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Based on the square of opposition we can conclude a few truths and falsities about the statement a-certain bird is blue. First, we look to the law of subcontraries to determine what is true and false, this law states that “if one is false, the remaining is true, and not conversely, for they can both be true at the same time when the matter is contingent” (1.14, p. 7). Essentially, the law of subcontraries, is the exact opposite of the law of contraries. In this case, we can see that they can both be true, a-bird can be blue, while another bird may not necessarily be blue, this is because the matter is contingent; the predicate can either be present or absent from the sentence. When we look to the superalternate, based on the law, we can see that it is not necessary that the universal be true, even if the particular is true. Every bird does not have to be blue for a-certain bird to be blue, on the other hand, every bird cannot be blue, but that does not mean that a-certain bird cannot be blue. Finally, we can look to the contradictory and based on the law, we can see that because a-certain bird is blue it must be false that no bird is blue.
Peter also defines simple, accidental and contrapositive conversion, where he states that a “simple conversion is making a predicate out of a subject and conversely, while quality and quantity remain the same” (1.15, p. 7). In this case we can see that this could be described as “no A is B“ converting to ”no B is A”. An accidental conversion “is making a predicate out of a subject and a subject out of a predicate, while quality remains the same, but quantity is changed” (1.15, p. 7). We could take this to mean that “every A is a B” can be converted to “a-certain A is a B”. Finally, contrapositive conversion is “making a predicate out of a subject and a subject out of a predicate, while quality and quantity remain the same but limited terms are changed into unlimited terms” (1.15, p. 7). This could be interpreted, as “every A is B” converting into “a-certain B is A”.
Considering the proposition “every man is risible”, we cannot convert this proposition in a simple conversion because it would not make sense to say that “every risible is a man”. We can attempt to convert this proposition accidentally, in which case it could be the case that “a-certain main is risible”, this statement would hold true, and be considered an accidental conversion. If we try to convert this statement contrapositvely we will see that we would be trying to say “a-certain risible is a man”, this statement also does not make sense because risible means being able to laugh, and because it is a verb, we cannot make it the subject of the sentence. In the cases of a simple conversion and a contrapositive conversion, in the case of the proposition “every man is risible” we cannot convert it in either way because there is no way to switch the predicate and the subject in these two sentences, based on Peter’s rules the only way to make the conversion is to switch the predicate and the subject.
Through Peter’s logic, the reader can come to understand the validity of certain propositions as well as come to figure out their truth and falsity based upon the square of opposition. Throughout the book, he explains his ideas, and keeps the reader aboard his voyage to gain more knowledge and insight into the world through the use of knowledge.
Peter also defines simple, accidental and contrapositive conversion, where he states that a “simple conversion is making a predicate out of a subject and conversely, while quality and quantity remain the same” (1.15, p. 7). In this case we can see that this could be described as “no A is B“ converting to ”no B is A”. An accidental conversion “is making a predicate out of a subject and a subject out of a predicate, while quality remains the same, but quantity is changed” (1.15, p. 7). We could take this to mean that “every A is a B” can be converted to “a-certain A is a B”. Finally, contrapositive conversion is “making a predicate out of a subject and a subject out of a predicate, while quality and quantity remain the same but limited terms are changed into unlimited terms” (1.15, p. 7). This could be interpreted, as “every A is B” converting into “a-certain B is A”.
Considering the proposition “every man is risible”, we cannot convert this proposition in a simple conversion because it would not make sense to say that “every risible is a man”. We can attempt to convert this proposition accidentally, in which case it could be the case that “a-certain main is risible”, this statement would hold true, and be considered an accidental conversion. If we try to convert this statement contrapositvely we will see that we would be trying to say “a-certain risible is a man”, this statement also does not make sense because risible means being able to laugh, and because it is a verb, we cannot make it the subject of the sentence. In the cases of a simple conversion and a contrapositive conversion, in the case of the proposition “every man is risible” we cannot convert it in either way because there is no way to switch the predicate and the subject in these two sentences, based on Peter’s rules the only way to make the conversion is to switch the predicate and the subject.
Through Peter’s logic, the reader can come to understand the validity of certain propositions as well as come to figure out their truth and falsity based upon the square of opposition. Throughout the book, he explains his ideas, and keeps the reader aboard his voyage to gain more knowledge and insight into the world through the use of knowledge.
