The key point of this is that there was never a sudden jump from “apple” to “non-apple.” The properties that causes the apple to become something else was already latent in the apple to begin with, and upon further analysis, you will always find that there is never a sudden “jump” but that every transition between categories is, in physical reality, actually connected through an infinite series of interconnected steps.

“Hard-and-fast lines” that separate things don’t really exist, because again, nature is really a singular interconnected whole, so those hard-and-fast lines always disappear upon deeper analysis. This doesn’t just apply to transitions over time, such as, one object changing into another over time, but also over space, such as, if you place two objects next to each other at the same time, there is no hard-and-fast line you can draw that unambiguously defines where the first object ends and the second object begins.

If one quality is perceived to change to another, it therefore logically necessitates that this change must, upon further analysis, be caused by an infinite series of quantitative interconnected steps connecting the two qualities together. The purpose of this law is to capture the concept of “continual change.”

The third law Engels mentions is negation of the negation, but this one is a lot more complicated and deals with a process of development, and there is debate as to whether or not it even belongs as a foundational logical principle. Mao, for example, did not think so and believed negation of the negation should not be there as a logical principle, and so if you read his On Contradiction, it explains basically everything I have said so far but makes no mention of negation of the negation.

Negation of the negation refers to any sort of system that has an internal cycle such that it always returns back to where it starts, but never exactly to where it started; with slight differences each cycle. If this system can keep a memory, then these differences each cycle can accumulate, causing the system to grow in complexity over time. Systems that develop in nature tend to have this structure.

The core of dialectics, though, is really the rejection of the law of identity; it is the rejection of the view that reality is really made up of the abstract objects we imagine in our heads. The first two laws naturally flow from that singular assumption.

Abstract identity, like all metaphysical categories, suffices for everyday use, where small dimensions or brief periods of time are in question. The limits within which it is usable differ in almost every case and are determined by the nature of the object. For a planetary system, where, in ordinary astronomical calculation, the ellipse can be taken as the basic form for practical purposes without error, these limits are much wider than for an insect that completes its metamorphosis in a few weeks. (Give other examples, e.g., alteration of species, which is reckoned in periods of thousands of years.)

For natural science in its comprehensive role, however, even within each individual branch, abstract identity is totally inadequate. Although it has now been largely abolished in practice, theoretically it still dominates people’s minds. Most natural scientists imagine that identity and difference are irreconcilable opposites, instead of recognizing them as one-sided poles that represent the truth only in their reciprocal action: in the inclusion of difference within identity.

…

Abstract identity (a = a; and negatively, a cannot be simultaneously equal and unequal to a) is likewise inapplicable in organic nature. The plant, the animal, every cell is at every moment of its life identical with itself and yet becoming distinct from itself, by absorption and excretion of substances, by respiration, by cell formation and death of cells, by the process of circulation taking place, in short, by a sum of incessant molecular changes which make up life and the sum-total of whose results is evident to our eyes in the phases of life – embryonic life, youth, sexual maturity, process of reproduction, old age, death.

The further physiology develops, the more important for it become these incessant, infinitely small changes, and hence the more important for it also the consideration of difference within identity, and the old abstract standpoint of formal identity, that an organic being is to be treated as something simply identical with itself, as something constant, becomes out of date. Nevertheless, the mode of thought based thereon, together with its categories, persists.

— Engels, Dialectics of Nature

Dialectical materialism is also not the same as historical materialism. Historical materialism is dialectical materialism applied to analyze the socioeconomic of human societies. Engels once compared historical Marx’s historical materialism to “what Darwin did but for the social sciences.” While Darwin is often associated with “survival of the fittest,” that’s not what Engels was referring to, but instead Engels was referring to the “gradual change” part.

Historical materialism sees human societies as constantly undergoing very gradual and subtle change every time a new piece of technology is developed, a new structure is developed, the infrastructure is expanded, a new institution is built, etc. All of these create very subtle changes to how society organizes productions, and if you accumulate them over thousands of years, then a society can change in such a way that the production process could be unrecognizable to what it was thousands of years before.

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