# The Law of the Excluded Middle and Free Will

1. Dec 28, 2004

### Imparcticle

I was reading an essay (that has been simplied such that it takes on the format of notes but still is like an essay...not sure how to categorize it) at this webpage : http://www.sfu.ca/philosophy/swartz/freewill1.htm#intro
which concerns free will. At this time, I have only read through the two pages or so when I ran into an intriguing idea presented by the author:

For a bit of back ground for the particular paragraph of interest, read this:
And the following is the one of interest:

What the author is saying here is that the law of the excluded middle does not hold true for future truth values and that it is not possible within the present laws of logic which the author considered. However, the author failed to consider the possibility of probability, which if I may say so is the basis for a truth table. When one is making a truth table for a statement, one is assessing the possiblities of certain truth values that occur in correspondence with other truth values (within the same statement). As such, the truth value of a future event is also based on a structured probability. The author is basically assuming that all truth values must neccesarily be definite for every temporal direction. And with this, I disagree.

Am I flawed in my analysis?

Last edited: Dec 28, 2004
2. Dec 28, 2004

### Imparcticle

And by the way....
The author from the same website I posted on my previous post suggests this proposal also:

3. Dec 28, 2004

### loseyourname

Staff Emeritus
I think that's a pretty stupid proposal. It should be clear that once the battle has been fought, assuming that there is a winner, then the statement "A won" is either true or false.

4. Dec 28, 2004

### StatusX

This is all meanigless. Statements are human inventions and they say absolutely nothing about the true nature of reality. The rules of logic should be changed, if necessary (which I don't think it is) to fit reality, not the other way around.

5. Dec 28, 2004

### Bartholomew

The only circumstance under which A could justifiably slack off would be if A were told of his win, and this information for some reason is known to A to be infallible. Call this circumstance C.

If A will win no matter what he does, then A can slack off. If what A does is necessary to say whether he wins, then we know that A only does those things which ensure his win. That is, A can infer from C that he will choose to do nothing which is not conducive to his win. If not slacking off is necessary to win, then A can infer he will not slack off. You can say, "But what if A then set his mind to slack off?" and this is not a valid question. Given C, and given that if A sets his mind to slacking off he will succeed, we can infer that A will not set his mind to slack off; he is not of that disposition.

Then you ask, what if A _were_ of a disposition, when presented with C, to set his mind to slack off just to see what happens? If A had that disposition, C would have been false (because the information of A's win would have been false), so A could never have been presented with it, and the premises of the whole situation are impossible.

6. Jan 8, 2005

### Philocrat

THE PROBLEM WITH LEM

One of the gravest intellectual errors that is now plagueing nearly every discipline is the assumption that only one of the many comepeting theories or theses about a given subject is correct. LEM is one such theories that now gravely labours under this error. All that the advocates of LEM would have done is to state the 'EPISTEMOLOGICAL STATUS' of LEM objectively thus:

It is sometimes, and not always, true that 'every statement is either true or false'

instead of making it appear as if they are implying:

It is always, and not sometimes, true that 'every statement is either true or false'

Those who teach this topic to their students should have excercised the highest degree of caution by honestly telling their students that there are in actually fact specific instances when LEM may materially and adequately apply without disputes. But equally that there are also instances when LEM is quantitatively and logically inadequate. They shoud have been honest and told their students that;

LEM materially and adequately applies only to any proposition which consists of ABSOLUTE OPPOSITE CONSTITUENT TERMS (AOCT) that cannot occupy the same logical space (note that this is also true even if the opposite terms have middle terms that range over, the fact still remains that none of the opposite terms and their associatted middle terms can occupy the same logical space at once). For example consider the the following types of statements:

a) The Dog with closed eyes is either dead or asleep and not both at once
(or equivalently, dead or not dead and not both / sleep or not asleep and not both)

b) The man is either dead or alive and not both at the same time.

Yes, statements (a) and (b) are consistent with LEM because the propperty of being dead and the property of being asleep cannot occupy the same logical space, and the same is true of the property of being dead and the property of being alive, given that we take being alive to also include being in a vegetative state. In both cases, only one or the other can be true, at least as long as the human form remains as it currently is.

