Limits of Formal Logic

I've often had a love/hate relationship with formal logic. 

It makes things simple and easy.  I love that.  I rely on it like crazy for computer programming, and it's a wonderful tool for being able to argue and debate with effectiveness and clarity.

But there is a point where we take it too far, I think.

If you can find one premise that is invalid or unsound, you can dismiss the whole argument and its conclusion.  That's how the game works.  In programming terms it's like this:

if ( A && B && ( C || D ) )
  conclusion = true;

If A is 0 (false), then we don't care about B, C, D, or the conclusion.  Because obviously the conclusion is false.  Why bother with anything else?

Toss the whole thing out, move on.  Right?

But humans are not computers.  What if by thinking in such rigid terms we come to dismiss the whole thing as an untruth, even if there is some truth to it?

I'm not saying this as best I can, so bear with me.  The way I deal with a philosophical argument (especially the classical type, dealing with how to best live one's life), is to start by looking for what *is* true about it.  Look for the truth in it.  Ways that it could be said differently, the overall point or goal (which isn't always the conclusion), what the person is really trying to get at, and why they are presenting the argument in the first place.

The more I learn about the world and the viewpoints in it, the more I realize that our time is better spent trying to collect what is valuable from each in order to improve our own worldview rather than trying to find ways to dismiss another's viewpoint as illogical and inconsistent.

What is missing from many people is the ability to synthesize.  Formal logic is necessarily a tool for analization, as it breaks things down into their simpler parts in order to declare a simple truth or falsity label to the whole thing.  That's great, and necessary, but incomplete.  We need more than that.  We cannot progress without synthesis.

It reminds me of something one of my philosophy professors said one time:

Undergraduate students need a lot of handholding.  It's all about understanding the argument. 

Grad students are like attack dogs.  They understand the argument and immediately look for ways to disarm and dismiss it.

Once you move out of these two phases, you can then start to come up with original thought.

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  1. It's like the classical argument of book smarts vs. street smarts.The successful person will find a way to combine the two. In a statistics course I recently completed, the professor (herself a jaded engineer) talked about how easy it is to spot what she called a "green engineer" because of the reams of data they present with no graphs or analysis to explain what it all means.I agree with you, synthesis is a necessary component in the progress and growth in both the person and the society.

  2. You pulled out the geek in me by using the programming example, so I'm going to run with it.The problem isn't so much logic, as how people inherently structure arguments/discussions/debates. If you've logically refuted a point, then all you've actually done is logically refute that point.Since it's been way too long since I've done any actual programming, I can't re-write that code for you in the way I'd like to better illustrate my point. Essentially, you break it all up so that logic could tell you at which point things start falling apart. Looking at it backwards, if the conclusion is false, was it A, B, or C||D? The way the code is written now means that everything falls apart once something is proven wrong (which is actually appropriate, as that's how most people tend to think). If it was written as a series of If/Then statements, you would know exactly where a difficulty arose.Discussion needs to be organic and adaptive, and people need to be well aware of exactly what they're discussing. Things tend to fall into chaos when those involved start discussing different points without actually realizing it.Of all that was tangential or even completely off, I'm kinda sorta working on a speech at the moment. Which I really need to get back to . . . .

  3. I see your point. It does depend on how logic is used. But most people tend to subscribe to the short circuit method (which is written into many computer languages), as it makes things simpler.But one limit of logic *is* that it is a form of analyzation only. Of simplifying and modeling the argument. So that part remains. πŸ™‚

  4. Well put!
    Sometimes the world is not wholely reducible to nor describeable by logic.

  5. Huzzah! You've made your specific point and by our acknowledgment of it, we can continue to dance.The power of organic discussion.I'm not really sure where this falls, but I've found that people often expect too much of logic. Logic answers "How?" not "Why?" Philosophy tends to focus on the latter question, so things start to get a little prickly when people start trying to insert logic into discussions.

