Epitext for Differential Logic and Dynamic Systems

Stand and unfold yourself.

Hamlet, 1.1.2

A Functional Conception of Propositional Calculus

Out of the dimness opposite equals advance . . . .      Always substance and increase, Always a knit of identity . . . . always distinction . . . .      always a breed of life.

— Walt Whitman, Leaves of Grass, [Whi, 28]

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Qualitative Logic and Quantitative Analogy

Logical, however, is used in a third sense, which is at once more vital and more practical; to denote, namely, the systematic care, negative and positive, taken to safeguard reflection so that it may yield the best results under the given conditions.

John Dewey, How We Think, [Dew, 56]

Philosophy of Notation : Formal Terms and Flexible Types

Where number is irrelevant, regimented mathematical technique has hitherto tended to be lacking. Thus it is that the progress of natural science has depended so largely upon the discernment of measurable quantity of one sort or another.

W.V. Quine, Mathematical Logic, [Qui, 7]

The Analogy Between Real and Boolean Types

Measurement consists in correlating our subject matter with the series of real numbers; and such correlations are desirable because, once they are set up, all the well-worked theory of numerical mathematics lies ready at hand as a tool for our further reasoning.

W.V. Quine, Mathematical Logic, [Qui, 7]

Theory of Control and Control of Theory

You will hardly know who I am or what I mean,
But I shall be good health to you nevertheless,
And filter and fibre your blood.

Walt Whitman, Leaves of Grass, [Whi, 88]

Reality at the Threshold of Logic

But no science can rest entirely on measurement, and many scientific investigations are quite out of reach of that device. To the scientist longing for non-quantitative techniques, then, mathematical logic brings hope.

W.V. Quine, Mathematical Logic, [Qui, 7]

Tables of Propositional Forms

To the scientist longing for non-quantitative techniques, then, mathematical logic brings hope. It provides explicit techniques for manipulating the most basic ingredients of discourse.

W.V. Quine, Mathematical Logic, [Qui, 7-8]

A Differential Extension of Propositional Calculus

Fire over water:
The image of the condition before transition.
Thus the superior man is careful
In the differentiation of things,
So that each finds its place.

I Ching, Hexagram 64, [Wil, 249]

An Interlude on the Path

There would have been no beginnings:
instead, speech would proceed from me,
while I stood in its path - a slender gap -
the point of its possible disappearance.

Michel Foucault, The Discourse on Language, [Fou, 215]

The Extended Universe of Discourse

At the moment of speaking, I would like to have perceived a nameless voice, long preceding me, leaving me merely to enmesh myself in it, taking up its cadence, and to lodge myself, when no one was looking, in its interstices as if it had paused an instant, in suspense, to beckon to me.

Michel Foucault, The Discourse on Language, [Fou, 215]

Intentional Propositions

Do you guess I have some intricate purpose?
Well I have . . . . for the April rain has, and the mica on
     the side of a rock has.

Walt Whitman, Leaves of Grass, [Whi, 45]

Life on Easy Street

Failing to fetch me at first keep encouraged,
Missing me one place search another,
I stop some where waiting for you

Walt Whitman, Leaves of Grass, [Whi, 88]

Back to the Beginning : Some Exemplary Universes

I would have preferred to be enveloped in words,
borne way beyond all possible beginnings.

Michel Foucault, The Discourse on Language, [Fou, 215]

A One-Dimensional Universe

There was never any more inception than there is now,
Nor any more youth or age than there is now;
And will never be any more perfection than there is now,
Nor any more heaven or hell than there is now.

Walt Whitman, Leaves of Grass, [Whi, 28]

The clock indicates the moment . . . . but what does
     eternity indicate?

Walt Whitman, 'Leaves of Grass', [Whi, 79]

Example 1. A Square Rigging

Urge and urge and urge,
Always the procreant urge of the world.

Walt Whitman, Leaves of Grass, [Whi, 28]

Back to the Feature

I guess it must be the flag of my disposition, out of hopeful
     green stuff woven.

Walt Whitman, Leaves of Grass, [Whi, 31]

Tacit Extensions

I would really like to have slipped imperceptibly into this lecture, as into all the others I shall be delivering, perhaps over the years ahead.

Michel Foucault, The Discourse on Language, [Fou, 215]

Example 2. Drives and Their Vicissitudes

I open my scuttle at night and see the far-sprinkled systems,
And all I see, multiplied as high as I can cipher, edge but
     the rim of the farther systems.

Walt Whitman, Leaves of Grass, [Whi, 81]