No, a proof is sufficient but NOT necessary. A true proposition is true regardless of whether humans ever construct a proof for it. One more time: a proof pertains to justification, not truth — aletheist
"Proof" has the connotation of rigorous demonstration. We believe all kinds of things for which we do not have "proof" in this strict sense, but we nevertheless are justified in believing them.What is justification if not proof? — TheMadFool
There are reasons why the standard modern philosophical definition of knowledge is "justified true belief," rather than merely "true belief." Moreover, we are fallible knowers; some of our justified beliefs will turn out to be false.Why do we need justification if not to establish truth? — TheMadFool
What is justification if not proof? — TheMadFool
Why do we need justification if not to establish truth? — TheMadFool
All proofs are justifications, but not all justifications are proofs. — alcontali
What is justification if not proof? — TheMadFool
Proof, on the other hand is complete, 100%, justification - it's impossible to deny the truth that a proof supports. — TheMadFool
Do you agree with me? In other words I'm saying that justifications are not actually 100% sufficient to establish truth but a proof is 100% sufficient to do that. — TheMadFool
Most of our current beliefs are true, which is why we are generally able to get around successfully in the world, but we cannot know for sure that any one in particular is true. — aletheist
Yet the ultimate inability of rational analysis to defend any given proposition doesn't mean the proposition is false, with Zeno's paradox being the paradigmatic example — sime
There is no "proof" in induction, only evidence.Induction is a weaker system than deduction and what is justification in the former is proof in the latter. — TheMadFool
Induction is really the last step in inquiry, although it is ultimately cyclical. First is retroduction, the formulation of a plausible hypothesis. Next is deduction, the explication of what follows necessarily from that hypothesis in order to make predictions. Then comes induction, the testing of the hypothesis to see whether the resulting predictions are corroborated or falsified.However note that the utility of inductiom lies in deduction being applicable to knowledge so gained. — TheMadFool
First is retroduction, the formulation of a plausible hypothesis. — aletheist
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