A logical tautological contradiction

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Neil D
 
Reply Thu 25 Jun, 2009 06:21 pm
Ive learned a new word recently, its tautology,and I understand it to mean something such as "it will either rain tomorrow, or it wont rain". A statement that will always be true no matter the circumstance.

This made me think of a couple things. First, theres something in Physics called the measurement problem(some of you may know about it). It has to do with subatomic particles not having a definite state until they are measured(observed).

Now the logical tautology "the cat is dead or alive" will always be true,
and the contradiction "the cat is dead and alive" can never be true. However, in schroeders cat experiment, when the cats life depends on the definite state of subatomic particles. It is possible for the cat to be both dead and alive. You can read more about the measurement problem, or Shroeders cat to get the complete story if you wish.

There is also another Physics experiment in where one photon can be in two different places at the same time.

Thought this might be interesting for anyone who doesnt know about it.
 
Zetetic11235
 
Reply Thu 25 Jun, 2009 06:55 pm
@Neil D,
:Glasses:The Schrodinger's cat thought experiment was supposed to be a criticism of the Copenhagen interpretation of Quantum Mechanics, claiming that it leads to absurd results. This is a standard technique for observing the logical inconsistencies of a claim. Turns out his critique was flawed due to his inflexibility on certain issues, which lead him to believe that QM(in the case of the Copenhagen interpretation) was absurd.

Here is a nice little article about it:



At any rate, it is by no means something that is meant to make you think that a tautological contradiction is something that makes sense. In fact those two words together have no meaning behind them at all. Its like saying 'there is a black white over there! How strange!'.Smile
 
Whoever
 
Reply Fri 26 Jun, 2009 08:05 am
@Neil D,
Neil;72230 wrote:
Ive learned a new word recently, its tautology,and I understand it to mean something such as "it will either rain tomorrow, or it wont rain". A statement that will always be true no matter the circumstance.

Hi Neil. I want to nitpick. I think that this may be a truism rather than a tautology. And it is not even really a truism This pair of assertions, taken together, state that there will be a tomorrow. This is certainly not a tautology.

Quote:
Now the logical tautology "the cat is dead or alive" will always be true.

Hmm. What about "the unicorn is dead or alive".

Quote:
and the contradiction "the cat is dead and alive" can never be true.

I'm afraid this is not dialectic contradiction. The contradiction would be between 'is alive/is not-alive' or 'is dead/is not-dead'. Aristotle is very clear about this. A true contradiction must involve a reversal of the copula, not the introduction of a new term. Thus the assertion that the cat is both neither dead nor alive is not a contradiction, even it appears to be impossible. This is a crucial point, because if we take your view of contradiction then quantum mechanics and mysticism become paradoxical. We want to be able to say the the unicorn is neither dead nor alive without falling foul of the rules of logic.
 
ValueRanger
 
Reply Sat 4 Jul, 2009 11:23 am
@Neil D,
Same difference.

Take the postulate "we all come from the same source", and "everyone is different". These test consistently true, but are in opposition to one another (note "one another" is an axiom, or tautology).

Essentially, because we are byproducts of the law of opposites in physics, any spacetime object thusly contains contradictions in the set. And since reality is modular and scalar, consistency proves...


An excellent exercise: hierarchically map your values according to need, resolving to life-and-limb. This is a consistent mathematical progression, like Maslow's Hierarchy of Needs, that you can apply through your life.

When you get proficient at this, this philosophy (software choice) directly corresponds to hardware (genetic inheritance) that you pass on from generation, to generation. This Golden sequitur is necessary to sustain for a species gaining ever more control over the forces that control us.

God dot.
 
richrf
 
Reply Sat 4 Jul, 2009 12:31 pm
@Neil D,
Neil;72230 wrote:
Ive learned a new word recently, its tautology,and I understand it to mean something such as "it will either rain tomorrow, or it wont rain". A statement that will always be true no matter the circumstance.

This made me think of a couple things. First, theres something in Physics called the measurement problem(some of you may know about it). It has to do with subatomic particles not having a definite state until they are measured(observed).

