I'm referring to logical rules such as law of excluded middle, identity and contradiction.

Is logic a superset of another thing?

I'm a beginner in philosophy and I keep hearing that logic is just another language and another way of thinking among many, not sure what to make of it.

I am having a hard time of thinking anything outside of the given rules of logic.

Is there an example of such thought? I want to broaden my horizon on this subject and explore it, it's interesting to say the least.

  • Law of excluded middle does not always work: see intuitionist logic. Regarding law of identity it depends on what do you mean by "think". Law of noncontradiction also can be shown to be false: it is day now | no, it is night now on the opposite side of Earth.
    – rus9384
    Jun 20, 2018 at 19:23
  • Nocontradiction doesn't break in that case. It seems to be a misunderstanding in semantics, because we both know we talk about two different locations, nocontradiction would break if we talked about the same place being both night and day, no? Jun 20, 2018 at 19:43
  • No, because first sentence does not involve particular location. At the same time it does not mean former part is wrong, since it indeed is day somewhere (this side of Earth). I would say that every formal logical system is context-free, while real things depend on context.
    – rus9384
    Jun 20, 2018 at 20:21
  • @rus9384 >formal logical systems is context-free Yeah you are right, if we use logic as formal sentential system then I'd say most real life situations can't work in that system. But I'm more interested in the laws of logic as foundational concepts. Context included, we both can agree that you can't have square triangles and your screen can't be a square and a triangle at the same time? Jun 20, 2018 at 20:30
  • @rus9384, you are wrong. Philosophy teaches deductive reasoning different from math and rhetoric. In deductive reasoning SENTENCES are not used whatsoever. The LEM does indeed mean x is the same x at the same time location and context. The excuse that the sentence does not say all of that shoes lack of understanding and only literal reading. All you read is not literal so at best this is a hit or miss method of reasoning.
    – Logikal
    Jun 20, 2018 at 20:43

2 Answers 2


Consider writing a piece of music. You will have to admit that involves thought. You can argue there is a kind of logic, an aesthetic one maybe. But it is nothing like formal logic.

Natural language is full of https://en.m.wikipedia.org/wiki/Vagueness and formal logic is abstracted out of it, rather than preceding it, similarly to mathematics. Private language is as meaningless as private money, language and money derive their currency and value from communities of practice.

Even physics has to face this. Abstractions relate to real things, and can be evaluated as being more or less correct. Laws, including logic, then are created based on the given abstractions - but the laws are only as real as the abstractions are good, the laws don't truly have their own existence. This view is developed in 'How the Laws of Physics Lie by Nancy Cartwright' http://www.oxfordscholarship.com/mobile/view/10.1093/0198247044.001.0001/acprof-9780198247043

It must be noticed that abstraction always simplifies, it looks for core dynamics, it seeks to make things more computable. But reality remains ontically irreducible, and whatever it does that is what it is and how it behaves, however that violates our expectations or 'laws'.

"Meaning gets going because we move around and act on a world of other objects and agents; pragmatic engagements in the world, which logically precede language. It is these practical engagements, rather than the shared logical form of the Tractatus, that enable meaning. We do not mirror reality. We are enmeshed in it." https://www.the-tls.co.uk/articles/public/ludwig-wittgenstein-honesty-ground

It comes back to Popper also, who pointed out that science cannot be purely inductive, deriving results only from observations. Hypothesis generation is an essentially aesthetic practice, but only one held to the standard of being falsifiable but not being falsified. Mathematics also goes like this, with creativity, insight, and aesthetic judgements required, as well as logic.

Edit to add: You might also consider meditative states of mind, where a person shifts entirely to observation of mental formations, rather than engagement or participation with them. This state can be linked with 'flow', also an active way of being present in what you are doing, rather than analysing and critiquing it.

This topic put in mind also, of how philosophers have used logic to knock itself down, to draw out it's inadequacies and inconsistencies that show the limits of logical thought: https://absoluteirony.wordpress.com/2014/09/17/nagarjuna-nietzsche-rorty-and-their-strange-looping-trick/amp/For Wittgenstein the 'superset' is language games.

  • Can you give me a direct example where the rules of logic are bypassed or somehow don't work? I read your post, interesting stuff but I can't pull a clear example out of those so I can wrap my head around it. Jun 20, 2018 at 19:55
  • I re-read thought about it, I think everything you listed falls under rules of logic. Maybe it's a failure on my part but I don't see how they contradict the fundamental rules/laws of logic. Jun 20, 2018 at 20:06
  • Aesthetic choices. How is that not clear? My broader point that they are involved in all creative activity, even the application of logic. Music is especially illogical, because great writers like Bach generate their own musical logucs on the fly, like great poets generate new rhyming structures or reinvent them for new purposes. Logic is useful, I don't deny that it is meaningful. But I do deny that is foundational, or tells us neccessary truths about the world, only necessary truths derived from our mental toy-models of the world.
    – CriglCragl
    Jun 20, 2018 at 20:55
  • Perhaps my phrasing of the question was wrong. Generally I'm trying to find contradictions, examples where logic fails or is contradictory. For example the claims "Africa is on the planet earth" and "Africa is not on the planet earth", can't be true at the same time. I'd say aesthetic preference is just subconscious choice. they don't contradict logic. Jun 20, 2018 at 21:05
  • +1. But I've just noticed a typo : 'Even physics has to fa e thus.'. 'Face' ? And possibly 'face this' rather than 'thus'. 'Thus' could stand but I think you may well have intended 'thus'. Best : GT
    – Geoffrey Thomas
    Jun 20, 2018 at 21:14

Poincare didn't think so, he wrote:

What is the nature of mathematical reasoning? Is it deductive as commonly thought? Careful analysis shows us it is nothing of the kind; that it participates to some extent in the nature of inductive reasoning and for that reason is fruitful.

What he means by inductive reasoning by the way has nothing to do with formal mathematical induction - which of course is another form of deduction. He goes on to say:

The analytic process of construction does not compel us to ascend, but only to stay at the same level ... we can only ascend by mathematical induction, for from it alone can we learn something new. Without ... induction, construction would be powerless to create science.

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