Law of the Excluded Middle


Law of the Excluded Middle:  [in logic]  1. The principle of one (and only one) of two contradictory propositions must be true.


 

Aristotle (384 b.c. - 322 b.c., Greece) gave us the three (3) Laws of Rational Thought:

The first is the Law of Identity,     A = A

The second is the Law of Non-Contradiction,     Not [ A and Not A ]

The third is the Law of the Excluded Middle.     Either [ A or Not A ]

[ if your thinking is outside of the above Laws - - you are an IRRATIONAL THINKER ]

 

Just as any less-than a three (3) legged stool will not stand on it's own - - so it is with the above three (3) Laws.....

Don't think for a minute that I'm intentionally slighting the first two (2) Laws - - nothing could be further from the truth.....

It is, for want of a better expression, a TRINITY of rationality.

Three (3) separate Laws, intertwined & interrelated - - comprising one (1) multi-faceted body of Rationality.....

 


 

Welcome to the Law of the Excluded Middle.....          [ L.O.T.E.M. ]

 

The core "Principle" of EVERYTHING is the Law of the Excluded Middle.....

Either it is - - or it isn't.

Even the Principle ITSELF is self-evident & self-proving - - either it is, or it isn't.

NO ONE is "immune" - - either you are, or you aren't.

 

 The Law of the Excluded Middle is relatively simple.....

 

It is the only way to, ultimately, unmask Objective Truth.

 

When all spurious factors are discarded, we discover the answer to a specific question:

           "Right or Wrong" - "True or False" - "On or Off" - "A or B"

              - - OR - -

                                                      "Correct", to the absolute exclusion of all other possibilities.                                          

 

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Commentary:      I'd like to add just a bit to the Law of the Excluded Middle, if I may - - - - - It may ALSO be that two contradictory

                                  propositions may BOTH be false, that NEITHER is true.  The example of this would be:  2+2=6 and 2+2=7.

                                  Contradictory, but neither is actually true.  The point is, there are INFINITE wrong answers to "2+2", but ONLY ONE (1)

                                  right answer - - to the absolute exclusion of any other possibility.

 

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As you will notice - - the "Middle" is ALWAYS "Excluded"!!   [ otherwise, it wouldn't be the Law of the "Excluded" Middle - duh ]

 

>>>>>  You should realize that not all questions amass sufficient facts to prove a definite conclusion.  <<<<<

This does NOT negate the Law of the Excluded Middle!

ANYTHING can be reduced to only Two (2) possibilities:

One (1) of which MUST be the CORRECT answer - - to the absolute exclusion of the other.

'Proof' of NEITHER is required.....

  

You should also realize that in most cases, 'Ground Rules' need to be agreed upon by all parties.....

[See the 'flipping the coin' example, below.....]

 

"Statistics" play NO PART in the Law of the Excluded Middle, EVER.  With the purchase of a "Power Ball" ticket - your 'chance' of winning is EXACTLY 50/50 each and every time - - and can NEVER be anything else.  You either purchased a winning ticket or you didn't.  Now, admittedly, the mathematical odds of you picking what turns out to be the right numbers for any one particular 'Drawing' is hundreds of millions to 1.  This is EXACTLY what draws people to the 'game'.  Well, that plus LOTS of MONEY!  No one actually CARES what the 'mathematical' odds are!  They know, intuitively, that their chance is exactly 50/50!

So..........YOUR TICKET is either a winner, or a loser - - no other possibility.....

 

Tell me - - WHAT ELSE CAN IT BE????

 

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Before we go any further, I'm going to throw in a couple of 'subtleties' which must be included for the sake of completeness...

 

The first is the concept of a proof by "Reductio ad Absurdum".

Take the time to research this yourself - - but the gist of it is as follows:

You have your 'True - False' argument - - or an 'A' or 'B' argument - - etc.....

One side appears to be difficult or impossible to 'prove', so you attempt to prove the 'other' side of the 'argument'.

The obvious fact is that if you're attempting to 'prove' the 'B' side is 'True', it's just as possible to discover that it's 'False'.

If the 'B' side actually IS True - - fine.  'A' is therefore 'False' - - and the argument is over.

