We explain what a tautology is in logic and we show you examples. Also, what are contradiction and contingency.
What is a tautology?
In the disciplines of logic and the rhetoric, the term tautology is used to refer to those self-evident, obvious or redundant statements, that is, that are true from any possible interpretation, since they explain and affirm themselves. Hence, a tautology is a argument fallacious, invalid, empty.
This term comes from the Greek voices tauto ("The same") and logos ("Word" or "know"), and its logical formulation often consists of A = A, that is, as something that is identical to itself, and therefore is not really proposing anything. This generally occurs in propositions that include the conclusion in its premises, such as "it is what it is" or "I saw it with my own eyes." In rhetoric, pleonasms are cases of tautology.
The simplest logical way to discover a tautology is through the formulation of truth tables: those cases that are true no matter what the expressed values are, will necessarily be tautological.
Examples of tautology
The following statements are examples of tautology:
- A man is a man.
- I ran the distance on my own feet.
- Everything that is more is left over.
- Things fell down.
- I climbed up the ladder.
- The cold is caused by the drop in temperature.
And in logical terms, an example of tautology is the expression: (p ^ q) → p, whose truth table would be the following:
| p | what | p ^ q | (p ^ q) → p |
| V | V | V | V |
| V | F | F | V |
| F | V | F | V |
| F | F | F | V |
Contradiction and contingency
In addition to tautology, contradiction and contingency are often spoken of in logic, as follows:
- Contradiction. Contrary to tautologies, which are true in any possible formulation, contradictions are false regardless of the values of their premises, since in their argumentative structure the conclusion to be obtained is denied. An example of this would be the statement "we fell to the heights", or the logical statement p ^ p 'when p is never equal to p'.
- Contingency. In this case, we are talking about formulas whose true or false value will not depend on the value of its premises, so it will be neither true nor false. Or what is the same: a contingency is a statement that is true in at least one possible world and false in another, so that it will always depend on the case. An example expressed in logical terms is the following statement:
(p ↔ q) v [(p → q) ^ (q → p)].