  6. Okay, here's a bibliography that should keep you busy for the next few years or so. In many cases Amazon lets you search inside the book, so you can look at the table of contents, the index, the back cover and even read an excerpt. This should give you a better idea than I could here of what these books are about.
    Briefly, though, they represent a movement within cognitive science to build a model of human thought as "embodied cognition" rather than simply "rational computation". The point is that we must use our peculiar situation in the universe, our bodies, our human scale, etc. to understand it. Whereas traditional rational philosophy requires that we abstract ourselves out of the universe in order to understand it, embodied cognition insists that we must use our immediate experiences to understand more remote and abstract concepts by extension (often metaphorically). Even logic mathermatics and logic ultimately derive, metaphorically, from our more immediate, physically-grounded understandings of the universe.
    Lakoff and Johnson catalogue a wide variety of "conceptual metaphors" by which we understand many of the more abstract aspects of our lives. Johnson believes that instead of deriving a definitive set of moral principles whose application to the real world will always be questionable philosophers would do better to cultivate rich moral imaginations. Turner, in "The Literary Mind", discusses parable — which have served as vehicles of just such moral imaginings in the past. Etc.
    Metaphors We Live By – George Lakoff and Mark Johnson (try to forget, for our purposes, that Lakoff is the author of "Don't Think of an Elephant")
    The Literary Mind: The Origins of Thought and Language – Mark Turner
    The Moral Imagination: The Implications of Cognitive Science for Ethics – Mark Johnson
    The Body In The Mind: The Bodily Basis of Meaning, Imagination, and Reason – Mark Johnson
    While the above can by no means be described as "easy reads" the following must be considered more difficult still. They are, I think, all clearly written and should be accessible to anyone willing to take the time necessary to think about what is being said but they are unquestionably complex and demanding:
    Women, Fire, and Dangerous Things – What Categories Reveal About the Mind – George Lakoff
    The Way We Think: Conceptual Blending and The Mind's Hidden Complexity – Gilles Fauconnier and Mark Turner
    Philosophy In The Flesh – The Embodied Mind and Its Challenge to Western Thought – George Lakoff and Mark Johnson
    Where Mathematics Comes From: How The Embodied Mind Brings Mathematics Into Being – George Lakoff and Rafael Nunez

  7. Very cool Baslow. It seems like in many circles we are moving away from the cold objectivity and mere rationality of the post-Enlightenment world. The same sort of movement is happening within religious circles (all too slowly, if you ask me) as a way of counteracting fundamentalism.I like this idea quite a bit. I doubt I'll have the time to read many of those books, so if you could recommend one or two out of them that are must reads, that would be extremely helpful! As it is I have a whole shelf of things to read at home.Also, I'm not afriad of dificult reads. πŸ˜‰

  8. Well, "Metaphors We Live By" is seminal, so you should certainly read that. I'm inclined to say that the other book should be "The Way We Think" but maybe you should read the readers' comments on the Amazon page and maybe try looking inside the book. Try reading the excerpt and clicking on "Surprise Me!" a few times. If you wanted to go for a third book, "Women, Fire and Dangerous Things" is as seminal for the theory of linguistic categorization as "Metaphors We Live By" is for the theory of conceptual metaphors…

  9. To get you started, here is an article entitled Blending and Metaphor which argues that conceptual metaphor theory and blending theory are complementary.

    While the metaphor theorist strives to capture generalizations across a broad range of metaphoric expressions, the blending theorist typically focuses on the particulars of individual examples.
    Here is an article by Mark Turner and Gilles Fauconnier on blending as a Mechanism of Creativity

  10. I cashed out of the Academy before I could get to the attack dog phase and I've ended up somewhere with a total absence of Truth. I'll turn things over in my mind and see how, depending on which things are considered axioms (e.g. the rights of the individual are tantamount, God exists, etc.), certain arguments become true and others become false. It sort of makes having opinions a little difficult, so I just post random songs and videos all day long while programming web sites. Hehe.

  11. "if ( A && B && ( C || D ) ) conclusion = true;
    If A is 0 (false), …Toss the whole thing out, move on. Right?"
    Maybe I'm not following you, but when a faulty premise A results in tossing out an entire argument, that does not preclude any individual statement within that argument from itself being true. Furthermore, in some instances, we might reject the assertion of a premise A as true, but that would not necessarily mean we throw out A forever as proven false.
    As for what to do with falsified theories, I like the critical rationalist method, which seeks to determine a hierarchy of truthlikeness for the set of propositions explaining the same thing differently. As humans we can safely assume we are almost always working with flawed theories anyway, so if we refuse to use flawed theories we won't be getting far in the pursuit of truth…
    Re: "We cannot progress without synthesis", this might be a dangerous statement, because it implies a dichotomy of simple truths and false theories, to be resolved by synthesis, something which tends to lead to the dreaded (by critical rationalists at least) Hegelian and Marxist dialectics, which both resolve thesis-antithesis contradictions by changing them via synthesis. It's too easy to use arbitrary anti-thesis and denials of the presuppositions in order to direct a thesis towards a foregone conclusion via synthesis. Hegel does it idealistically in an attempt to reconcile being and nothing with "becoming", Marx does it materialistically to justify his historicism and communist revoltion, and both systems are fundamentally flawed IMO.
    So, I would say that if you think our knowledge is finite, our ignorance is infinite, and that scientific theories about the universe are capable of providing infinite informative content, then you might be inclined to worry less about synthesizing simple truths with falsified theories, and worry more about demarcating irrefutable, unverifiable explanations of the universe from the refutable, verifiable, testable scientific explanations, and of course ultimately with creating the truthlikness heirarchy amongst the competing scientific theories exaplining any given thing.
    Finally, I wholeheartedly agree that "our time is better spent trying to collect what is valuable from each in order to improve our own worldview", but that inherently implies "dismiss"[ing] another's viewpoint as illogical and inconsistent", in order to determine what indeed is valuable. That is where I think the demarcation of irrefutable theories and the truthlikness hierarchy of the refutable theories comes into play.