Likewise, if you can logically prove that the 'B' side is 'False' - - by reducing the argument to a self-contradictory (and therefore 'Absurd')

conclusion - - you 'Prove' the 'A' side of the argument to be 'True' whether it is ultimately 'provable' or not.....

[ Self-contradictory positions violate the 2nd law of Rational Thought ]

 

[ concoct an equation where one side MUST be the square root of a negative number, or something divisible by Zero - - you get the idea ]

 

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The second brings Sir Arthur Conan Doyle and his super-sleuth, Sherlock Holmes into the picture.....

"Once you eliminate the impossible, whatever remains, no matter how improbable, must be the truth."

Notice that YOUR 'belief' in "whatever remains" is not necessary.  The TRUTH must, can & will stand on it's own.

YOUR failure to 'believe' is exactly that - - YOUR FAILURE!!!

[ this is the concept of "Objective Truth" - - truth that stands outside of Human influence ]

[ the only alternative to "Objective Truth" is "Subjective Truth" ]

[ 'Subjective Truth' is an oxymoron - - and violates the 2nd Law of Rational Thought ]

 

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Just because you can't 'Prove' a point doesn't mean it's NOT a valid point - - especially if the opposing view is demonstrably false!

If NEITHER point is 'provable' - - it doesn't negate the 'argue-ability' of either point, or, ultimately, the truth of one of them.

[ see 'Examples' section, below!! ]

 

This brings us to the CRUX of the Law of the Excluded Middle - - - how YOU accept the results.....

Truth is Truth is Truth - - it's what YOU do with it that matters.....

Deny Truth - - continue to live & believe the demonstrable LIE - - and that's MY definition of INSANITY & EVIL!!!

Even 'Truth' that's discovered via our 'Reductio ad Absurdum' model, above - - having no direct, positive 'Proof'.....

MUST be accepted as TRUTH!!!

 

If you can't see it, or hear it, or smell it, or touch it, or taste it - - it's generally not believable by anyone.....

BECAUSE it's TRUE - - you have to take it on "Faith".....

 

NOT some Pollyanna, preschool "Faith" - - rather, "Faith" being the acceptance of Objective Truth over the demonstrable Lie.....

 

FAITH - - isn't believing in 'a wish & a prayer' - - or some blind adherence to unsubstantiated dogma.....

FAITH - - "is the substance of things hoped for, the evidence of things not seen".  [ Hebrews 11.1 - - KJV ]

FAITH - - is the dawning of comprehension of the absolute INVIOLABILITY of the Law of the Excluded Middle.

 

 

 

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Let's start with some examples - - and what we mean by 'ground rules'.....

  1.      Whole numbers - - they're either even, or odd.  Neither is 'Right or Wrong', but there is no other possibility.
  2.      Binary Language - - it operates with both "One's" (1) & "Zero's" (0) - and nothing else - no other possibility.
  3.      Flip a coin - - Heads or Tails (see example below).
  4.      2+2 being equal to 4 - - 2+2=4, to the absolute exclusion of all other possibilities 

 

If we talk about the 'odds' of flipping a coin to determine the statistical results of 'Heads or Tails' consider the following:

  1. Gravity exists - - when we 'flip' the coin, it doesn't leave the solar system, or the galaxy.....
  2. We are on (for the sake of argument) Earth - - the coin is 'flipped' and eventually comes back down.....
  3. We are on dry land - - this obviously wouldn't work in the open ocean, etc.....
  4. We are working with a flat, hard, horizontal surface as our target - - not mud, not sand, not snow, etc.....
  5. No obstructions or aids to "Lean" upon.....
  6. A sufficiently rounded circumference so that the coin will, eventually, tip to the 'Head' or 'Tail' side.....
  7. No milled, sharpened circumference so that the coin could, or would 'stick' into the target surface occasionally....
  8. We are NOT 'flipping' a two-headed coin - - duh.....
  9. Etc, etc, etc.....     You get the idea.....

With the 'Ground Rules' agreed upon, when said coin is 'flipped' there are only two (2) possible outcomes.

It lands either 'Heads', or 'Tails' - - no leaving the solar system, no sinking to the bottom of the sea, no "Edgies".....

