Demonstration, n.
Etymology: [L. demonstratio: cf. F. démonstration.]
1. The act of demonstrating; an exhibition; proof; especially, proof beyond the possibility of doubt; indubitable evidence, to the senses or reason. Those intervening ideas which serve to show the agreement of any two others are called "proofs;" and where agreement or disagreement is by this means plainly and clearly perceived, it is called demonstration. Locke.
2. An expression, as of the feelings, by outward signs; a manifestation; a show. Did your letters pierce the queen to any demonstration of grief Shak. Loyal demonstrations toward the prince. Prescott.
3. (Anat.)
The exhibition and explanation of a dissection or other anatomical preparation.
5 more senses
4. (Mil.) a decisive exhibition of force, or a movement indicating an attack.
5. (Logic)
The act of proving by the syllogistic process, or the proof itself.
6. (Math.)
A course of reasoning showing that a certain result is a necessary consequence of assumed premises; -- these premises being definitions, axioms, and previously established propositions. Direct, or Positive, demonstration (Logic & Math.), one in which the correct conclusion is the immediate sequence of reasoning from axiomatic or established premises; -- opposed to Indirect, or Negative, demonstration (called also reductio ad absurdum), in which the correct conclusion is an inference from the demonstration that any other hypothesis must be incorrect.
Shades of meaning
Demonstration, in the strict and proper sense, is the highest form of proof, and gives the most absolute certainty, but can not be applied outside of pure mathematics or other strictly deductive reasoning; there can be proof and certainty, however, in matters that do not admit of demonstration. A conclusion is the absolute and necessary result of the admission of certain premises; an inference is a probable conclusion toward which known facts, statements, or admissions point, but which they do not absolutely establish; sound premises, together with their necessary conclusion, constitute a demonstration. Evidence is that which tends to show a thing to be true; in the widest sense, as including self-evidence or consciousness, it is the basis of all knowledge. Proof in the strict sense is complete, irresistible evidence; as, there was much evidence against the accused, but not amounting to proof of guilt. Moral certainty is a conviction resting on such evidence as puts a matter beyond reasonable doubt, while not so irresistible as demonstration. Compare hypothesis; induction.