into some of the more entertaining mental conundrums that pervade philosophy, but is by no means exhaustive.

 

Molyneux's Problem

This conundrum was posed by William Molyneux to John Locke goes as follows:

A man who is born blind is taught to distinguish between the shape of a sphere and the shape of a cube by feeling them with his hands and fingertips. Then, the two objects are placed next to one another on a table. The man is then sat at the table and his vision returned. Will he be able to distinguish between the sphere and the cube before touching them, just with sight?

The resolution to this issue is not easily achieved, since both Locke and Molyneux believed that the objects couldn't immediately be identified by sight alone, given the disparity in the way different senses perceive the external world.

"… there is no problem in the history of the philosophy of perception that has provoked more thought than the problem that Molyneux raised in 1688. In this sense, Molyneux's problem is one the most fruitful thought-experiments ever proposed in the history of philosophy, which is still as intriguing today as when Molyneux first formulated it … (SEP 2011)."

 

Sorites Paradoxes

These paradoxes make use of language, relying primarily on the vagueness and ill-defined predicates to wreak havoc on the mind. The name of these paradoxes come from the Greek word soros, meaning "heap". The classic formulation of this would be to ask if a person considers one grain of sand to be a heap. Obviously, the answer is no. Would two grains of sand be a heap? Again, no. Three? No. And so on and so forth until one million grains of sand is reached.

The opposite example is also works. Assume a heap of sand consists of a million (or some other large number) of grain. Would taking away a single grain unmake the heap? No. How about a second? A third? When does it stop being a heap? What does a "being a heap" actually mean?

The galling aspect of this style of paradox is that "heap" is assumed to have a precise meaning but in reality, it does not. By not giving the heap a precise definition, the individual faced with the paradox is simply stating that the heap does or does not exist in some form. Defining a change in any object requires specific boundaries. As such, the Sorites paradox is what's referred to as an unsolved problem in philosophy, meaning there is no one universal solution to the conundrum.

Surprise Test Paradox

This is a type of epistemic paradox, that is, they are related to the discipline of epistemology and hinge on our conception of knowledge. The earliest of these riddles began with the Skeptics of Ancient Greece.

However, this more modern incarnation involves a teacher informing his class of a surprise test in the upcoming week of classes. One of his students claims that a surprise test would be impossible. Why? Because the class only meets on Monday, Wednesday, and Friday. If the test is given on Friday, this would be predicted by Thursday. If it's given on Wednesday, it would be predicted by Tuesday. In either case, it would not be a surprise. That leaves Monday, as the only possibility, meaning the "surprise test" would not be a surprise at all.

"The riddle is: Can the teacher fulfill his announcement? We have an embarrassment of riches. On the one hand, we have the student's elimination argument. On the other hand, common sense says that surprise tests are possible even when we have had advance warning that one will occur at some point. Either of the answers would be decisive were not for the credentials of the rival answer. Thus we have a paradox. But a paradox of what kind? ‘Surprise test' is being defined in terms of what can be known. Specifically, a test is a surprise if and only if the student cannot know beforehand which day the test will occur. Therefore the riddle of the surprise test qualifies as anepistemic paradox (SEP 2011)."

The paradox arises from the announcement of the surprise test. The student knows that next week there will be a test and he or she can rationally deduce which day it is most likely to be (Monday). The argument is based on whether or it is truly a "surprise".

Liar Paradox & the Barber Paradox

This paradox is created by the self-referential nature of a statement itself, such as "I am a liar" or "this statement is false". Taken at face value, the person who claims "I am a liar" is either lying, in which he is telling the truth, or not lying, thereby negating the statement entirely by making it truthful.

            Created by Welsh mathematician and philosopher, Bertrand Russell, the barber paradox goes as follows: In a village, the barber shaves everyone who does not shave himself, but no one else. Who shaves the barber?

Sophisms

            Sophisms are another category of paradoxes. A famous example is the crocodile paradox. In this puzzle, A slim crocodile living in the Nile took a child. His mother begged to have him back. The crocodile could not only talk, but was also a great sophist and stated, "If you guess correctly what I will do with him, I will return him. However, if you don't predict his fate correctly, I'll eat him." What statement should the mother make to save her child?

            Another sophism goes as follows: "Yes, greedy man gives his cash with sorrow. However, he doesn't have the cash with sorrow, so he gives what he doesn't have."

            A final sophism is the following: No cat has eight tails. One cat has one more tail than no cats. Therefore, one cat has nine tails.