Now the logical tautology "the cat is dead or alive" will always be true,
and the contradiction "the cat is dead and alive" can never be true. However, in schroeders cat experiment, when the cats life depends on the definite state of subatomic particles. It is possible for the cat to be both dead and alive. You can read more about the measurement problem, or Shroeders cat to get the complete story if you wish.

There is also another Physics experiment in where one photon can be in two different places at the same time.

Thought this might be interesting for anyone who doesnt know about it.


Hi Neil,

I too am interested in the philosophical implications of quantum mechanics. Though there appears to be some inconsistencies between the way the micro and macro world appear, it is interesting to note that all of our senses are dependent on the operation of the elementary particles which are the domain of quantum mechanics. So ... make of it what you will and happy exploring!

Rich:)
 
parker pyne
 
Reply Sat 4 Jul, 2009 09:29 pm
@Neil D,
I'm afraid I cannot give you a response, because I have nothing to say.


Haha, yeah this was a failed joke on tautologies.
 
kennethamy
 
Reply Sun 5 Jul, 2009 07:06 am
@Neil D,
Neil;72230 wrote:
Ive learned a new word recently, its tautology,and I understand it to mean something such as "it will either rain tomorrow, or it wont rain". A statement that will always be true no matter the circumstance.

This made me think of a couple things. First, theres something in Physics called the measurement problem(some of you may know about it). It has to do with subatomic particles not having a definite state until they are measured(observed).

Now the logical tautology "the cat is dead or alive" will always be true,
and the contradiction "the cat is dead and alive" can never be true. However, in schroeders cat experiment, when the cats life depends on the definite state of subatomic particles. It is possible for the cat to be both dead and alive. You can read more about the measurement problem, or Shroeders cat to get the complete story if you wish.

There is also another Physics experiment in where one photon can be in two different places at the same time.

Thought this might be interesting for anyone who doesnt know about it.



The term, "tautology" is a technical logical term. It means, "true, regardless of what constants are inserted into the variables". And tautologies test out true on a standard truth table. Where 'P' is a proposition, then the statement form, P or ~P is a tautology. Whether "It is raining, or it is not raining" is a tautology, depends on whether it is a substitution instance for the statement form, P or ~P. If for example we interpret P or ~P so that it is not true because it may be just drizzling, then it is raining or it is not raining will not be considered a proper substitution instance of that form.

Naturally, if you use the term, "tautology" in a way in which it deviates from its technical sense in logic, it is up for grabs what you will say. That is the danger of starting with a technical term, and then giving it a popular but inaccurate interpretation. (The same thing happens to science in quantum theory, or relativity theory. Or in mathematical logic when Godel's theorem is distorted). You will then end up by saying not only false, but nonsensical things.

There are no "tautological contradictions" in any intelligible sense of "tautology", since No tautologies are false, and all contradictions are false. But, the negation of every tautology is a contradiction, and the negation of every contradiction is a tautology.
 
goapy
 
Reply Mon 6 Jul, 2009 05:39 am
@kennethamy,
kennethamy;75049 wrote:
If for example we interpret P or ~P so that it is not true because it may be just drizzling, then it is raining or it is not raining will not be considered a proper substitution instance of that form.


So, as long as we interpret P or ~P so that it is true, then is it true. But if we interpret P or ~P so that it is not true, then it is not true?
 
Whoever
 
Reply Mon 6 Jul, 2009 06:25 am
@Neil D,
Quote - "Take the postulate "we all come from the same source", and "everyone is different". These test consistently true, but are in opposition to one another.'

This is a well known problem. Identity and difference are co-dependent concepts. We can't have one without the other. For two things to be different they must be in some respect identical, and if the are in some respect identical they must be different.

This is not a contradiction. This is because the propositions 'x & y are identical' is not the contradictory of 'x & y are different'. It is the copula that must be negated for a true contradiction. (E.g. 'x % y are identical' and 'x & y are-not identical.') This might seem a small point, but when using the dialectic to refute philosophical propositions it is a crucial one. It means that the two assertions 'an electron is a wave' and 'an electron is a particle' do not form a contradictory pair, and could both be true or false without any modification to Aristotle's three laws. This is a point missed by many physicists.
 
kennethamy
 
Reply Tue 7 Jul, 2009 06:01 am
@Whoever,
Whoever;75293 wrote:
It means that the two assertions 'an electron is a wave' and 'an electron is a particle' do not form a contradictory pair, and could both be true or false without any modification to Aristotle's three laws. This is a point missed by many physicists.