No middle ground - - the 'Middle' is EXCLUDED.....

 Black or White - - with no possibility of any shade of Grey.....

 

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 Now, let's talk about 2+2=4 - - spectacularly simple.....

Two (2), in and of itself, is pretty self-explanatory - - It's not any more or less than Two (2) - period.  By definition, it can't be.

Add a couple of them together - each exactly equal to the other - and you end up with Four (4).

Also, in and of itself, pretty self-explanatory - no more & no less - - again, by definition.....

 

It makes NO DIFFERENCE how much you 'wish', or cry, or scream - - throw a tantrum - - pout, hold your breath until you turn blue.....

Or use ANY specious or spurious argument to try & make it anything other than 4.

 

Two (2) plus Two (2) equals Four (4).  To the absolute exclusion of any & all other possible answers.

 

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From this point forward, you should (or must) have a rather thorough grasp and understanding of :

CAUSALITY - - - Consequence - - - and 'Instant Karma'.

There is no "Cause" that doesn't have a concomitant 'Effect' - - ('consequence') - - and likewise, generates 'Instant Karma'.

Likewise - - there is no 'Consequence' - - ('effect') - - and 'Instant Karma' - - that appears without an appropriate "Cause".

[ Ex Nihilo, Nihil Fit - - From nothing, comes nothing ]

 

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I probably should have prefaced this entire web page by saying that all parties to the discussion MUST be willing to grant the others the same respect of their positions & opinions as they, themselves, wish to be respected.  One presumes grace, maturity, logic, respect & manners - - but it's never a given, or a guarantee.....     If there is contention, at least we can agree to disagree - politely!!

  

Now, shall we have a go at a couple of examples where the "facts" appear to be insufficient to reach a conclusion?

 

Rather than attempt long-winded definitions & explanations of the two parts involved here, I think we'll go straight to examples.....

 

  In our quest for Truth, the next pair of hurdles pivot on what we will designate as 'Unknowable Facts'.

In the first example, without possibly 'Knowing the Facts' - - we CAN come to an absolute "A - or - B" conclusion.

In our second example, again without possibly 'Knowing the Facts' - - we CAN come to a similar conclusion.

In BOTH examples we are stymied by "Insufficient Data" and "Untestable Theories".....

From each 'example', One (1) answer will ultimately be proven correct, to the absolute, Eternal exclusion of the other.....

Again, both are predicated on agreeing to 'Ground Rules', and our mutual ability to respect the other's position.

 

 

First Example:     Is there life after death?

Let's start with a partial list of the 'Ground Rules'.....

  1. We exist - - we are not some part of a butterfly's dream.....     [ 1st Law of Rational Thought ]
  2. We are alive - - in whatever sense we can agree upon - - and that at some point this 'Life' will stop, we will die & disintegrate.
  3. That we are more than matter in motion - - we are self-aware.....
  4. We operate, mentally, at a level above the animals.....
  5. No parties to this discussion have positive, provable first hand knowledge, either way.....
  6. That the L.O.T.E.M. parameters dictate Two (2), and only Two (2) positions - - either there is NOT "life after death", or there IS.

This "argument" is over before it starts, really.....  NONE OF US CAN EXPERIENCE THE ANSWER UNTIL AFTER WE 'DIE'.....

 

Upon 'Death' we either become extinct, or we don't.  Without objective fact(s) to the contrary we CANNOT know.....

[ Does this then not become the search FOR "Objective facts to the contrary"????? ]

[ Just a 'hint' - - - - - - there ARE "Objective facts to the contrary"!!!!! ]

 

If we become 'extinct' - - great - - end of story.   [ and neither of us will EVER know ]

 If not - - great - - we pass into our next 'existence' where absolutely anything else is a possibility.....

With One (1) of those possibilities being the ACTUAL OUTCOME - - to the absolute exclusion of all others.

 

This CAN be rationally argued to L.O.T.E.M. conclusions WITHOUT ANY EVIDENCE WHATSOEVER!

 

If you were paying attention, earlier, you'll remember that I mentioned "Untestable theories"

The "Test" of this 'Theory' would be to either intentionally kill someone with the 'hope' that they would come back with

a report, or to have someone already dead - - come back with personal testimony.....