  12. Yes, I think Womby made that point above. My first objection turns out not to be a failing of logic but of those who use it. It is the short-circuit method that is very often used in computer programming. Many people I have seen are like the attack dogs I mentioned. They see an argument and immediately look for a way they can dismiss and discard it and move on. :)I guess I've just noticed lately that all of our focus is on the
    conclusion, which is not always the objective of the argument. I've
    noticed people missing the wisdom of a viewpoint/argument because they
    are so fixated on making sure every premise is sound.About synthesis: I get the references to both Hegel and Marx, but it was not my intention to actually reference them. πŸ™‚ I was going to the basic definition. As a compliment to analysis, which is breaking things up into small pieces, synthesis is building things up. Looking for consistencies across arguments and building new arguments from there. This is not to say that analysis and logic are bad. As you said, we still need to be able to see inconsistencies and irrationality. But I feel like people tend to focus on these inconsistences to the point of exclusion of anything of value. Note that this is a very general statement, with many exceptions. I'm not saying we need to completely reevaluate how we work, just our priorities. It's not just about winning an argument, but about seeking truth.Thanks for the comment!

  13. I agree with you here: "I've noticed people missing the wisdom of a viewpoint/argument because they are so fixated on making sure every premise is sound." For instance, I find a lot of great wisdom in Vedic Hinduism, but I hardly accept their theory of the universe as truth. I've also made a related observation, that people are typically more interested in the confirmation of their own beliefs over the pursuit of objective, verifiable truth.
    As for the basic definition of synthesis, I think I followed what you were saying, I guess I just see the process differently. I see it like, a given theory (theory 1) is comprised of many sub arguments and facts, and if proven wrong, we would "toss out" theory 1, but not necessarily all it's sub parts. Where we go from there in search of truth is the question I suppose. The way you word it, it sounds like an an attempt at an ad hoc rescue of failed but useful theory 1 via synthesis of its thesis/anti-thesis contradiction, whereas I would word it like the creation of an alternate theory 2, which may build from theory 1, but undergoes the entire critical theory building process from scratch, hopefully offering a better explanation of the elements that led to the falsification of theory 1 in the first place.
    It's probably just a semantical disagreement, but I guess I'd argue that truth lies in conjectures and refutations, rather than in contradictions and synthesis. My reason for avoiding the contradiction/synthesis method is that it's too easy to arbitrarily select the anti-thesis & counter-presuppositions to fix the results. Because the synthesis is usually an exercise in rhetoric by changing some underlying assumptions, or semantic interpretations, of the contradictory elements, it usually leaves a lot to be desired in terms of getting closer to a verifiable truth. Marx and Hegel are just good examples of that happening to very intelligent thinkers who also happen to have very good and logical points embedded into faulty systems. I didn't mean to imply you were a Marxist or Hegelian, they just seemed like fitting examples…
    In Popper's words: "The whole development of dialectic should be a warning against the dangers inherent in philosophical system-building. It should remind us that philosophy should not be made a basis for any sort of scientific system and that philosophers should be much more modest in their claims. One task which they can fulfill quite usefully is the study of the critical methods of science."
    Like I said, I think it's possible we are both beating around the same bush here.

  14. I think we are. πŸ™‚

  15. this bush isn't burning, is it? };^D

  16. Wow, I had a whole bunch of stuff to say……then I read the comments and realized I'm a tad out of my league. I'm more philosophy than logic and this conversation has definitely grabbed hold of the logic end, so I'm out.But what a great post! Thanks, lcn!

  17. Don't worry Kirk! Post your thoughts! Feel free to grab hold of the philosophy end. I'd love to hear what you think. πŸ™‚

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