Abstract
In this chapter I consider the role played by fundamental metaphysical categories and, in particular, their relation to metaphysical commitments regarding the status of logic, in the philosophy of Leibniz, Kant and Peirce. In doing so, I show how Kant’s critical project is deeply grounded in his response to Leibniz’s categorical metaphysics, and I assess the implications for Kant’s critical project of the decisions he makes concerning the philosophical status of logic. In particular, Kant’s response to Leibniz dovetails with Kant’s overall tendency in the critical project to prioritize practical over theoretical rationality. Peirce, in turn, takes up Kant’s prioritization of practical over theoretical rationality but with a renewed commitment to a more traditional logical orientation, with the consequence that theoretical rationality is collapsed into practical rationality in Peirce’s pragmatic philosophy.
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Notes
- 1.
I have replaced Adam’s translation ‘requirement’ by ‘requisite’, which is cognate to the Latin term. I see no good reason not to use the cognate English term, and indeed translating the term as ‘requirement’ abets Adams ’ construal of it as a necessary condition.
- 2.
Walford and Meerbote translate the Latin term ‘consequenter’ by “consequentially,” but again here I see no reason to depart from the English cognate.
- 3.
Kant does not make this point explicitly, referring the reader back to the earlier discussion of the syllogism, but the point seems clear.
- 4.
My basic view is that although anti-psychologism remains an unattainable ideal, it is an important ideal nonetheless, and one susceptible of progressive, partial attainment.
- 5.
Note that the form of appeal would in this case be entirely different than Kant’s appeal to a priori spatial and temporal forms of intuition. Brouwer and Husserl would be potential candidates, depending on how their positions are understood.
- 6.
The Turisi edition of the Lectures supplies a comma here, which is missing in the Indiana edition. Since I do not understand the sense with the comma supplied, I have omitted it.
- 7.
For now, the reader is recommended simply to substitute ‘generality’ for the term ‘Thirdness’; it corresponds to the category of Representation in the “New List of Categories” discussed above.
- 8.
It seems there is potentially a problem here analogous to the problem we have met repeatedly above: is Peirce assuming the possibility of the Pragmatic Principle having a meaning in order to determine its meaning? This recapitulates the assumption of the Cartesian ontological argument which Leibniz criticized. For now, I defer this issue.
- 9.
One consequence of Peirce’s approach is that his resolution of the paradox will hold equally for a game in which a (countably) infinite number of players play simultaneously against the bank.
- 10.
This ‘p’ should not be confused with the ‘p’ above representing the probability; Peirce’s choice of letters is unfortunate.
- 11.
Since p is a variable function of n in this problem, it doesn’t ultimately matter whether this proportion (more accurately: the derivative) is constant, but it helps to make this simplifying assumption in thinking of the problem. What is required is the infinitesimal linearity of the derivative, or, in the case of a problem in finite, discrete mathematics that the scale of the problem is “large enough.” We also do not require that the derivative be everywhere small: it is enough that it be close enough to zero near the optimal value.
- 12.
There are further issues about hunting for maximum versus minimum values that I also leave aside.
- 13.
The notion of total variation may profitably be compared to the notion of total form, as in William Blake . Indeed, we might conjecture that the former is a differential version of the latter.
- 14.
For a counterexample, see the conclusion of Hands Across the Table, directed by Mitchell Leisen, with Fred MacMurray and Carole Lombard .
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Bassler, O.B. (2018). Principles and Categories from Leibniz to Peirce in Five Easy Steps. In: Kant, Shelley and the Visionary Critique of Metaphysics. Palgrave Macmillan, Cham. https://doi.org/10.1007/978-3-319-77291-2_3
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