It was found in Peirce's unpublished papers that he defined the NAND operator and discovered that all classical logical operators could be replaced by combinations of NAND. What are some possible motivations for Peirce's use of only one operator(his NAND) to recreate the "and", "or" and "not" operators?

  • 3
    The issue about "minimization" of concepts/symbols/axioms is a driver for science and mathematics (as well as philosophy) development. Nov 9, 2020 at 10:37
  • Yes but there may have been more specific motivational forces guiding Peirce's efforts at minimization of operators. Perhaps De Morgan's laws or some remark by earlier logicians that 2 of the classical operators suffice to express all 3 if one of the 2 is "not"
    – GEP
    Nov 9, 2020 at 10:48
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    If you are studying logic, as opposed to using logic, then it is helpful to reduce it to its simplest form. If you are trying to prove something general about logical connectives, then the fewer there are the better. Also, it has practical consequences: electronic circuits often consist of a bank of NAND gates. It is useful not to have to create separate gates for different connectives.
    – Bumble
    Nov 9, 2020 at 17:53
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    It meant that he only had to have one type of IC in his parts bin.
    – Hot Licks
    Nov 9, 2020 at 18:22

2 Answers 2


See Charles Sanders Peirce, Collected Papers : Volume 4. The Simplest Mathematics (1933), page 13:

[4.12] A Boolian Algebra with One Constant [untitled paper c.1880]

Every logical notation hitherto proposed has un unnecessary number of signs. It is by means of this excess that the calculus is rendered easy to use [...]; at the same time, the number of primary formulae is thus greatly multiplied, those signifying facts of logic being very few in comparison with those which merely define the notation. [...] The apparatus of the Boolian calculus consists of the signs, [...]. In palce of these seven signs, I propose to use a single one.

Two propositions written in a pair are considered to be both denied.

And see [4.264] [from The Simplest Mathematics (1902)], page 215:

for example x⋏y [a sort of "harpoon" symbol] signifies that x is f and y is f. [...] With these two signs, the vinculum (parentheses, braces) and the sign , which I will call ampheck (from Ancient Greek ἀμφήκης, "cutting both ways") all assertions as to the values of quantities can be expressed.

  • I was hoping that you would post the descritpion of some attempt to minimize the operators before Peirce.
    – GEP
    Nov 9, 2020 at 16:44

Actually, my slightly snide comment above may be close to an answer. All possible logical operations can be produced with some combinations of NAND operations, meaning that only that one operator needs to be studied. While I have no idea how this would "simplify" philosophical problems, it would at least regularize the notation and perhaps make contemplation easier for folks with a "mechanical" thought process.

This certainly made early digital electronics simpler to deal with.

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