No natural turn for mathematics




Triadic Philosophy is post-mathematical. That is, it sees math as a utility somewhat like logic itself. It needs some prompting from freedom and will so that it is not used for nefarious purposes. Logic stands above it a bit because it is more clearly good, even though it too can be put to the lesser objectives.

Misrepresentation based on logic and mathematics is hardly foreign to us. We should remember that Triadic Philosophy is in full agreement with Peirce on the following premises:

The condition of existence is continuty.

The character of existence is agapic laced with a good measure of fallibility.

Noting similarities between logic and mathematics is Peirce’s way of suggesting that logic is no less exact and beautiful than its companion.

It is easier to progress in math as it requires no real contact with the world. It is abstraction. Its contact is ultimately an application of its abstractions to reality.

With logic, we must engage in a conversation with the hearts and minds of individuals. I have little doubt that this is where we are headed. Getting there is what this is all abut.

Peirce: CP 2.81 Cross-Ref:††

81. Some mathematicians, eminent for their success in their science, and who have particularly attended to the philosophy of it, regard Mathematics as a branch of Logic.†3 This is the more worthy of notice because it might with much justice be contended that mathematics is almost, if not quite, the only science which stands in need of no aid from a science of logic. Moreover, according to the opinion defended in the present treatise, logical truth is grounded upon a sort of observation of the same kind as that upon which mathematics is grounded. For these reasons, it is desirable at once to examine the nature of the mathematician’s procedure pretty thoroughly. I have reason to be confident that this study will be of aid to some of those who have no natural turn for mathematics. At the same time, I am bound to say that mathematics requires a certain vigor of thought, the power of concentration of attention, so as to hold before the mind a highly complex image, and keep it steady enough to be observed; and though training can do wonders in a short time in enhancing this vigor, still it will not make a powerful thinker out of a naturally feeble mind, or one that has been utterly debilitated by intellectual sloth.