Module 8: Basic Meaning of Proposition and Its Kinds.
What is a proposition? Its basic definition states that a proposition is a statement in which anything is affirmed or denied. An example of a proposition includes: “GOD exist” wherein the subject “GOD” is affirmed by the word “exist.” The proposition “A cat is an animal.” Is another proposition since attribute “animal’ affirms or describes the subject “cat”. What about truth and falsity? Do proposition have truth-value? Let us proceed in the discussion.
Sentences tha are not declarative in structure do not have a truth-value. For instance, one cannot say that the claim “Ouch!” is true or false. There is nothing in the claim which allows one to verify or assess whether it it is true or false. It will also be funny to think of someone saying that “Ouch!” is true or false. When somebody says “Ouch!” we just listen to what this person said and we do not say that it is true or false. Can you imagine somebody saying tha the expression “Ouch!” is invalid? I think it will be a strange topic to begin with.
In logic, therefore, one first needs to ask if the sentence follows the structure of a declarative sentence. If it does, then the statement can be assessed as whether true or false and can be used in logical analysis. If it does not, then there is no statement that can be logically assessed.
A categorical proposition is that which either affirms or denies something which is either true or false. Its basic structure follows this formula: subject-copula-predicate. These elements will be significantly explained in the next module. For now, just look at the following samples of categorical propositions to see how the formula in instanced in each proposition.
A conditional proposition is made up of two categorical propositions that are situated in the ‘if then’ frame. The proposition introduced by the term ‘if’ is referred to as antecedent, while the proposition introduced by the ‘then’ term is called the consequent. As antecedent, a proposition states the condition, and the consequent, the proposition stands for the outcome or result. Let us check these examples:
A conjunctive proposition unites two propositions using the term ‘and’. By using the term ‘and’ is observed/applied in the proposition. Here are some samples of conjunctions:
A disjunctive proposition provides two choices or alternatives by using the term ‘either or’ With these option, the logician’s interest is to assess if the disposition to make an option is truly upheld in the proposition. Kindly look at these samples:
With these types of proposition, we may now realize that for every type of proposition a specific type of logical tool and analysis shall be used. In ensuing modules, we shall demonstrate this point. In the case of categorical propositions, however, our treatment will be longer. In fact, the three other kinds of proposition are only significantly dealt with in the module on symbolic logic. This topic, however, is not yet included in this text-book.
The Nature of Categorical Proposition
In traditional Aristotelian logic, the categorical proposition is most useful in logical analysis. Its capacity to unconditionally deny or affirm something makes this kind of proposition a highly relevant platform in understanding and assessing the process of the interference from premises to conclusions in arguments. Hopefully, students will master the logical rules governing propositions of the categorical type.
The Subject. This part of the proposition refers to that which is affirmed or denied. In the sentence, “All cats are cute.” the subject of the proposition is ‘cats’. It is affirmed by the word ‘cute’. However, it is important to distinguish the logical subject from the grammatical subject. Let us look at this example: “We should elect John.” In this proposition, the grammatical subject is “we”. Is this the part of the proposition which is affirmed or denied? No. The proposition does not affirm or deny the term “we.” Rather, what is being affirmed is “the one that we should elect” which is the subject, while “John”
who will be elected is the logical predicate of the proposition. Just raise this simple question to identify which is the subject of a given proposition: What is being affirmed or denied?