They can both be false, since an electron may be neither. But they cannot both be true. Logicians would say that they are contraries, and not contradictories. That animal is a cat, and that animal is a dog, are also, contraries, but they are not contradictories. They can both be false, but they cannot both be true.
 
Whoever
 
Reply Tue 7 Jul, 2009 06:25 am
@Neil D,
Why can't they both be true?
 
kennethamy
 
Reply Tue 7 Jul, 2009 06:41 am
@Whoever,
Whoever;75581 wrote:
Why can't they both be true?


Why can't an animal be both a cat and a dog? Because cats and dogs are different species. Why cannot something be both a wave and particle? You will have to ask physicists. Of course, we may not know which it is, or it may be a wave at one time, and a particle at another.
 
Whoever
 
Reply Tue 7 Jul, 2009 08:07 am
@Neil D,
But surely if it is a wave at one time and a particle at another then it would not be breaking any rules to say it is both. At least, it would not be a contradiction to say it is both. The actual situation would be an empirical matter, but we're only concerned with the logic. If an entity (God, say) is a cat and a dog then it is possible to be both a cat and a dog. To say an entity is both is just to say it is not exclusively one or the other.

To be clear, I was suggesting that x can be both y and z as long as x=y and x=z do not form a true contradictory pair.
 
kennethamy
 
Reply Tue 7 Jul, 2009 10:17 am
@Whoever,
Whoever;75623 wrote:
But surely if it is a wave at one time and a particle at another then it would not be breaking any rules to say it is both. At least, it would not be a contradiction to say it is both. The actual situation would be an empirical matter, but we're only concerned with the logic. If an entity (God, say) is a cat and a dog then it is possible to be both a cat and a dog. To say an entity is both is just to say it is not exclusively one or the other.

To be clear, I was suggesting that x can be both y and z as long as x=y and x=z do not form a true contradictory pair.


What is the difference between a "true" contradictory pair, and just a contradictory pair? How do you tell? A contradictory pair would be, Susan is not five feet tall, and Susan is five feet tall. A non-contradictory pair is, Susan is 5 feet tall, and Susan is 6 feet tall, since Susan can be both. In fact if she is 6 feet tall, then she must be 5 feet tall.
 
Whoever
 
Reply Tue 7 Jul, 2009 10:41 am
@Neil D,
Aristotle deals at length with contradictory pairs in De Interpretatione. Here, for the dialectic, he gives the rule for contradictory pairs, or the formal conditions under which it is legitimate to apply the LNC and LEM.

Of every contradictory pair, one member is true and the other false.
 
ValueRanger
 
Reply Sat 11 Jul, 2009 04:02 pm
@Neil D,
Yes, false is both false and true, and true is both true and false.

This is because space and time persist, so do differences/contradictions.

Hypothesis: the more balanced/equal a set becomes, the less needed that value set is. So since humans, like any other spacetime set (light/dark energy, law of opposites, etc.) that strives for easiest path of resistance (order), need to integrate opposites to stay adaptable, we need to proportionately scale hard-to-easy, or weak-to-strong.

This is why accepting your weaknesses augments your strengths, and layered self-interest is key to the human species persisting.

What is "layered" self-interest? It is like the Christian Serenity Prayer: knowing when you are in proximity to another that is better at the task at hand, and letting them take the lead. Then, in consequential proportion (The law of inverse proportion, or, The Golden Proportion), the Heraclitean Flux shifts to your best.

Some consistent physics progressions: perfect fifths in music, 6:1 Golden Ratio, 7th day sabbatical (fight/rest equation), six degrees of separation, six moves ahead in chess, and so on. Consequently, every categorical imperative can be rationalized thusly.

What most logic-leaning people have trouble with: spontaneity. Conversely, most fly-by-the-seat-of-your-pants, spontaneous people have trouble with: logic (sequitur).

So does logic contain spontaneous, gut instinct in the set? Does torsion space convey charge, and did Heraclitus nail reality thousands of years ago?
 
 

 
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