We all pride ourselves on being logical thinkers (yes, dear reader, you are correctly perceiving a slight scorn in my statement; you have no idea how many times I’ve come across a job candidate who called himself “logical, conceptual thinker, creative, goal-oriented… do they know what this implies about them? Do they realize what kind of person you have to be to have all these attributes?! Have they ever seen a truly creative and logical person?!). While in general being able to use the laws of logic to make decisions and communicate is a good idea, a shallow understanding of “logical thinking” can be detrimental.
For one, in my view (if you know more about the theory of logic than I do, and it’s likely you do, forgive me for being sloppy here) logical thinking is nothing else than the process of manipulating statements in a way that preserves “truth”, however that is defined. Logic allows you to, for example, declare in a standardized way that one statement is equivalent to another in when it can be applied. But what most people forget is that logic is built atop fundamental claims (axioms) that cannot be manipulated further. Everyone has their own set of axioms, even if they don’t realize it. The axioms derive from one’s values (and hence their sense of purpose in life and their interpretation of the Universe). Some people have very few axioms, others have many (which is why you can be religious and a logical thinker! Religious logical thinkers have simply a larger set of axioms that they use to make decisions. Their axioms, just like those of highly irreligious people, are fundamental (you can’t show how one is equivalent to any combination of the others) and should be consistent (for example, they shouldn’t contradict each other; this makes the logic system sound). Similarly, you can’t compare axioms–you can’t claim that one of your axioms is superior to one belonging to another person. Similarly, it’s hard to compare entire sets of axioms (provided that they are consistent). For example, if you tried to answer the question of which of two sets of axioms apply in more instances (more completely cover a given universe of statements), you would have to to prove every statement in that universe using your axioms. It’s a lot of work!
What I see a lot is people who call themselves logical thinkers disagree at very fundamental levels–levels of philosophies. Philosophies are statements which are very close to the individuals’ axioms. And, like axioms, philosophies are very hard to compare. Real logical thinkers should stop their conversation as soon as they realize they’ve hit that point.
As an aside, this view of logic should also help understand cyclical behavior, and the seemingly chaotic was our life goals change. Small changes in the set of axioms (resulting, perhaps, from a new, deeper understanding of a tiny portion of the Universe) ripple through the philosophy and the rest of one’s knowledge base. The set of statements in the world which used to be “true” has changed entirely (the change is significant because there are many fewer axioms than there are statements in the world). Cyclical behavior, specifically, is in my opinion just this phenomenon but viewed through the lens of selection bias: suddenly statements which used to be “true” (for example, “Whenever I go to the City, I should take the train”) are no longer true (“Whenever I go to the City, I should drive”).
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While I think this is a good start in understanding others who try to apprehend the profound or the mysterious, it’s also deeply wrong. Or as Wolfgang Pauli might say, “It’s not even wrong.”
To further extend your logical system metaphor: it’s not just that different people start from different axioms. They can have different transformation rules altogether. If two “logical” thinkers disagree on whether A and B imply C, you can set yourself on a fool’s errand if you try to tease out the axiom that only one holds in his pocket. They might just be overlaying different rules.
Also – what are we talking about here, anyway? Human beings, right? What’s to say that the set of transformation rules and axioms that a person employs is constant among contexts? It’s plainly a different set employed when we talk about math and when we talk about love. (Perhaps there are some so consistent that they would use the same set, but what’s the use of worrying about people like that?)
But the thinness is this framing is put into relief when you consider the disagreements, or the disagree-ers. What’s the axiomatic base of religious vision? Or aesthetic revelation – or even aesthetic comparison? Logic is so weak when it comes to “meaning” in its human sense. Logic is no handrail down these staircases. Just walk slowly and with open eyes.
Thank you Rudolf, I struggled to disagree with anything you said. In fact, I imagined folding your exploration into my metaphor by relaxing the definition of an “axiom”–that is, turning the rules of logic into axioms themselves, in a way analogous to noting the duality of program (the algorithm) and data of a van Neumann architecture as every program can be encoded as data.
You did, however, touch upon much more fundamental problems that people will encounter when they attempt to use logic as a common framework (and I guess such was my point; countless times I’ve heard my friends agree to “use logic to discuss” a particular point. Something had to be done about it, even if it is just a rant somewhere…)
Suppose there is something wonderful and impractical to talk about. If a person starts off with, “let’s use logic to discuss” – oh, girls or Being or silence – how could s/he possibly have something worth saying?
This quote amps up the pretension, but I think it’s perfect. Nietzsche’s opening lines from Beyond Good and Evil…
“Supposing truth is a woman – what then? Are there not grounds for the suspicion that all philosophers, insofar as they were dogmatists, have been very inexpert about women? That the gruesome seriousness, the clumsy obtrusiveness with which they have usually approached truth so far have been awkward and very improper methods for winning a woman’s heart?”
That kind of says it all
[...] twentieth century, mathematicians realized that logic doesn’t actually get you that far. As described previously, logic is as strong as a set of axioms behind it. This is fine in a highly contrived world, like [...]