The basis for it is a mathematical principal of a limit, wherein a mathematical object is defined as a value or geometric construct that arises from indefinitely approaching but never actually attaining a specific output value as the input changes, which is useful for working with transfinite or hypperreal numbers and results in math that is otherwise undefined, like calculus.

In a similar manner of thinking, I was looking at post-humanist arguments and found this recurring tendency to break down the boundaries between arbitrary distinctions with gradual vagueness; that there is no black and white, no distinction between two ideas such as human and machine, or living and non-living, male and female, etc.

This was initially as a response to colonial Eurocentricism by breaking down the boundaries between different races and to overcome gender discrimination. What it did was show the gradient of middle grounds between any two bodies of people in order to overcome discrimination by showing they are ultimately the same.

But, in an increasingly technological civilization, it has diffused into many other subjects.

For one example in Donna Haraway's Cyborg Manifesto and Catherine Hayle's many critiques of society, they both look at the idea of breaking down the barrier between human and machine by perpetually pushing the boundary between the two until they become indistinguishable. A person may modify themselves with inorganic components, like a handicapped person may use prosthetic limbs, but taken to a greater extreme a person may modify their sensory to perceive new senses like Niel Harbisson or modify their brain to take out or insert modes or thought and alter their own DNA with research from the CRISPR experiments. This leaves one with the concept of the "cyborg" as an entity that can qualify as both organic and machine, which, itself is along a similar line to the ever popular singularity. This asks a question such as "If a person can turn into a machine, where do you draw the line?" The lack of an answer to which leads one to the conclusion that both human and machine must be categorizable under one functional relationship.

Or take for instance with the distinction between animals and humans: one can argue that the boundary between the two has been broken as any aspect someone considers unique to humanity can be found in other animals: dolphins (and possibly elephants) are capable of language and complex thought, perrots or ravens and many other birds are capable of empathy, many carnivora and rodents like dogs and rats are capable planning and coordinating with each other, some primates as well as some birds and some cephalopods are capable of creating and/or using technology, etc. And, unsurprisingly, biologists scientifically classify all animals and humans under the same taxonomical kingdom "anamalia."

I have seen this kind of limit logic argument where, one construct can gradually but perpetually approach the definition of a similar construct or their distinction made gradually vague, the conclusion is that they are (in some way) inevitably the same. It occurs somewhat frequently, so I am wondering if there is a consensus on the proper term for this kind of vague boundary argument.

  • In mathematics, there is a precise definition of limit. In general, I do not know any "logical" argument supporting the deduction of the identity of two "things" becoming gradually "more similar". – Mauro ALLEGRANZA Feb 4 '18 at 10:55
  • You can see Hegelian Dialectic for a mode of (not logical) argument that conclude from different (contradictory) "states" to a "unified" one. – Mauro ALLEGRANZA Feb 4 '18 at 10:57
  • On a conceptual point - In order for two things to be different they must be identical in some way, and in order for them to be identical they must be different in some way. The philosopher who comes to mind immediately is Hegel, and Kant seems relevant. For a complete formal reduction of all differences and distinctions there is also George Spencer Brown. I do not know a term for the specific approach you mention. – PeterJ Feb 4 '18 at 13:20
  • Nope. If I have two functions that describe a physical circumstance, neither of them ever have to be equal to each other in any way. I can have y=2t, and y=2t+1, and those equations have no solution where they are equal. – John Joe Feb 9 '18 at 16:31
  • Aha. It just came to me. The word is 'sublation'. – PeterJ Feb 15 '18 at 14:00

There is a term for such arguments, most commonly the sorites paradox, "also known as little-by-little arguments, which arise as a result of the indeterminacy surrounding limits of application of the predicates involved". The predicates susceptible to soritic reasoning are usually called vague rather than ambiguous ("ambiguity" is reserved for cases when the same term has a few sharply separated meanings rather than a continuum of variations). The prototypical vague predicate is "being a heap", "sorites" is derived from Greek σωρός, “heap”. One grain is not a heap, adding a grain does not make something a heap, therefore there are no heaps.

Soritic reasoning is often considered faulty, hence the alternative names like continuum or line drawing fallacy, the idea that distinction can not be made unless there is a "bright line" separating the two sides. But there is a genuine difficulty with pointing out where exactly the argument goes wrong, classical logic has to be modified or supplemented to do it formally. Still, in applications existence of grey areas does not preclude distinguishing clear cut cases and acting accordingly.

Soritic reasoning is common in postmodernist thinking, in some sense "dissolving all distinctions" is its signature move. It did not go unchallenged, however. The resonant Sokal hoax paper parodying postmodernist texts was sarcastically titled Transgressing the Boundaries. Zammito's Nice Derangement of Epistemes is a critical review of the history of postmodernism in science. His critique of Rorty's views applied more broadly:

"Setting out from Quine, Kuhn, and Davidson, Rorty has executed several elegant turns through Gadamer and Heidegger to come more and more to partner with Derrida... Rorty dissolves too many distinctions; his new "pragmatism" entails a cavalier disdain for rational adjudication of dispute. There has been a derangement of epistemes. Philosophy of science pursued "semantic ascent" into a philosophy of language so "holistic" as to deny determinate purchase on the world of which we speak. History and sociology of science has become so "reflexive" that it has plunged "all the way down" into the abime of an almost absolute skepticism".

Latour, a prominent American postmodernist, in Why Has Critique Run out of Steam? publicly regretted that social critique has gone too far:

"I myself have spent some time in the past trying to show “‘the lack of scientific certainty’” inherent in the construction of facts. I too made it a “‘primary issue.’” But I did not exactly aim at fooling the public by obscuring the certainty of a closed argument — or did I?.. And yet entire Ph.D. programs are still running to make sure that good American kids are learning the hard way that facts are made up, that there is no such thing as natural, unmediated, unbiased access to truth, that we are always prisoners of language, that we always speak from a particular standpoint, and so on, while dangerous extremists are using the very same argument of social construction to destroy hard-won evidence that could save our lives. Was I wrong to participate in the invention of this field known as science studies? Is it enough to say that we did not really mean what we said?"

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    It seems like Sorite's Paradox suffices, thank you for bringing that up. However, why is that argument itself called a paradox specifically? Why is it not simply something like "Sorite's Arguement?" In fact why are all those old paradox arguments themselves called paradoxes when the paradox is the thing they're trying to resolve? – John Joe Feb 5 '18 at 0:44
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    @JohnJoe Paradox generally refers to situations when two (or more) reasonable assumptions can not all be true, or at least seemingly so. The corresponding arguments are not trying to resolve it but rather to show that the assumptions are incompatible. It seems reasonable that adding a grain to not a heap won't make it a heap, and that heaps exist, yet under classical logic both can not be true, paradox. Currently there is no uncontroversial resolution to the sorites paradox, skeptic can say that all predicates are vague and all distinctions are illusory/subjective/pragmatic, etc. – Conifold Feb 5 '18 at 1:33

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