# Re: [peirce-l] Mathematical terminology, was, review of Moore's Peirce edition

```Irving wrote, quoting Peirce MS L75:35-39:

>"Deduction is only of value in tracing out the consequences of
>hypotheses, which it regards as pure, or unfounded, hypotheses.
>Deduction is divisible into sub-classes in various ways, of which the
>most important is into corollarial and theorematic. Corollarial
>deduction is where it is only necessary to imagine any case in which
>the premisses are true in order to perceive immediately that the
>conclusion holds in that case. Ordinary syllogisms and some deductions
>in the logic of relatives belong to this class. Theorematic deduction
>is deduction in which it is necessary to experiment in the imagination
>upon the image of the premiss in order from the result of such
>experiment to make corollarial deductions to the truth of the
>conclusion. The subdivisions of theorematic deduction are of very high
>theoretical importance. But I cannot go into them in this statement."
>
>
>[...] Peirce's characterization of theorematic and corrolarial
>deduction would seem, on the basis of this quote, to have to do with
>whether the presumption that the premises of a deductive argument or
>proof are true versus whether they require to be established to be
>true [...]```
```
I would disagree with this reading of the Peirce passage.  It seems
to me that the distinction he is making is, rather, between (1) the case
where the conclusion can be seen to follow from the premisses
by virtue of the "logical form" alone, as in "A function which is continuous
on a closed interval is continuous on any subinterval of that interval"
(whose truth is obvious without requiring us to imagine any continuous
function or any interval), and (2) the case where the deduction of the
conclusions from the premisses requires turning one's imagination
upon, and experimenting with, the actual mathematical objects
of which the theorem speaks, as in "A function which is continuous
on a closed interval is bounded on that interval".

-malgosia

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