Nov 25, 2009

Philosophical Phun - Classical Logic :o)

Today, logic is both a branch of mathematics and a branch of philosophy. In most large universities, both departments offer sequences of courses in logic, and there is usually a lot of overlap between them. Formal languages, deductive systems, and model-theoretic semantics are mathematical objects and, as such, the logician is interested in their mathematical properties and relations. Soundness, completeness, and most of the other results reported below are typical examples. Philosophically, logic is the study of correct reasoning. Reasoning is an epistemic, mental activity. This raises questions concerning the philosophical relevance of the mathematical aspects of logic. How do deducibility and validity, as properties of formal languages--sets of strings on a fixed alphabet--relate to correct reasoning? What do the mathematical results reported below have to do with the original philosophical issue? This is an instance of the philosophical problem of explaining how mathematics applies to non-mathematical reality.

When mathematicians and many philosophers reason, they occasionally invoke formulas in a formal language to help disambiguate, or otherwise clarify what they mean. In other words, sometimes formulas in a formal language are used in ordinary reasoning. This suggests that one might think of a formal language as an addendum to a natural language. What do deducibility and validity, as sharply defined on the addendum, tell us about correct reasoning in general?

As an engineer by training, this one hits pretty close to home.  What do you find relevant, and more importantly, WHY ???


  1. I tend to think of things in the abstract. The way that objects and actions interact based on the not readily seen or easily observed.

    The reason that I do this is that I have found that the underlying purpose of a thing or an act often has as much meaning as the observed purpose of that thing or action.

  2. As a scientist, I rely a lot on logic and rational thinking. However, the emotional, gut instinct can also be valid, and provide a humanistic element. We just have to learn how to find the balance between logic and emotion.

  3. The universe isn't logical, yet isn't chaotic, and we live in it but conflicted by the perfect mathematics it reveals. I'm open to philosophize about it but I'll never be "correct" and in that dichotomy it's easy to see one needs the perfection of mathematics to quantify what surrounds us, IMHO. So I can reason then, that all science is theory waiting to be proven - and everytime I make that discovery I disabuse myself of that same notion! It's complex and intriguing! Like Beth we attempt to seek what's reasonable, but again have nothing to measure it against. What's correct reasoning? Isn't your ability to reason out a dilemma as valid as one who sees it differently? "Correct" IMHO is an absolute, like "alive" or "dead". I like your take on language and its formality vs. naturalness. Some would proffer it's just a sound we're able to make because we have a larynx, and we've certainly proven we can communicate w/o it. So who knows? Very enlightening stimulating post! O yes, to answer your question: I find *you* relevant, because you exist. I think all life is profound, as it confounds lol.

  4. Ken...hope you and Beth have a wonderful Thanksgiving. Linda in WA


Tell Me What You Think, Don't Make me go Rogue on you :o)