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“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, I Want to be a Mathematician: An Automathography

“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.â€� 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

“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, Philosophy of Science: A Very Short Introduction