Can U falsify(prove false) a tautology or a self-evident proposition(ie axiom)? What kind of proposi

Can U falsify(prove false) a tautology or a self-evident proposition(ie axiom)? What kind of *meaningful* propositions can you falsify?

Can U falsify(prove false) a tautology or a self-evident proposition(ie axiom)? What kind of propositions can?windows messenger

A tautology is a statement that is true by definition. More precisely, it is a statement in which the subect and the predicate contain the same information. e.g. "A bachelor is an unmarried man."

It makes no sense to speak of proving a tautology false.

Disproving an axiom doesn't make sense either: accepting axioms like the law of contradiction (A and not A is always false) are preconditions for proving anything at all.

HOWEVER, one can prove that an axiom is unnecessary, and should therefore be either discarded or treated as one of a number of alternative axioms.

A good example of the latter would be the fate of the parallel postulate--an axiom of geometry that states that two parallel lines have no points in common.

This axiom was regarded as a necessary truth from the time of Euclid to the nineteenth century. Then some prominent mathematician (I forget his name) tried to create a geometry in which which parallel lines always meet at two points.

To the surprise of those who thought that Euclid's geometry represented necessary truths, this new geometry proved to be consistent. In fact, assuming that parallel lines meet at two points produces the geometry of the surface of a sphere, rather than a Euclidian plane. The "lines" on the sphere are great circles, or circumfrences, which always meet at two points.

Other geometries have been developed too.

Can U falsify(prove false) a tautology or a self-evident proposition(ie axiom)? What kind of propositions can?microsoft works internet explorer

Obviously, one can not falsify a tautology as such. One might falsify a proposition that had been mistakenly thought to be a tautology, though.

This could happen through the discovery of an unexpected ambiguity in the terms of the initial statement.

Example: "Atoms can't be divided."

On one level, this is a tautology. "Indivisible" is the literal meaning of the Greek word "atom". Indivisibles are indivisible. What could be more tautological than that?

But what could have been more convincingly falsified?

The way out of confusion here is to see that there is a important distinction (unknown to the Greeks, and still unknown to those who first developed atom-based chemistry in the modern era) between chemical division and physical division.

Atoms are the smallest units of chemistry. By definition, they can't be divided further by chemical means or into "chemical" units. But they can be physical "split" as the death count at Hiroshima testifies.