Originating from soros, the Greek word for “heap,” sorites arguments utilize statements with miniscule differences which are centered around vague keywords to arrive at very paradoxical conclusions. For instance, one would typically be able to agree with the following statements:
1. A man with no hairs on his head is bald.
2. A bald man, if given one more hair, is still bald.
These two statements, however, can be used to say that everyone is bald. For example, consider a man with no hairs on his head. He is, by definition of statement 1, bald. When he is given one hair, he is still bald by definition of statement 2. This process can be repeated over and over again, to the point that we are able to conclude that a man with 10,000 hairs is bald, …show more content…
Modus ponens, which says “if p, then q; p, therefore q” is applied many times consecutively in these arguments, to the point that we ultimately arrive at paradoxical conclusions. The use of the “degrees of truth” approach, however, is able to solve this paradox by ultimately suggesting the invalidity of modus ponens and therefore rejecting the reasoning of these arguments. While the rejection of modus ponens is undoubtedly a controversial decision to make, it is ultimately supported due to the idea that modus ponens is only true for statements that are completely true or completely false. For everything in between, it tends to “leak” a small amount of truth, and over multiple applications this small loss in truth value is enough to show the invalidity of the argument. This approach to vagueness is refuted by many philosophers due to the idea that a vague question is given a vague answer, but it is important to understand that truth values ultimately describe confidence in the trueness or falsity of the answer. For that reason, vague questions must always have intermediate truth values. For this reason, the “degrees of truth” approach to vagueness provides a very acceptable theory for the sorites
1. A man with no hairs on his head is bald.
2. A bald man, if given one more hair, is still bald.
These two statements, however, can be used to say that everyone is bald. For example, consider a man with no hairs on his head. He is, by definition of statement 1, bald. When he is given one hair, he is still bald by definition of statement 2. This process can be repeated over and over again, to the point that we are able to conclude that a man with 10,000 hairs is bald, …show more content…
Modus ponens, which says “if p, then q; p, therefore q” is applied many times consecutively in these arguments, to the point that we ultimately arrive at paradoxical conclusions. The use of the “degrees of truth” approach, however, is able to solve this paradox by ultimately suggesting the invalidity of modus ponens and therefore rejecting the reasoning of these arguments. While the rejection of modus ponens is undoubtedly a controversial decision to make, it is ultimately supported due to the idea that modus ponens is only true for statements that are completely true or completely false. For everything in between, it tends to “leak” a small amount of truth, and over multiple applications this small loss in truth value is enough to show the invalidity of the argument. This approach to vagueness is refuted by many philosophers due to the idea that a vague question is given a vague answer, but it is important to understand that truth values ultimately describe confidence in the trueness or falsity of the answer. For that reason, vague questions must always have intermediate truth values. For this reason, the “degrees of truth” approach to vagueness provides a very acceptable theory for the sorites