On Challenging the Laws of Logic

R.N. Carmona

In the past, I’ve argued that the laws of logic can be challenged or even violated. A response to my post on procedural realism and the Moral Argument mentioned that the laws of excluded middle and non-contradiction have been challenged by analytic philosophers. I found it curious that there was no mention of a challenge to the law of identity, since I think it’s the most easily challenged.

In order to challenge the law of identity, one need only challenge its underlying assumption, namely essentialist ontology. “The essentialist tradition, in contrast to the tradition of differential ontology, attempts to locate the identity of any given thing in some essential properties or self-contained identities” (see here). According to modern physics, as it now stands, all objects are atoms in flux and empty space. Where then is the atomic glue that holds a table or chair together and how does one differentiate between two chairs that look precisely alike without presupposing the essentialist tradition?

The essentialist tradition begs the question when concerning identity, since there’s no way to prove that any one object has essential properties. Interestingly, the reason for presupposing the essentialist tradition might have everything to do with personal identity. People are animate objects, but objects nonetheless. Without essentialism, we can no longer assume that we have a distinct identity. Physically, we are atoms in flux and empty space as well and thus, what we’re left with are second order grounds for personal identity. In other words, we can avoid talk of atoms and empty space and instead look to DNA, neurons, brain anatomy, and so on. In this way we retain our uniqueness without first order grounds.

That aside, if we instead argue from the basis of differential ontology, the law of identity is no longer as unassailable as it appeared. As stated, we would rely on second order grounds. “Differential ontology…understands the identity of any given thing as constituted on the basis of the ever-changing nexus of relations in which it is found, and thus, identity is a secondary determination, while difference, or the constitutive relations that make up identities, is primary.” We would therefore ignore notions of a stable identity and instead look to differences between objects.

Given this, the law of identity (A = A) will be replaced with the law of distinction, i.e., something like A =/= B or C or D and so on. Since A is not B or C or D, then we identify A because it is contrasted with objects in relation to it. We are no longer assuming that there are essential properties that make A, A. This is, after all, what we say of ourselves. We do not say I am me because I have essential characteristics. Instead we contrast ourselves with others; we factor in physical appearance, ethnicity, gender, personality, and so on. We then add other factors like level of income and education, personal tastes, and so on. Clearly none of these characteristics are essential.

Ultimately, the law of identity is not unassailable and can be challenged by uprooting its essentialist assumption. One way of doing so is by positing differential ontology. One can, however, do so by positing human consciousness. In other words, another traditional philosophical assumption (contra-pragmatism) is that there’s a deeper reality that goes beyond our everyday experience; perhaps quantum mechanics hints at this. On the basis of this, we cannot draw ontological conclusions on the basis of our faculties. In other words, the four chairs and dining room table in my living room look distinct because my faculties see them as such. In reality, however, there’s nothing but atomic flux and empty space. This is in no way an attempt to undermine the usefulness of our faculties, but if there’s a deeper layer to reality that we cannot capture, then there’s no way we can argue for essential properties. Furthermore, we wouldn’t be able to argue from difference either. We would, in other words, have to assume the accuracy of our faculties in order to argue for a law of identity.

One comment

  1. 문재경 (Moon)

    I don’t think the law of logic is unassailable or self-evident truth, but I also think your argument against the law of identity is highly questionable because of following reasons:

    1. I don’t understand how our modern physics undermine the identity or the difference. If this argument succeeds, then there are nothing differentiable in reality. But that conclusion is obviously absurd. Yeah, there are only atoms in flux and empty space in atomic level, but that doesn’t make something indiifferentiable to another because that atoms in flux and empty space make properties which make something differentiable to another. some atoms and empty space makes some distinct properties to chair like hardness and some other atoms makes some distinct properties to water like inflammability. Even seemingly same kind of things have different properties like locations, timing, etc. This means there are actual identities and differences in reality and there are no needs to appeal to the accuracy of our faculties to get this conclusion. Moreover, I just wonder, do atoms not have distinct properties? are they indifferentiable to the other? Is one atom exact same as the others? If not, then the identity and the difference is preserved even if your argument succeeds.

    2. I don’t think essentialism begs the question. To say something begs the question, you must show that it has its conclusion in its premise. But what you show us is just essentialism merely assumes there are essential prorperties. This mere assumption doesn’t make it beg the question. That fact just make it baseless. And actually, I don’t even think essentialism is baseless. You think that to make philosophical stance not be baseless there are some way to prove it empirically. But I think that standard is too high. All we need to make it have basis is just some evidence which is directly or indirectly towards it and philosophical arguments about it. There are many of them for essentialism(given by Aristotle and many philosophers in history), so the basis of essentialism is obtained.

    3. I don’t think differential ontology makes a challenge to the law of identity. If you want to challenge the law of identity, then you must show us that A≠A and A=~A which means something isn’t itself. But differential ontology doesn’t show that. Differential ontology only argues that essentialism falsely assumed that difference is made by essential identity and insist that actually the identity is made by the difference. In other words, It argues that essentialism thinks A=A makes A≠~A and in contrast differential ontology thinks A≠~A makes A=A. So as you can see, It just insists that the difference is more fundamental that the identity, and doesn’t show us something isn’t itself. Yeah, maybe identity in differential ontology is constantly changing and not a single, essential one, but as long as it doesn’t make A≠A, it isn’t problem for the law of identity. As a result, differential ontology doesn’t make a challenge to the law of identity. And this conclusion implies the law of identity doesn’t assume essentialism because it can stand without it.


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