Logical puzzles versus logical philosophy

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Aedes
 
Reply Thu 13 Nov, 2008 11:12 pm
I'm a fan of abstract logic puzzles and games. I like Sudoku, I like chess, etc.

In these puzzles and games, however, there are strict rules that are beyond any interpretation. The rules engender a method that is predictable and efficient once one becomes experienced. This is how chess masters can comment on other historic games and call certain moves "mistakes", and there is a great degree of uniformity in what are considered good moves and bad moves. Chess masters (and I'm sure Go masters as well) see patterns within a complex logical system.

But unlike these games and puzzles, human logic when used to make reasoned arguments is NOT a closed system. Part of this is the lack of complete correspondence between a thought and a way of expressing it with no ambiguity. Symbolic logic seems to take some of the vagaries out of it, but symbolic logic only solves the syntactical problems. It doesn't make a conclusion or an idea inevitable in the same way that putting your king in check forces you to protect it.

This makes me think that any appeal to logic or reason in philosophy must of necessity acknowledge their fallibility, and therein any derived conclusions. Many ethical problems and basically the whole of metaphysics is thus undermined. If even mathematics cannot be a pure tautology, as Godel taught us, then reason certainly cannot. So how can we be sure that any philosophical therefore really means anything?
 
Deftil
 
Reply Fri 14 Nov, 2008 08:45 am
@Aedes,
Hi Aedes.

I'm not sure I COMPLETELY follow you, but I think I do to a degree. Tell me what you think based on what I say, if you will.

If what you say and imply is true, then doesn't the philosophical therefore of your own argument being meaningless? If one concludes that no conclusion is inevitable, then doesn't that conclusion itself also fall short of being inevitable? It seems to create a paradox to me. If what you say is true, then, is it possible to ever know it is with certainty? So is it untrue, or simply possibly true, but unknowable?

Also, a game like chess can allow for a situation to arise that is inevitable, such as one where having your king put in check forces you to protect it, by first establishing strict rules, as you say. These rules of the game are assumptions, or premises, that it is agreed the game will proceed by. Then, from these premises certain actions can become inevitable. Inevitability in chess only becomes possible by first accepting certain premises. Can't the situation in logic be exactly the same? Can't the game of chess be viewed as an actual logic problem? If the premises of a logical argument are set up strictly, as they are in chess, then can't the same sort of inevitability be reached in a logical argument as it is in chess when you are forced to protect your king?

In chess we just accept the rules. They are what they are, and they have been around for a very long time. We don't really give much, if any, thought to questioning the premises/ assumptions/ rules, we just play it. In logical arguments however, we almost always give considerable thought to questioning the premises. Well, we could do this with chess too, and would realize that the game only creates a closed system by complete acceptance of the premises.

In the end, I think we reach the point of recognizing a Cartesian skepticism, with the conclusion that nothing can be held to be certainly true without acceptance of certain assumptions first, except for the existence of one's own mind. The conclusion that one's own consciousness exists would then be the only philosophical therefore that can "mean" anything. (using "mean" here in the same sense as you have in your final sentence)


So what do you think? Am I hot, cold... lukewarm? Did I get the point but make a mistake in my reasoning or just say something that you disgaree with?
 
jgweed
 
Reply Fri 14 Nov, 2008 09:04 am
@Aedes,
In chess or in contract bridge there are rules defining the pieces or deck of cards, and then rules and procedures for correctly using them. But in logic, the first part is entirely missing, and you end up with rules and procedures without really defining the objects to be manipulated. In chess, on the other hand, the variables are strictly limited to a specific set of objects.
 
Aedes
 
Reply Fri 14 Nov, 2008 10:52 am
@jgweed,
jgweed;33291 wrote:
In chess or in contract bridge there are rules defining the pieces or deck of cards, and then rules and procedures for correctly using them. But in logic, the first part is entirely missing, and you end up with rules and procedures without really defining the objects to be manipulated. In chess, on the other hand, the variables are strictly limited to a specific set of objects.
Yes, that's largely my point. But in argumentative logic it's beyond just rules -- I mean the constituent ideas are complex and lack a perfect correspondence with the words that express them, so there isn't even a possibility of making strict rules.

Deftil;33286 wrote:
If what you say and imply is true, then doesn't the philosophical therefore of your own argument being meaningless?
Yes, but I'm just making conversation. I'm not rigorously trying to put forward an airtight logical argument.

Quote:
If one concludes that no conclusion is inevitable, then doesn't that conclusion itself also fall short of being inevitable?
Take an utterly simple logical puzzle. You have a two sided coin; on one side is heads and the other side is tails. You flip the coin and it lands with the head facing up -- THEREFORE the other side is tails. There is nothing at all that compromises the inevitability of this. A Sudoku puzzle is no different -- there is only one possible solution, and it can be deduced (eventually) from the information given in the beginning.

Quote:
Inevitability in chess only becomes possible by first accepting certain premises. Can't the situation in logic be exactly the same?
But it's NOT exactly the same. When is a a set of ideas so closed that it cannot be bent with different assumptions or interpretations?

Quote:
In the end, I think we reach the point of recognizing a Cartesian skepticism... The conclusion that one's own consciousness exists would then be the only philosophical therefore that can "mean" anything.
I don't necessarily accept Descartes' exercise or his conclusion, so I'm not sure that skepticism leads us inevitably there. But that's not really the point anyway -- I'm talking about how logical argumentation is inevitably going to be in a widely open system, and thus no logically-derived conclusion can ever have the same inevitability as the solution to a Sudoku puzzle.

