Mathematics is not a deductive science - that's a cliche. When you try to prove a theorem, you don't just list the hypotheses, and then start to reason. What you do is trial and error, experimentation, guesswork.

~ Paul R. Halmos

Paul R. Halmos Cliché Deductive Logic Experimentation Guesswork Hypotheses Mathematics Prove Reason Trial

Theologians, and religionists in general, start with a fantasy premise and then proceed to apply rigorous formal logic to tease out its implications. Stark himself points out that “theology consists of formal reasoning about God.” This is admirably exact. Theologians, beginning with a wished-for creation of their own minds, analyze that creation’s characteristics by rigorous application of the principles of formal—that is, deductive—logic.

~ Andrew Bernstein

Andrew Bernstein Deductive Logic Fantasy Logic Reasoning Religionists Theologians Theology

The word 'proof' should strictly only be used when we are dealing with deductive inferences.... Popper claimed that scientists only need to use deductive inferences.... So if a scientist is only interested in demonstrating that a given theory is false, she may be able to accomplish her goal without the use of inductive inferences.... When a scientist collects experimental data, her aim might be to show that a particular theory...is false. She will have to resort to inductive reasoning.... So Popper's attempt to show that science can get by without induction does not succeed.

~ Samir Okasha

Samir Okasha Deductive Logic Inductive Logic Karl Popper Logic Philosophy Philosophy Of Science Science