If there is no "Life after Death", your 'scientific' murder victim's consciousness, or "Soul" would instantly become 'extinct' upon

'Death' and be unrecoverable - - as would be the "Soul" of your already deceased person - - and hence

no report or personal testimony would be forthcoming.....

However - - - - - If there IS "Life after Death" - - - - - Two (2) specific 'hurdles' remain.....

The first becomes the question of 'Re-animating' the deceased.

Perhaps, because this has been an unsolvable puzzle, up to this point - - that's why we have no 'scientific' report or testimony.....

The second is the quintessential question of "BELIEVABILITY" of the 'testimony' of our 're-animated' corpse(s).....

As mentioned earlier - - if you can't see it, hear it, feel it, taste it or smell it, it's generally not believable by anyone.....

This is especially true if each 'testimonial' varies markedly in detail - - not to mention the dearth of such resurrections.....

There is, however, significant historical evidence of single, and mass resurrections of the dead - - with concomitant personal

testimonies - - sufficient, in my opinion, to NOT dismiss them, or the possibility of such, out of hand.....

It's not to distinguish whether such resurrections are 'True' or 'Untrue' - - rather, if they ARE 'True', how we handle said TRUTH.....

If they are "Untrue" - - fine, end of story.  If they are "True" - - then we MUST accept this TRUTH and act accordingly.....

[ or, again, reject demonstrable truth and continue to believe and live a lie - - deny, defy & remain delusional ]

 

HERE is where we have to show our maturity - - respect each other's position - - agree to disagree, if necessary.

 

Just don't fall into the trap of being 'legalistic' & demand that this is strictly an intellectual exercise - WITH NO CONSEQUENCES.....

[ Causality demands balance - - if you think it (or speak it - - or do it) - - THERE WILL BE CONSEQUENCE(S)..... ] [ and 'Instant Karma' ]

[ The "scariest" thing I know of in this life is that I will be held responsible for every thought, word & deed of my entire life. ]

[ As will you - - - - - for your life. ]

[ Of course - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - there is the "Cure". ]

 

If you're going to put forth an argument - - have the testicles to put your money where your mouth is.....

 

Sell out to, and LIVE your position - - and when, ultimately, you're found 'Right' - - don't gloat - - REJOICE!!!!!

 

And when, ultimately, you're found 'Wrong' - - don't whine - - take what comes - - after all, it WAS YOUR CHOICE!!!

 

You were, after all, given your WHOLE LIFE - - and a brain - - to determine which is the actual, CORRECT answer.....

 

In this life - - we see as through a glass, darkly - - eventually, all will be revealed     [or it won't]

 

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Second Example:          Does GOD exist?

Let's start with a partial list of the Ground Rules.....

  1. Mentally, we have the capability to think conceptually - - we can reason, understand abstract ideas, think logically, deduce.....
  2. Because we have the concept of 'God', or 'a god', it must be included in our discussions - - if we can reject one, or any, concept arbitrarily or out-of-hand - we can reject, or accept, any other for the exact same non-reason.....
  3. No parties to this discussion have positive, provable first hand knowledge, either way.....               [ or do they.................................??? ]
  4. That the L.O.T.E.M. parameters dictate Two (2), and only Two (2) positions - - either there isn't, or there is.....

Again, this "argument" is over before it starts, really.....  NONE OF US CAN EXPERIENCE THE ANSWER UNTIL AFTER WE 'DIE'.....

  

Now, we both know that this has been THE "Question of the Ages" - - and this web page is not the place to come to a conclusion.

[ of course, if you'd actually like to KNOW - - POSITIVELY - - that GOD exists, follow the link: Proof of God ]

 

Again, the only point I'm trying to make, here & now, is that this CAN be rationally argued to L.O.T.E.M. conclusions 

WITHOUT ANY EVIDENCE WHATSOEVER!

 

Pick a position, sell out to it, LIVE IT - - and either REJOICE - - or stand aghast and live with your choice - - FOREVER.....

 Or - - - become extinct - - - like you'd actually know at that point - - duh.....

 

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