Quote:
So what do you think? Am I hot, cold... lukewarm? Did I get the point but make a mistake in my reasoning or just say something that you disgaree with?
I think we're having the same conversation, more or less, and I agree with your point that yes it's all about a priori assumptions and rules. That said, human ideas can NEVER have sufficient clarity and sufficiently foolproof rules that logical conclusions will be airtight; and there ARE logical deductions we can make (like what's on the other side of the coin) that are completely airtight.
 
jgweed
 
Reply Fri 14 Nov, 2008 02:13 pm
@Aedes,
Logic can help determine if statements and arguments are valid, but cannot determine if the premises and statements are true. Under most circumstances, if one can establish their truth, then the conclusion if validly drawn would be true.
The hard part is to present something like a substantial argument for the truth of the premises; much of philosophy has been just such attempts. Not only does one have to show that the premises are actually true, but one must also show that the way one got to the premises is appropriate, or warranted. At times, logic can help in this process by exposing fallacies (say of composition or division) that question whether the data upon which the argument is based are representative or applicable.

To call an argument logical is not, therefore, to confine it (strickly speaking) to the use of logic; there are all sorts of other criteria we normally look for to judge its soundness.
 
Deftil
 
Reply Tue 18 Nov, 2008 06:56 am
@Aedes,
Aedes,

I've been meaning to respond to your last post but I'm afraid I haven't been able to organize my thoughts well enough to put forward the type of response I'd like to. Still, I'll go ahead and make a few brief comments.

Aedes;33324 wrote:
Yes, but I'm just making conversation. I'm not rigorously trying to put forward an airtight logical argument.

That's fine of course and I didn't mean to imply otherwise. But if you granted that my point was true, it would verify that we were on the same page. Also, I have to admit, I thought I was being a bit clever there.

Quote:
But it's NOT exactly the same. When is a a set of ideas so closed that it cannot be bent with different assumptions or interpretations?

I accept that it might not be exactly the same, but I'm still not convinced that it is the case. I'll have to collect and organize my thoughts on this to see if I can try to prove my case. Basically, I don't think it's often the case that a set of ideas seems so closed to be conducive to completely perfect and straightforward interpretation, but I don't feel this means that it is impossible.

Quote:
I don't necessarily accept Descartes' exercise or his conclusion, so I'm not sure that skepticism leads us inevitably there. But that's not really the point anyway -- I'm talking about how logical argumentation is inevitably going to be in a widely open system, and thus no logically-derived conclusion can ever have the same inevitability as the solution to a Sudoku puzzle.

2 things here:

1) Have you ever made any posts here about why you would object to Descartes' exercise or conclusion? If so, I would read that.

2) Actually, I'm thinking that it is relevant in a way that might not be immedaitely obvious, but I have to dig deep to figure out how to explain why I think so, so I'll try to get back to you about that.

Quote:
I think we're having the same conversation, more or less, and I agree with your point that yes it's all about a priori assumptions and rules. That said, human ideas can NEVER have sufficient clarity and sufficiently foolproof rules that logical conclusions will be airtight; and there ARE logical deductions we can make (like what's on the other side of the coin) that are completely airtight.

Yes, I'm confident we are having the same converstion now, so that's certainly a good start, if nothing else! More thought on my part is in order here, so as I've previouly stated, I'll try to come back with a good response when I feel ready.
 
democritus
 
Reply Sun 1 Feb, 2009 05:22 pm
@Aedes,
Aedes wrote:
[1]unlike these games and puzzles, human logic when used to make reasoned arguments is NOT a closed system. Part of this is the lack of complete correspondence between a thought and a way of expressing it with no ambiguity.
[2]This makes me think that any appeal to logic or reason in philosophy must of necessity acknowledge their fallibility, and therein any derived conclusions.
[3]If even mathematics cannot be a pure tautology, as Godel taught us, then reason certainly cannot. So how can we be sure that any philosophical therefore really means anything?
There are 3 argument above connected to each other. Let us examine the argument [1] with logical rephrasing:

(a)There is lack of complete correspondence between thought and the way of expressing it.
(b)Therefore, this creates ambiguity.
(c)Therefore, the premises [in a human logic] will be inevitably ambiguous.
(d)Therefore, the argument may or may not be a sound argument.

If all the premises above true the conclusion can not be untrue.

However, the first premise is the most important statement in this argument and need attention.
Listen to this:
jgweed wrote:
Logic can help determine if statements and arguments are valid, but cannot determine if the premises and statements are true. Under most circumstances, if one can establish their truth, then the conclusion if validly drawn would be true. The hard part is to present something like a substantial argument for the truth of the premises; much of philosophy has been just such attempts.

The ambiguity in the first premise (a) is that it doesn't tell us whether it means all or some of the statements/premises are ambiguous. The following argument assumes that all statements are inevitably ambiguous. We know that it isn't true. Listen to this:
Aedes wrote:
Take an utterly simple logical puzzle. You have a two sided coin; on one side is heads and the other side is tails. You flip the coin and it lands with the head facing up -- THEREFORE the other side is tails. There is nothing at all that compromises the inevitability of this
So, it is possible to construct a human logic without ambiguous premises.

Therefore, premise (a) is false and the conclusion (c) is false.

Since, the argument [2] and [3] based on the truthfulness of the premise (a) it needn't be debated further.

Thanks
democritus
 
 

 
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