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What are some popular theories/opinions in philosophy against the certainty placed on the laws of logic and its results?

You would think philosophers wouldn't ever criticize or try to debunk logic or any part thereof, considering philosophers deals with logical ideas; but you would at least think that there were some doubts, theories and ideas that were advanced that put some doubts to the foundation of logic, parts thereof, and results derived from it.

Can you think of any such theories/opinions?

  • Most philosophical ideas are not "logical", and philosophers criticize existing logics and develop new ones all the time since Aristotle, you'll have to be more specific. See e.g. SEP The One Right Logic? on the modern criticisms of classical logic. – Conifold Aug 20 at 20:02
  • Logic is not my “specialty” but you may like this book “Walking the Tightrope of Reason” Robert Fogelin. amazon.com/Walking-Tightrope-Reason-Robert-Fogelin/dp/… – Gordon Aug 21 at 1:33
  • All logic is constrained by time, space, and causation; it is limited to the empirical world. Buddhistic and Vedantic philosophy recognizes that all logic is eventually circular and self-referential. – Swami Vishwananda Aug 21 at 5:14
  • It seems to me philosophers debunk logical results as a matter of course. Most endorse views that fail in logic then blame logic for being useless. It's an odd business. It leads to the view that metaphysics is useless, a view that depends entirely on rejecting ordinary logic. . . – PeterJ Aug 21 at 11:18
  • @PeterJ "It leads to the view that metaphysics is useless, a view that depends entirely on rejecting ordinary logic" What? How does dismissing metaphysics entail dismissing ordinary logic? (Also, what precisely is "ordinary logic"?) – Noah Schweber Aug 21 at 21:25
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There are various paradoxes of logic that indicate to a certain degree that it is not entirely certain. The one of these that has gotten the widest coverage is Russel's paradox that demonstrated the naive notion of containment has a flaw, and cannot be arbitrarily combined with both negation and universal quantification. "Does the set of all things that do not have themselves as elements have itself as an element?"

This relatively simple question precipitated a deep concern within the Philosophy of Mathematics, which given our modern take on logic as a part of mathematics, is the same field that would cover the certainty of logic. The primary reactions were basically:

1) Mathematical Platonism: ignore the problem and assume paradoxes are simply so strange in form we remain safe, because no important argument will be nearly that strange. The approaches within this range argue about why this should be the case, about how the paradoxes are or are not 'real enough' and ultimately about different theories of idealism and realism in general.

2) Type Theory: be suspicious of self-reference and referential loops in general and assume the rest of logic is safe. This flows into thinking about recursive function theory, proof theory and category theory, which have their own ways of looking at ordered or simultaneous circular references, and more casual theories like Douglas Hoffstadter's notions of the 'strange loop'.

3) Constructivism or Intuitionism: insist all statements of existence rely upon finite extensions of arguments about finite things (ruling out the idea that infinite or ambiguous things are either true or false.) The different approaches here disagree on what it means for an extension of an argument to be finite.

4) Formalism or Fictionalism: deny that the objects reckoned about are real in any important sense and stick with finite syntactical transformations as ways to preserve truth, excluding the problematical ones as we encounter them. (So in this case, we propose a set of syntactical rules that identify what sets it is safe to discuss. If we really need to discuss more general things, we will add more rules.) The different approaches disagree on whether how we treat the cases we are ruling out -- are they false? are they ambiguous? do we need a hierarchy of models that covers each possible case (a la Woodin's investigations)? or should we just remain open to encountering them as we go along.

There is a lot of discussion about the positive and negative aspects of these theories starting from Russel's era and intensifying through the mid 1970's, when a resurgence of ancient observations about definitions and language resurrected by Quine and the postmodernists reduced the relevance of foundational arguments.

All of these remain interesting theories. (Even the first one.) And the gaps between them are far from resolved.

And the paradox that precipitated all of this is not among the most interesting to many people. These approaches and variants on them may also consider the Barry Paradox, Curry's Paradox, Zeno's paradoxes of continuity and the related Banach-Tarski paradoxes of space and measure, paradoxes of instantaneous ambiguity and symmetry in physics related to the ancient 'ass' and 'sorites' problems, and many others.

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It seems to me philosophers debunk logical results as a matter of course. Most endorse views that fail in logic then blame logic for being useless. It's an odd business. It leads to the view that metaphysics is useless, a view that depends entirely on rejecting ordinary logic.

So, examples of views that assume classical logic is flawed are all the views held by philosophers who endorse theories that do not work in metaphysics, which is all but one of them.

Few philosophers bother with classical logic. If they have a view they like they tend to ignore the fact it fails in logic. They would rather assume classical logic is flawed. Examples of theories that assume this logic is flawed are all theories that fail under analysis, which is all theories promoted and examined in academic metaphysics.

What are some popular theories/opinions in philosophy against the certainty placed on the laws of logic and its results?

The most popular theory/opinion states that the failure in logic of all positive metaphysical theories is due to a flaw in logic and is not a proof of their falsity. This view is so ubiquitous that we could generalise and say that in Russell's 'Western' tradition nobody places any certainty in the laws of logic and its results. It's a condition of membership. The preferred view is that the logical results of metaphysics should be ignored and a new form of logic should be invented that allows us to hold on to our favourite views and theories.

This approach allows a thousand theories to flourish, which is fun, but it reduces philosophy to a hopeless muddle.

  • "all but one of them" That one being ...? And, can you give any examples of or evidence for these rather sweeping claims? – Noah Schweber Aug 21 at 21:24
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    'not complete and perfect in every way' does not equal 'useless' – user9166 Aug 22 at 0:21
  • @NoahSchweber - Only one theory is correct, so only one works in logic. My evidence would be the history of philosophy, during which nobody has found a second theory that works. For a single source I'd cite either Nagarjuna's 'Fundamental Wisdom of the Middle Way', Brown's 'Laws of Form' or Bradley's 'Appearance and Reality'. – PeterJ Aug 22 at 10:41
  • @jobermark - Okay. No argument from me. – PeterJ Aug 22 at 10:41
  • This is entirely opinion, it is not clear what philosophers or schools of philosophy you are talking about, but what you are saying is not true of most of them, which is what you claim. As noted, you claim most philosophers label classical logic useless when they are fascinated with its flaws, but really they are often really just amazed either that there are any flaws there at all, or that we can function as well as we do given that there are any flaws in so basic a necessary part of our thinking. (explaining my downvote) – user9166 Aug 22 at 14:48

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