But in cases such as these:

c) The book is red and not red

d) The Bottle is filled with water and not filled with water.

(C) would imply in our natural language (NL) that the book is partially red (partly red and partly not red) and (d) would equivalently imply that the bottle is half-filled with water. This will also cater for some of those statements that usually contain vague terms such as 'bald', 'wet' etc. So that if you say 'The man is bald and not bald', you would be implying in NL that the man is partially bald.

NOTE: Well, in (a) someone had once argued that 'SLEEPWALKING' is logically equivalent to being both asleep and not asleep or being both asleep and awake at once, such that if you said "The man is both asleep and not asleep", you would be violating LEM. The controversy rages on!

Last edited: Jan 8, 2005
7. Jan 13, 2005

### Alkatran

The bottle is filled with water and not filled with water.

It's not true that it would be half full. Not being full doesn't imply emptinance. It could be ALMOST full. The simple fact is that it is NOT full. It can't be not full and full.

8. Jan 16, 2005

### Philocrat

Correction taken. What about partially full and not partially full? Or partially full and partially empty Does this mask the middle terms or values? I was only thinking of how to express myself normally in NL without logic doing my head in.

A bottle half-filled with water is completely empty!

In trading places, if anyone ever say this to you, you should turn around and say to him or her:

My dear friend, you are trying to cheat me in broad day light. I am a native speaker of a natural langauge and I do know when a bottle is completely empty!

Last edited: Jan 16, 2005
9. Jan 16, 2005

### Philocrat

Ok, if LEM is a viable logical theory, how come that one group of people in our society (Politicians) have perfected complex methodologies in NL to effectively violate it? Haven't you seen time and time again in the media how journalist try to push politicians to the corner and get them to respond to LEM-type questions with 'yes' or 'no' answers, and the politicians cleverly respond by claimining that the answers are both 'yes' and 'no' at once. In fact, it is not only politicians alone, I have seen many of my friends and other members of the public do the same. I even came across some responses on this PF that did the same thing.

What I am trying to point out here is that, in NL, when you ask someone a question, as it is usually the case in a normal conversation, and expect that person to say yes or no and the person responds by claiming that the answer is both 'yes' and 'no', this does look as if the person is violating LEM. Or is it not? But is this not a normal thing that the native speakers of NL do everyday? What is wrong in saying that the truth value of a given response to a question is both is partly the case and partly not the case?

If LEM is worth anything in the mainstream logical system, it must be properly clarified and made relevant to the life-blood of the native speakers of NL.

Last edited: Jan 17, 2005
10. Jan 17, 2005

### Mentat

If statements say nothing about the true nature of reality, then how is it that a statement could say anything about how worthwhile or "meaningless" a line of reasoning "truly" is?

11. Jan 17, 2005

### Mentat

Imparcticle,
I think one of the most important problems, with the reasoning you presented in the first paragraph, is the idea that propositions exist independent of space and time. What is important to the discussion (in this case) is time, so we should focus on that: Can you make the statement, "A won", coherently, if the battle has not yet been fought? What would it mean? Should we instead use the statement "A will win" (reference to the future instead of the past)? If so, will that not be bound by the same uncertainty as any prediction?

The law of excluded middle (be it really valid or not) applies to all statements on which one can reason. But can one reason on the validity (or truthfullness) of a statement that hasn't had a chance to be true yet?

12. Jan 18, 2005

### Philocrat

Transitional Logic (TL) accommodates all dimensions of time in its formal structure. When it comes to truth, TL treats the three dimensions of time (past, present and future) as a single time frame. The native speakers of Natural Language (NL) are encouraged think, speak, write and act clearly because NL aleady contained all the logical and quantitative components to do so. How do you do this? By actually teaching Clarity at all levels of the human education. At each level of inductrination, the native speakers of NL must be encouraged to learn how to map incomplete statements in a given time dimension to the remaining time dimensions using an appropriate logical forms or constructs that are available in NL already and made apparent by TL.

So, it seems that expecting the truth value of a future proposition to be true or false is almost pointless, if not completely irrelevant in the first place.

