Science of Logic also incorporates the traditional Aristotelian syllogism: it is conceived as a phase of the "original unity of thought and being" rather than as a detached, formal instrument of inference.
Thus Hegel's Science of Logic includes among other things analyses of being, nothingness, becoming, existence, reality, essence, reflection, concept, and method.
Hegel wrote Science of Logic after he had completed his Phenomenology of Spirit and while he was in Nuremberg working at a secondary school and courting his fiancée.
"[3] The German word Hegel employed to denote this post-dualist form of consciousness was Begriff (traditionally translated either as Concept or Notion).
The process of Being's transition to the concept as fully aware of itself is outlined in Book Two: The Doctrine of Essence, which is included in the Objective division of the Logic.
Conceptual (begrifflich) movement with respect to Being and Nothing is called Becoming, and takes the form of reciprocal Coming-to-Be (Entstehen) and Ceasing-to-Be (Vergehen).
[8] Hegel borrows Kant's example of the "hundred dollars" [Critique of Pure Reason (1787)] to emphasize that the unity of Being and Nothing in Becoming only applies when they are taken in their absolute purity as abstractions.
This term, the traditional English translation of the German word aufheben, means to preserve, to maintain, but also to cease, to put an end to.
[13] Hegel contrasts his logically derived concept of Reality from the earlier metaphysical one present in the ontological "proof" of God's existence, specifically Leibniz’s formulation of it.
[16] (Hegel's view is in this way contrasted with Kant's noumenon, the unknowable "thing in itself": Being-in-itself taken in isolation from Being-for-Other is nothing but an empty abstraction and to ask "what it is" is to ask a question made impossible to answer.
Yet they are held to be separate by this stage of thought and so the two terms are eternally stuck in an empty oscillation back and forth from one another.
True Infinity is properly represented by the "circle, the line which has reached itself, which is closed and wholly present, without beginning and end.
[40] The idea that the One is entirely self-subsistent and can exist without the Many is, according to Hegel, "the supreme, most stubborn error, which takes itself for the highest truth, manifesting in more concrete forms as abstract freedom, pure ego and, further, as Evil.
[43] Although in Hegel's estimation a triumph of the explanatory power of metaphysics over the physics based on sense perception as it was then practised, he believed that Kant’s Metaphysische Anfangsgründe der Naturwissenschaft [Metaphysical Foundations of Natural Science] (1786) retained many of the errors committed by the latter, foremost among these being that, since matter is given to the senses as already formed and constituted, it is taken to be such by the mind as well.
"[47] Hegel here sharply criticizes Kant's antinomy, put forth in his Critique of Pure Reason, between indivisibility and infinite divisibility in time, space and matter.
By taking continuity and discreteness to be entirely antithetical to one another, instead of in their truth which is their dialectical unity, Kant becomes embroiled in self-contradiction.
Although the progress through these modes displays the same sort of dialectical evolution as does the Logic proper, they are nonetheless entirely external to it because there is no inner necessity in the various arrangements imposed on them by arithmetical procedure.
As for math as a pedagogical tool, Hegel presciently had this to say: "Calculation being so much an external and therefore mechanical process, it has been possible to construct machines which perform arithmetical operations with complete accuracy.
At bottom of all these ideas, says Hegel, is an absolute opposition that is held to exist between the ego and its other, this latter taking the form, respectively, of art, nature and the non-ego in general.
The opposition is supposed to be overcome by the positing of an infinite relation between the two sides, the ego's level of morality, for example, ever increasing in proportion to a decrease in the power of the senses over it.
[61] Hegel here engages in a lengthy survey of the history and development of the Differential and Integral Calculus, citing the works of Cavalieri, Descartes, Fermat, Barrow, Newton, Leibniz, Euler, Lagrange, Landen, and Carnot.
The inexactitude of this method of procedure results, says Hegel, primarily from their failure to distinguish between Quantum as the Quantity that each individual term of a differential co-efficient represents, and the Qualitative nature of their relationship when in the form of a ratio.
The constant is nonetheless present as a simple Quantum, and is not an eternal beyond, making its self-mediation through the two terms of the ratio an example of True Infinity.
However, if we then take the constant produced by the ratio of the two sides as a self-subsistent Something in its own right, that is, a Being-for-Self, then the two formerly entirely distinct Qualities become its own sublated moments, their very natures now seen to have been in fact derived from this relation of Measure in the first place.
If this constant is adopted as the Unit, instead of an individual Real Measure, then what were two incommensurable series are now made commensurable with each other in a common denominator.
So, with a so-called "Quantitative" change, "one factor becomes preponderant as the other diminishes with accelerated velocity and is overpowered by the first, which therefore constitutes itself the sole self-subsistent Quality."
The immediate particular upon which Kant's judgement works is, in actuality, simply a nothingness posited by Reflection itself solely in order to generate its equally null universal, Essence.
The hidden, internal unity that bound the two moments of Identity and Difference together despite their apparent mutual indifference becomes explicit once they are mediated from the outside by Likeness and Unlikeness.
In a (uncharacteristically) readable three paragraph remark, Hegel criticizes the misuse of formal grounds, claiming that the sciences are basically built upon empty tautologies.
In the third major piece within the Science of Logic, Hegel introduces his idea of pure concepts within which he extends Kant's basic schemes of judgement and syllogism classification.