Logical Limits

I've come across some very profound ideas from what can be implied using logic, and I figured I'd itemized them here:

  • super-determinism
  • linguistic
  • epistemological


The Bell Test experiments in the late 1900s seemed to show the world that determinism was incompatible with reality as quantum states were unpredictable and thus undetermined. However, in determinism's place super-determinism arose. This theory postulated that if everything is deterministic, then our thoughts were too. Thus it is feasible that our determined thoughts compelled us to perform experiments in such a way that we believe there to be no determinism. This is extremely troubling as the backbone of science is independence experiments, i.e. that it is possible to redo the experiment with varying non-confounding (or suspected non-confounding) variables to determine a real cause. However, if it is impossible to perform experiments independent of non-relevant physical world variables, then it is possible that our experiments aren't truly measuring reality, only some cosmic coincidence. The way I think of it is, if the universe has some "order" of instructions to do things, then makes sure result a only occur when experimenter Alice does her experiment, then switches back to result b, then it is impossible to know. To aid in understanding, the current assumption in science is that if the universe was doing this, then we could do the experiment when the universe is producing result b and "catch" it in the act. Thus free-will is important and assumed in science.


When we think, we think in symbols. But these symbols have limitations. Suppose super-determinism is true. I claim that it is impossible to fully realize the extent of your determinism as an intrinsic limitation of language. Suppose you think a thought, and that thought realizes the full extent of super determinism. However, it can't have done that as that thought was newly determined and thus couldn't have been a part of the extent to which your past thoughts have been determined. QED. In simpler terms, let t be the thought and T(t) be realizing the full extent of thoughts E. Then T(t) = E, but E must realize the thought realizing the extent, so E = T(T(t)). By induction, there is an infinite thought required to do this and thus is impossible (although some people do reject the principles of induction because of infinity, maybe a future post, I need to ruminate further on this). For an expansion on this issue, see [1].


The existence of the problem of the criterion is very profound for logic. Consider we claim to know something, A. Then we can simply ask why or how and we would need to know another thing to justify it. Obviously we believe we know things, so there must be some resolution to this being accepted. This is the Münchhausen trilemma, which says that we either accept knowledge unfounded (dogma), need an infinite chain of reasoning, or use circular logic. Even the application of logic is problematic. Suppose we have that p->q. Then we have p. Now it seems obvious that q is true, however, this has to be assumed through use of modus ponens. I found this was very easy to understand through What the Tortoise Said to Achilles [2]. This thought was very troubling for my previous idealistic philosophy, as it implied that humans with free-will and intellectual thought are unfounded and illogical at its very core. Furthermore, the premise of logic is to get at the truth through deduction, but the act of deduction seems to have more logical justification for its acceptance. This weakens my previous belief in mankind's ability to solve problems with logic and thought. Moreover, in using logic we assume that we follow the Laws of Thought (no contradictions, every statement is true/false [by far the weakest one], and whatever is, is). Thus this suggests the existence of other Laws of thought and arbitrariness into logic.

I find the existence of these issues with the premise of logic compelling reasons to simply just accept sensualism and live life with no mind. This idea will be built further in a later post on reality.

[1] https://listed.to/@vt/34211/logical-limits
[2] https://en.wikipedia.org/wiki/What_the_Tortoise_Said_to_Achilles

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