Last edited: Jan 18, 2005
13. Jan 18, 2005

### StatusX

The argument is that since all statements must be either true or false, a statement like "The world will end tomorrow" is either true or false right now and so it is already determined. But the fact is (and this is a fact of epistemology) that we don't know that the law of excluded middle accurately reflects reality. The argument rests on the certainty that this law is true, and since this premise is false, and the conclusion is invalid

Last edited: Jan 18, 2005
14. Jan 22, 2005

### Alkatran

But all statements aren't true or false!
Example: "How much is three minus two?"

Assigning 'true' or 'false' to that makes no sense. (paradoxical statements also come to mind). I think a more practical law is that if something is true it can't also be false, but there is the possibility of being neither true nor false (non-applicable, paradoxical, fuzzy logic, etc...).

15. Jan 23, 2005

### Philocrat

As far as the Conversational Theory of Truth is concernced , every statement in a conversation must pass concrete information (directly or indirectly) to the next statement, hence effectively contribute to both the intermediate truth-values and the final truth-value of the whole conversation. So, a good conversation is measured by how effectively or consistently information of a truth-valued kind is passed from one statement to the next (without destroying that inforamtion) towards determining the overall truth of it.

If this is true, could we not equally claim that even a 'sneeze' (let alone a question, a command, an exclamation, or a metaphor ) is also effectively contributing in a truth-valued manner to the conversation? Or is it not?

Last edited: Jan 23, 2005
16. Jan 29, 2005

### jackle

I think every statement has both a true and a false aspect. Even clear cut things like "Today is Wednesday" doesn't get the same answer on different days. Likewise 1+1=3 is true to the person who interprets the sound "three" to mean the number 2. etc etc.

17. Mar 2, 2005

### moving finger

The flaw in the logic in the article you refer to is that the truth or falsity of the statement "A wins tomorrow" is dependent on the actions of A and B today, therefore it is incorrect to say (as the author says) that "no matter what A does today (or fails to do), it will make no difference". This is true whether or not one adheres to the law of the excluded middle; it also has nothing to do with probability. The world may be entirely deterministic, the law of the excluded middle may still apply, and yet the truth or falsity of "A wins tomorrow" is still dependent on the actions of A and B today.

18. Mar 16, 2005

### Tom Mattson

Staff Emeritus
I agree, this article is silly. When we say that "p is true", we mean "It is the case that p", not "It was, is, and always will be the case that p." The author of the article has it exactly ass-backwards. He is denying that real planning and real effort have causal efficacy, while he affirms that merely assigning truth values has such efficacy. What a crock!

19. Mar 18, 2005

### Philocrat

Well, this is Metaphyiscally Narrow and Epistemologically Impoverished. Metaphysically, if you catigorise the notion of 'Force' into (1) Overcomable Force and (2) Non-overcomable Force, you could argue that free will conveniently operates where one can physically and mentally overcome opposing forces. This introduces modal logic to interplay to take care of this metaphysical catigory: ability to overcome certain natural forces or constraints. When you possess the natural ability to overcome opposing forces on your pathway it is metaphysically equivalent to 'Freely Acting' unopposed. Overcoming physically opposing force is metaphysically equivalent to being physically unopposed. The modal Logic would then describe all the variants in such a world as follows:

1) If the conditions in world X is such that I am now overcoming a force or a set of forcess, then it is necessarily the case or true that I am now freely acting.

2) If some forces in world X are such that they are overcomable, then it is necessarily true that I sometimes act freely.

3) If some forces in world X are such that they are overcomable, then it is possibly true that I am now act freely.

4) If some forces in world X are such that they are overcomable, then it is possibly true that I will act freely tomorrow.

On the epistemolgical side of the arguemnt, you could argue that even if forced conditions existed in world X, so long as I knew how to overcome such forced conditioned, then it is immaterial or irrelevant whether forced conditions existed or not. For KNOWING HOW to overcome forced conditions in world X is metaphysically and epistemologically equivalent to ACTING FREELY in that world.

Last edited: Mar 18, 2005
20. Mar 19, 2005

### Chronos

Why are these arguments so complicated? Tom gave a very good answer and causality works. You are entitled to your objections, but it is up to you to show where causality breaks down... and don't resort to QM unless you have the math. Apologies, but that argument is a cowpie.
.

Last edited: Mar 19, 2005