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We need heuristic reasoning when we construct a strict proof as we need scaffolding when we erect a building.
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p. 113

 

George Polya

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Intelligence has two parts, which we shall call the epistemological and the heuristic. The epistemological part is the representation of the world in such a form that the solution of problems follows from the facts expressed in the representation. The heuristic part is the mechanism that on the basis of the information solves the problem and decides what to do.
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The right way to think about the general problems of metaphysics and epistemology is not to attempt to clear one's own mind of all knowledge and start with 'Cogito ergo sum' and build up from there. Instead, we propose to use all of our knowledge to construct a computer program that knows. The correctness of our philosophical system will be tested by numerous comparisons between the beliefs of the program and our own observations and knowledge.

 

John McCarthy

 

The essence of a software entity is a construct of interlocking concepts: […] I believe the hard part of building software to be the specification, design, and testing of this conceptual construct, not the labor of representing it and testing the fidelity of the representation.

 

Fred Brooks

 

When I look at a building, how can I know there was a builder? Can't see him, hear him, touch him, taste him or smell him, so how can I know there was a builder? Well, the building is absolute proof there was a builder. I couldn't want better proof that there was a builder than to have the building as evidence. I don't need faith to believe in a builder, all I need is eyes that can see and a brain that works. Now the same deep, rich, scientific principle works with paintings and painters.... And the same principle works with God. When I look at Creation how can I know there was a creator? Well, creation is absolute proof there was a creator. I don't need faith to believe in a creator, all I need is eyes that can see and a brain that works.

 

Ray Comfort

 

You wish to be great, begin from the least. You are thinking to construct some mighty fabric in height; first think of the foundation of humility. And how great soever a mass of building one may wish and design to place above it, the greater the building is to be, the deeper does he dig his foundation.

 

Augustine of Hippo

 

Logic, n. The art of thinking and reasoning in strict accordance with the limitations and incapacities of the human misunderstanding.

 

Ambrose Bierce