Friday, March 4, 2011

Wittgensteinian Ramblings on Logic

Logic is logic. Straightforward. Formal. Structured. Edifice. Lots of pipes, nuts and bolts. There are types of logics. Fuzzy, intentional, temporal, quantum (of which there are several varieties), mathematical, Reichenbach's, Russell & Whitehead's, Boolean, Tarski's, Quine's, Hilbert's, Gödel's, von Neumann's, Norbert Wiener's, algebraic, geometric, deontic, modal, etc. etc. etc.  I even playfully invented two axiomatic systems of my own. What the hell is logic?  Mmm, yes, I once used to swim in this ocean. 

Logic never states anything. Logic is merely form.

No idea can describe reality an sich.  The words are all jumbled up.  Please define 'idea', 'true', 'reality'. Please define 'meaning'.  These are very key words. They cannot be used lightly.

The "true meaning" (we'll go with it for now) is of the heart and mind. Yes. Yes. Yes. Beyond articulation, beyond propositions, beyond assertions, beyond sentential constructions, beyond morphisms and maps, that.

What is there to understand?

Yes, experience.  That's the bottom line.

Here we go again,  your dichotomous juxtapositions.  Reality (let's just go with the term for now) subsumes the all.  Is the all.  There can be no contraposition versus reality.

When dealing with validity one is dealing with structure and form, i.e., logic.

So what the fuck's wrong with feelings?  They are just as ephemeral, eidetically speaking, as thoughts.

You seem to be conflating 'faith' and 'belief'.  Are they the same thing?  Most conscientious religionists would tell you that they are not.

So which is the real logic? After all, each one of them is logic.  And yes, it works, it's got all the bells and whistles. Which logic do you choose?  Logic is logic, yes, but saying this seems to go beyond tautology; i.e., we can say that there is a logic to logics, and that somehow there is a supralogic, some sort of arche of which all possible logics are infrastructures or instances.

Let me be straightforward here. You are stuck, even in your mindset, in a two-valued world. It's called dualism.  Call it manichaenism.  It's called seeing things in black and white, either/or, disjunctively, exclusively.

You would say, yes, I'm sure. Or would you? I asked you how you can justify your approach, or how you would defend it.  I see your procrustean universe chopped up into blocks, some pieces set to the left
and some pieces to the right.  Chop, chop, chop, crunch, cruch, crunch. Click, click, click. You're constantly focusing on the on/off switch.  

Surely this is not how your mind works, or does it?  Is it just ex post facto analysis? There was a time I believed my thoughts worked this way. To me my brain and thought processes were a mathematical labyrinth of plugs and wires, all parts interconnected and analyzable.  

Couple years later I visualized this edifice crumbling, folding in on itself, huge rods and pipes falling, walls caving, floors giving out, the framework starting to shake, slowly untangling its monstrous self, like one big amazing knot, A Gigeresque alien, snapping, breaking, cracking, a gargantuan edifice, a brittle pinnacle, breaking apart, falling apart. Categories, allegories, topologies, geometries, algebras, sheaves, manifolds, cohomologies, lattices, etc. etc. 

It is entirely possible to be stuck in a two-valued world, you know, like the Twilight Zone sort of thing.

Ontology.  Quine: "To be is to be a value of a variable."

Nope. Unconscious. Not sub or supra or infra or anything else.  Creatures of habit, you know, always doing things by habit, unconsciously.

You're enamored with your tools. Your tools are obstructing the way. They have cast a spell on you. Too much clincking and clancking going on.  You love the oil and the WD-40, the slick finish and shine.

You see, you're looking for logical corrections. You're still stuck in the disjunctive Either/Or world. 

Logic is inevitable.

Logic is beautiful. Logic is sexy. Yes, those operators, those maps, those functors, those nebulae of nested sets, topoi of sheaves and cohomologies of fibers!  Oh, the manifolds, the rings, the varieties.  Like a kid in a candy store... mmm...the toys of the brain.

But Logic is inevitable.

Just don't sacrifice burnt offerings to it.

Exorcise the Mr. Spock demon. He's a fake. You can evolve without him.

Is Faith a logical conclusion to an argument? Is Faith faith in the verity of propositions? The validity of arguments?

Click, chop, click. Look, after a certain point of understanding, looking for logical errors becomes petty, silly and annoying, no?  

Sometimes annoyance is necessary, you know, a socratic perplexity, if you want to get somewhere. 

The world view of materialism...hmm...sounds like a nasty nightmare or a hangover or something. 

Concerning multivalent logics, consider the following schematic: Let 2-v denote the Boolean/ Aristotlean/Venn-diagrammatic/truthfunctional first order logic, let 3-v denote quantum logic of three values/Reichenbach's three valued logic/ other 3-v syntactical formal languages, let א(Aleph)-v denote a multi-valued logic with cardinality of values mapped injectively into the set of integers and let P(א)-v denote the uncountably transfinite multi-valued logic (fuzzy logic with cardinality of values mapped injectively into the set of real numbers, probabilistic logics, quantum logics and logics over Hilbert spaces, etc.). Let ⊂ denote 'is a proper subset of':

∅  ⊂  2-v  ⊂  3-v  ⊂  א-v  ⊂  P(א-v)

I include '∅' as the empty set because a logic over the empty set (a logic over a single value) is still a logic, though trivial.  It is necessary to generate the Boolean universe of two values, as well as the rest of the logics over which are founded upon the theory of the construction of the field of real numbers (algebraically and set-theoretically).

At every step of the inclusions there is no falsification nor abrogation of the cruder logic; rather, the cruder logics get more and more refined.  They become more subtle, less "combinatoric."

The tertium non datur stops at 2-v; it simply doesn't apply to the rest.  Why do you think I listed so many different logics at first? You're stuck on one kind of logic. There are other logics. That's one of my points. My other point is that there is also _intuition_, supralogical "thinking" (or "non-thinking," even "blinking" in the M. Gladwell sense).

No, the world is not either/or.  The world of your two-valued logic is "either/or."  There are alternatives. Of course, sticking tenaciously to the two valued world is convenient for religious apologetics; after all, religions by and large divide the world into two parts, in many superficial (and hopefully provisional) aspects:


And so on, respectively. Isn't this what it's all about, though?  Isn't that why the law of the excluded middle is so "logically" important to your apologetics?

So please explain to me, as my original question to you was, why, if I'm wrong in my assessment, you would still stick tenaciously to a bivalent logic and insist that reality as such can only be divided into two parts and two parts only.

Humans don't live by accuracy alone, no?  Let's say, then, that accuracy is absolutely important, religio-dogmatically speaking.  So why is a two valued logic more accurate than n-valued logic (n > or = 3)?

There are more than two points to the logic stick. In fact, the logic stick is the real line unit interval [0,1], endpoints included. It has an uncountably infinite number of points.
Here's a commentary: emotion is ok. Logic is ok. Anything is ok. Just use them, be their master (not the other way around).