Hypothesis has different interrelating meanings in different contexts, but no overarching simple definition that describes all of them exactly.
In Formal Logic and in Mathematics
The most primitive and original meaning of “hypothesis” appears to be simply whatever we’re reasoning FROM in a logical argument. This belongs to a view of logic that says the purpose of logic is not so much to establish absolute truths, but to find out what follows from what else. Then whatever something follows from is the hypothesis of the argument that the “something” indeed follows.
In formal logic and mathematics hypothesis is defined as: “The antecedent clause of a conditional statement.” Where antecedent is defined as: “The conditional element in a proposition” (as if A in “if A, then B”) and a conditional statement is a statement of the form “if A, then B”.
Example: If a number is divisible by 10, then it is divisible by 2 is a conditional statement whose hypothesis is: “if a number is divisible by 10” and whose conclusion is: “then it is divisible by 2”.
Quite commonly in mathematics we use the so-called “If-Then” statements.
- If two odd natural numbers are added, then the sum is an even natural number.
- If the same expression is added to both sides of an equation, then the new equation is equivalent to the original equation.
- If the product of two real numbers is zero, then at least one of the factors is zero.
- If a and b represent real numbers, then exactly one of the following is true:
- a < b
- a = b
- a > b
In each of these statements, the “if clause” is the hypothesis and the “then clause” is the conclusion.
As a technical term within logic, the meaning of “hypothesis” is exactly synonymous with “assumption”.
It is important to observe and remain aware of the fact that no assertion is made about the truth value of the hypothesis. Only that IF the hypothesis is true, then the conclusion must be true.
Consider the following statement:
If my children were born after 2000, then they are less than 50 years old.
That statement DOES NOT imply that my children are less than 50 years old. However, the statement is True.
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