By Reuben Hersh
Collection of the main fascinating fresh writings at the philosophy of arithmetic written by way of hugely revered researchers from philosophy, arithmetic, physics, and chemistry
Interdisciplinary ebook that may be valuable in numerous fields—with a cross-disciplinary topic sector, and contributions from researchers of assorted disciplines
Read Online or Download 18 Unconventional Essays on the Nature of Mathematics PDF
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Extra resources for 18 Unconventional Essays on the Nature of Mathematics
SOCRATES Then tell me, what is the difference between the rock and its reflection? HIPPOCRATES The rock is a solid piece of hard matter. It is made warm by the sun. If you touched it, you would feel that it is rough. The reflected image cannot be touched; if I put my hand on it, I would touch only the cool water. As a matter of fact, the reflected image does not really exist; it is illusion, nothing else. SOCRATES image? Is there nothing in common between the rock and its reflected HIPPOCRATES Well, in a certain sense, the reflected image is a faithful picture of the rock.
HIPPOCRATES Of course, he was right, and so were you, when you did not let us finish our discussion before we got to the heart of the question. But I think it is time for us to return to the city because the shadows of night are falling and I am hungry and thirsty. If you still have some patience, I would like to ask something while we walk. SOCRATES All right, let us start and you may ask your HIPPOCRATES Our discourse convinced me fully that I should start studying mathematics and I am very grateful to you for this.
But ‘plausible’, in the sense explained above, has nothing subjective or psychological about it. To assess whether a given hypothesis is plausible, one examines the reasons for and against it. This examination is carried out using facts which confirm the hypothesis or refute it, where these facts belong to the existing knowledge. Admittedly, such an assessment is fallible, because one’s choice of facts may be inadequate, and moreover the existing knowledge is not static but develops continuously, each new development providing further elements for assessing the hypothesis, which may lead to its rejection.