I am sometimes tempted by the following line of thought. But I am also deeply suspicious of it.
Are the 'laws of thought' 'laws of reality' as well? Since such laws are necessities of thought, the question can also be put by asking whether or not the necessities of thought are also necessities of being. It is surely not self-evident that principles that govern how we must think if we are to make sense to ourselves and to others must also apply to mind-independent reality. One cannot invoke self-evidence since such philosophers as Nagarjuna and Hegel and Nietzsche have denied (in different ways) that the laws of thought apply to the real.
Consider, for example, the Law of Identity:
Id. Necessarily, for any x, x = x.
(Id) seems harmless enough and indisputable. Everything, absolutely everything, is identical to itself, and this doesn't just happen to be the case. But what does 'x' range over? Thought-accusatives? Or reals? Or both? What I single out in an act of mind, as so singled out, cannot be thought of as self-diverse. No object of thought, qua object of thought, is self-diverse. And no object of thought, as such, is both F and not F at the same time, in the same respect, and in the same sense. So there is no question but that Identity and Non-Contradiction apply to objects of thought, and are aptly described as laws of thought. (Excluded Middle is trickier and so I leave it to one side.) What's more, these laws of thought hold for all possible finite, discursive, ectypal intellects. Thus what we have here is a transcendental principle, at least, not one grounded in the contingent empirical psychology or physiology of the type of animals we happen to be. Transcendentalism maybe, but no psychologism or physiologism!
But do Identity and Non-Contradiction apply to 'reals,' i.e., to entities whose existence is independent of their being objects of thought? Are these transcendental principles also ontological principles? Is the necessity of such principles as (Id) grounded in the transcendental structure of the finite intellect, or in being itself? Are the principles merely transcendental or are they also transcendent? (It goes without saying that I am using these 't' words in the Kantian way.)
The answer is not obvious.
Consider a pile of leaves. If I refer to something using the phrase, 'that pile of leaves,' I thereby refer to one self-identical pile; as so referred to, the pile cannot be self-diverse. But is the pile self-identical in itself (apart from my referring to it, whether in thought or in overt speech)?
In itself, in its full concrete extramental reality, the pile is not self-identical in that it is composed of many numerically different leaves, and has many different properties. In itself, the pile is both one and many. As both one and many, it is both self-identical and self-diverse. It is self-identical in that it is one pile; it is self-diverse in that this one pile is composed of many numerically different parts and has many different properties. Since the parts and properties are diverse from each other, and these parts and properties make up the pile, the pile is just as much self-diverse as it is self-identical. The pile is of course not a pure diversity; it is a diversity that constitutes one thing. So, in concrete reality, the pile of leaves is both self-identical and self-diverse.
If you insist that the pile's being self-identical excludes its being self-diverse, then you are abstracting from its having many parts and properties. So abstracting, you are no longer viewing the pile as it is in concrete mind-independent reality, but considering it as an object of thought merely. You are simply leaving out of consideration its plurality of parts and of properties. For the pile to be self-identical in a manner to exclude self-diversity, the pile would have to be simple as opposed to complex. But it is not simple in that it has many parts and many properties.
The upshot is that the pile of leaves, in concrete reality, is both one and many and therefore both self-identical and self-diverse. But this is a contradiction. Or is the contradiction merely apparent? Now the time-honored way to defuse a contradiction is by making a distinction.
One will be tempted to say that the respect in which the pile is self-identical is distinct from the respect in which it is self-diverse. The pile is self-identical in that it is one pile; the pile is self-diverse in that it has many parts and properties. No doubt.
But 'it has many parts and properties' already contains a contradiction. For what does 'it' refer to? 'It' refers to the pile which does not have parts and properties, but is its parts and properties. The pile is not something distinct from its parts and properties. The pile is a unity in and through a diversity of parts and properties. As such, the pile is both self-identical and self-diverse.
What the above reasoning suggests is that such 'laws of thought' as Identity and Non-Contradiction do not apply to extramental reality. No partite thing, such as a pile of leaves, is self-identical in a manner to exclude self-diversity. Such things are as self-diverse as they are self-identical. So partite things are self-contradictory.
From here we can proceed in two ways.
The contradictoriness of partite entities can be taken to argue their relative unreality. For nothing that truly exists can be self-contradictory. This is the way of F. H. Bradley. One takes the laws of thought as criterial for what is ultimately real, shows that partite entities are not up to this exacting standard, and concludes that partite entities belong to Appearance.
The other way takes the lack of fit between logic and reality as reflecting poorly on logic: partite entities are taken to be fully real, and logic as a falsification. One can find this theme in Nietzsche and in Hegel.