When is a statement true
It advises you to make sure you can count up to four crocodiles one crocodile, two crocodiles,…,four crocodiles before you reach the same object as the car preceding you. If we are going to prove that the statement "If A, then B" is true, we would need to start by making the assumptions "A" and then doing some work to conclude that "B" must also hold.
Regardless, what matters is that this sentence is the kind of thing that is true or false. But many large cardinal set theorists seem to espouse a view of this sort. When you have an ambiguous sentence, you need to decide which statement it is being used to express.
This insight is due to Tarski. When I say, "I believe that the Riemann hypothesis is true," I just mean that I believe that all the non-trivial zeros of the Riemann zeta-function lie on the critical line.
The word "true" can, however, be defined mathematically. Do you know any reference graspable by non-logicians? This is a false statement. It seems to me that the Incompleteness Theorem is really a statement about this model, that no theory can prove every statement that is true in it.
Examples of true and false statements
We saw an example of a question which by itself is not a statement, but can be used to express a statement. When you have an ambiguous sentence, you need to decide which statement it is being used to express. It advises you to make sure you can count up to four crocodiles one crocodile, two crocodiles,…,four crocodiles before you reach the same object as the car preceding you. More about Statements So sentences that can be true or false are statements. In mathematics, the statement "A implies B" is very different from "A if and only if B. True or false? Someone may impatiently complain that the trains are always late to express their exasperation with the train system, but strictly speaking what they say is false. For instance: Ivan Slotvsky, the famous Irish builder of Madrid, is eating ham steaks and chutney at this very moment. Definition: Statements are the kind of sentences that are either true or false. The conclusion we are making is that there must be a cloud in the sky. If humans evolved from monkeys, how come we still have monkeys? Now, suppose he tried to express this by saying: I beat my wife up everyday. Humans did not evolve from monkeys. But the statement is true if it will be the case some day that I have a creepy next door neighbour in the next 39 years. How can I stop tailgating?
Now, perhaps this bothers you. This means that when A is false, the statement doesn't conclude anything. Ambiguous Statements One difficulty with statements is that they may sometimes express two different things.
Note in particular that I'm not claiming to have a proof of the Riemann hypothesis!
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