In order to do any philosophy, one needs a little bit of logic. In the next few posts, I am going to try to provide a short introduction to some of the most important components of the study of arguments.
Suppose you are out for a walk on the beach. You come across a piece of paper. On it is a hand-written declarative sentence. You don’t know who wrote it, or where it came from. You consider the meaning of the sentence, and you think that what it says is false. When you understand a declarative sentence, you know the conditions under which it would be true. In this case, those conditions have not been met. Hence, it is false.
Suppose it troubles you that the sentence is false. You are irritated about such false sentences being left about for people to read and, perhaps, to believe. You don’t blame the sentence. After all, the sentence hasn’t done anything. So, you blame whoever wrote it.
As you look around, you realise that even if you find the person who wrote it, it will be a further question as to whether she used the sentence to say what she believed. Perhaps you find the author and it turns out she wrote the sentence to illustrate a point of grammar, or she was writing a script for a play. In those cases, the author won’t necessarily believe what she wrote.
Only if she asserted the sentence would you challenge her belief. Assertion is a kind of force for the use of sentence. One can use sentences with different kinds of force. Imperatival force is the use of a sentence to issue a command. If one uses a sentence to ask a question, one is using it with interrogative force.
Ordinarily, the grammatical form (or mood) of a sentence matches the force with which it is used. One usually uses questions with interrogative force, commands with imperatival force, and declarative sentences with assertoric force. But sometimes grammatical form doesn’t match the force of its use. A person might assert something by using a question (rhetorical question). One might also use a declarative sentence with interrogative force. Or someone might even use a command to ask a question. A declarative sentence used with assertoric force is a statement.
Suppose the sentence was written in German. You understand it and so does the author. Your friend who is with you doesn’t, so you translate it. Now you have two statements, one in English, the other in German. Both you and your friend disbelieve the statements. Do you and your friend disbelieve two things?
Many suggest that, strictly speaking, one doesn’t believe or disbelieve a sentence even when it is asserted (i.e., a statement). Consider two sentences, one in German and one in English. “Snow is white” and “Schnee ist weiß” are two different sentences saying the same thing. Hence, what is believed is whatever they both say. And so, we arrive at the object of belief. This object is a proposition, either an abstract or mental item capable of bearing a truth value, either true or false, and expressible in a statement.
Now, we have unpeeled the proposition from under its various layers, we need to know a few things about it.
Propositions are truth bearers
First, propositions bear or carry truth values. They are either true or false. Although sometimes contested, the principle of bivalence says that there are only two truth values. There are no such values as ‘truish’ or ‘falsish.’
Again, although sometimes contested, propositions follow the laws of thought. According to the law of noncontradiction, a proposition cannot be both true and false. Thus, it cannot be true that Jesus rose from the dead and Jesus did not rise from the dead. The law of identity says that if a proposition is true, then it is true. Sounds strange, but it is important because otherwise a proposition could be true for you and false for me. Jesus rose from the dead can’t be true for me and false for someone else. If it’s true, it’s true.
According to the law of excluded middle, a proposition is true, or its negation is true. If a statement is not true, then it is false. If a statement is not false, then it is true. In other words, if it is a proposition, it must have a truth value. The proposition Jesus rose from the dead can’t lack a truth value. It must either be true or false.
What makes a proposition true or false isn’t up to us or decided by convention. It is up to the way the world is. More precisely, a proposition is made true by a state of affairs in the world. The state of affairs of Jesus rising from the dead makes the proposition Jesus rose from the dead a true proposition.
We have attitudes towards propositions
Propositions are abstract or mental objects to which we have propositional attitudes. An attitude is a mental state towards something. Propositional attitudes are rational mental states that we have toward propositions. We believe them, disbelieve them, or withhold judgment on them. Usually, we have those attitudes based on reasons or a lack of reasons. Some beliefs we have automatically without any apparent reasoning process. We will have much to say about belief when we talk about theories of knowledge in a future post.
It is important to notice that we also have other kinds of attitudes towards propositions such as hope, fear, love, and delight. These kinds of attitudes are related to our desires and are vital to the Christian life. We both believe and delight that Jesus rose from the dead. We rely on the work of the Spirit to bring about delight and joy in our Christian beliefs.
Logical and modal statuses
Some propositions cannot be true, and some must be. For example, it cannot be true that Jesus rose, and he didn’t, or that God exists, and he doesn’t. Such propositions are self-contradictory. They are necessarily false, or not possibly true.
Some propositions must be true. For example, either Jesus rose from the dead or he didn’t cannot be false. He either did or he didn’t. The statement exhausts all the possibilities. If a weather presenter wants to avoid being wrong, she could deploy this strategy: “either it’ll rain or it won’t, either it’ll be warm, or it won’t.” Dull, but never wrong!
Some propositions are possibly true. For example, it is possibly true that Jesus rose from the dead. Someone might suggest that miracles are impossible, but they don’t usually mean logically impossible. They mean, given what we know about dead people (they stay dead) and the laws of physics, dead people don’t rise from the dead. But there isn’t anything illogical about a person rising from the dead.
Most propositions we express are contingently true. They are true but possibly false. Jesus rose from the dead is true but not necessarily so. God could have refrained from creating the world, or he could have made a different one in which Jesus didn’t die. Any contingently or necessarily true proposition is automatically possibly true.
Logical possibility is important for our doctrines. Many objections to the Christian faith are about whether they are possibly true. Defending doctrines of the incarnation and Trinity often involve showing that they are possibly true. Solutions to the logical problem of evil also involve possibly true propositions.
There are statements that, though logically possible, can’t be true due to the nature of an object. For example, it is not possible that I am a number. It isn’t in the nature of a human being to be a number just as it isn’t possible for a number to dance a jig.
Our theology is affected by this concept of necessity. In some arguments for the existence of God, it is claimed that God has existence by nature. Consider, “God exists” and “God does not exist.” Neither are contradictions. Hence, neither is logically impossible. But many believe the latter cannot be true. If God exists is true, it is necessarily so. It is not a logical necessity, but an informal one based on the nature of God. God has, as one of his properties, necessary existence. Since that is part of his nature, he cannot fail to exist. Hence, “Necessarily, God exists” is true. We will meet this kind of idea in the ontological argument for God’s existence.
Statements in arguments
Although I have been talking mostly about propositions, I will mostly refer to propositions used in arguments as statements. And what counts in our study of logic is the relationship between statements. Statements relate to one another in all sorts of ways. Some statements are consistent with one another. Both can be true at the same time. For example, the statement that Paul wrote the book of Romans is consistent with the statement that Paul never went to England.
Other statements cannot both be true. They are inconsistent. For example, the statement that Jesus rose from the dead is inconsistent with the statement that no one has ever risen from the dead. Statements often imply other statements. For example, if it is true that God created the universe, then it is also true that he created you.
Implication is a vital ingredient for an argument. It is a relationship between statements that moves the reader/hearer from one belief to another in a logical way. Arguments attempt to relate statements in such a way that one statement follows from other statements. The statement that follows is called a conclusion, and the statements from which the conclusion follows are called premises. It is to those sets of statements we will turn in the next post.