The Trivial Commandments
- Thou shalt read as much as thou canst.
- Thou shalt think for thyself.
- Thou shalt not take the name of “proof” in vain
Three meanings of “proof”
Proof means different things according to who’s talking. I see several current uses of the word: mathematical proof; scientific proof; religious proof.
Religious proof, or proof by faith, is explained by St. Paul [Heb.11]: </Faith is the assurance [proof] of what we hope for … the evidence of things unseen … It is faith that enables us to see that the universe was created at the command of God …”/>
Mathematical proof, based on formal logic, is structured on premises (“SOME | ALL | NONE | EXISTS” assertions). Such assertions are set out as material for reasoning/argument. Premises are then linked with logical operators (e.g. IF, TRUE, FALSE, NOT, AND, OR, THEN, IMPLIES, THEREFORE, IFF [short for “if and only if”]) to form an argument (e.g. syllogism, antilogism, sorites chain) in support of a conclusion (another assertion).
In case any of the premises of a logical proof be found false or uncertain, the argument falls, and hence the conclusion is unproven. If the structure of the argument (syllogism, antilogism, sorites chain) is faulty (fallaceous), the argument is unsound and the conclusion unproven.
Scientific proof treats of evidence collected from observations on phenomena and constructed experiments, enlisting formal logic, mathematical modeling, statistics. The discipline of mathematical proof (under the rules of formal logic) necessarily underlies the reasoning in scientific proof. When a logical fallacy appears on examining a scientific proof, the proof fails.
Religious proof exempts itself (by St Paul’s explanation in Heb.11) from the rules of mathematical (and thus also scientific) proof. For this reason, to confuse religious proof and formal, classical proof is an empty exercise.