Monday, May 30, 2005

Paraconsistent logic


Over at Philosophy, etc there is a discussion about paraconsistent logic. For the uniniated, that's a situation where you hold something contradictory to be true. The logical form of this would be (P & ~P), and a real example might be that a person is both alive and dead.

For that particular example, it's hard to see why you would want to. A lot of people get a bit weirded out by paraconsistent logic, making such impressive counter-arguments as "that's just dumb". And in some ways it is. But it lets you do interesting things. Let's pretend, briefly, that the world around us really allows some inconsistent things to be true. If that were the case, it would be a good idea to have a logic that could reflect this reality. So let me make a list of some incompatible statements which I think are both true :

* One can be both awake and asleep
* We are both obey physical laws and have free will
* I am both conscious and subconscious
* One can be both inside and outside of a room
* Light is both a particle and a wave
* Schrodinger's cat is both alive and dead
* There is and there isn't such a thing as time
* I am the creator of the world, but I am also its creation
* The universe both had a beginning and did not have a beginning.



Blogger Illusive Mind said...

Perhaps the fear behind adopting such a position is that accepting these kind of 'almost beyond our ken' propositions limits the ability of philosophers to analyse and neatly deconstruct reality into their particular schema.

I'm sure they would begin by saying that contradictory statements are only true when they are sufficiently vague, and by adding qualifiers they can be done away with.

5/30/2005 10:04:00 AM  
Blogger MelbournePhilosopher said...

Well, (P & ~P) is not very vague. I take the point, but disagree that it's true. Although perhaps it's true and not true.

Certainly vague statements are easy to interpret in multiple ways, and so one can argue that the seeming contradiction is dissolved by being more concrete about the interpretation. Although perhaps there is another contradiction in saying that you can actually dissolve something with concrete...

So it's certainly true that some contradictions can be resolved this way. It's probably also true that some genuine contradictions can be avoided through selective definition - i.e. looking at only a subset of the problem, or using a highly technical definition of the problem.

I would argue however that some contradictions are *not* vague at all, such as light being both a particle and a wave, or being both inside and outside a circle, or Xeno's paradox.


5/30/2005 10:20:00 AM  
Blogger lumpy pea coat said...

Those were supposed to be examples of statements that are both true and false? I cannot see how. They're all equivocal or ambiguous at best.

I think there's a misconception about what paraconsistent logic is. It is not just standard logic with a rejection of the law of noncontradiction. That logic is *dumb*.

5/30/2005 02:48:00 PM  
Blogger MelbournePhilosopher said...

I don't find any of my statements equivocal, although some of them could be interpreted as being equivical if you choose.

The free will / determinism claim is an example of that, but others are clearly not equivocal.

Some of the claims may seem ambiguous, but I don't think that's true. Perhaps they seem ambiguous because don't understand them, not merely because they are vague.

You don't make any arguments, you just make claims.

I don't think I make the mistake you mention - neither do you point out where I make it.

By doing those things, you are setting up a straw man which I cannot knock down.


5/30/2005 02:56:00 PM  
Blogger MelbournePhilosopher said...

Oh - another very clear example would be our justice system. I often think that the sentence handed down is both right and wrong. I think many moral actions are both right and wrong.


5/30/2005 07:54:00 PM  
Blogger lumpy pea coat said...

I don't see how it's a strawman, but for example:

(1)We both obey physical laws and have free will.

That simply begs the question. Do we really have free will if we obey physical laws?

(2)One can be both awake and a asleep.

I suppose that's simply wrong or I can't make sense of it. Suppose we can make sense of it and it is true. Then obviously there is some sort of ambiguous or equivocal meaning of either 'awake' or 'asleep' (or both).

Anyway, the point is simply that the supposed truth of contradictory statements is explained away by equivocation, ambiguity, indexicality, or sheer nonsense.

5/31/2005 08:38:00 AM  
Blogger MelbournePhilosopher said...

I have a question for you Peacoat.

In some sense, resolving ambiguity means to me taking a position that's very logically crisp.

"Anyway, the point is simply that the supposed truth of contradictory statements is explained away by equivocation, ambiguity, indexicality, or sheer nonsense."

Let's say we have a situation where something *appears* to be both true and false, and we want to resolve it. When I'm saying that one can both be awake and asleep, let's suppose I'm talking about dream states for the moment. You're not entirely unconscious, yet your consciousness is not directed towards the external world exactly.

Ordinarily, most people would take "awake" to be mutually exclusive to "asleep", but here is an example where those everyday interpretations don't fit.

Now, I'm willing to grant you that you could probably re-describe the situation in a different way, and avoid the contradiction.

But (a) do you think we can always do this, (b) is this definitely possible in this case, (c) do we always want to?

People are clearly capable of holding, and reasoning from, contradictory beliefs. If we are trying to, let's say, model that reasoning, might we not be better off using paraconsistent logic than writing more complex rules?

This is a bit like surface grammar - you can't use language without understanding the complex use patterns which under-write it.

I think that things like quantum physics and inside/outside dilemmas and Xeno's paradox don't yeild easily to standard logics.



6/01/2005 11:56:00 AM  
Blogger Bill Cooper said...

There are things in quantum physics such as whatshisnames cat, and light being a wave and particle. However they are not paradoxical it is just the way they are, we have not arrived at a point where we can explain them properly. However much of what you call true/false statements seem to be nothing other than what Orwell called doublethink. It's manifested in the media everyday, perhaps the better minds see through the easy contradictory thoughts but get caught up as the degree of difficulty increases. To me there is no real paradox just the lack of knowledge, words and concepts to adequately explain why.

6/01/2005 08:21:00 PM  
Blogger MelbournePhilosopher said...

This reminds me of an old joke. There is a mythological description of the Earth in which it is carried by four giant elephants standing on the back of a Turtle. This idea was borrowed by Terry Pratchett, but I think it has its origins in Zen mythology.

Two monks are discussing this idea, when one of them asks what the turtle is standing on. The first monk looks over the edge of the world, and replies "Looks like it's turtles all the way down".

6/02/2005 11:33:00 AM  
Blogger Nitin said...

Law of Non-Contradiction uses context as additional parameter.
This might simplify some seeming paradoxes.

Light is both a particle and a wave

For physicists light is only considered to be a wave or a particle depending on the nature (i.e. context) of the problem to be solved. Light is not considered to be both a particle and a wave at the same time

I am both conscious and subconscious

I guess unconscious is the opposite of concsious and not subconscious.Being conscious and subconscious isn't a real paradox.

6/02/2005 10:24:00 PM  
Anonymous Hannah said...

It is impossible for a person to be completely inside and completely outside of the same room .One could be in the middle of two rooms. For example- a person standing in a doorway. But, it's impossible for one to be completely inside and completely outside.

9/10/2015 12:14:00 AM  
Anonymous Hannah said...

Also, sentences issued by the justice system can't be completely right and completely wrong at the same time. There can be parts of a sentence that is right and parts that are wrong.

9/10/2015 12:18:00 AM  
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