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Robdemanc
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11 May 2012, 2:19 pm

We tend to believe that things are either true or false, yet some cultures believe things can be both true and false, or neither. What are your thoughts on this?

I believe all four are possible and we limit ourselves by supposing everything has either a true or false value attached to it.



snapcap
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11 May 2012, 4:37 pm

Slavery is good.

True.

That is the view of a family member that voluntarily gives up their children to slavery because they couldn't care for their kid anymore, and if they didn't go, they would starve to death. Even though slavery isn't good, it is good compared to the likelihood of death.


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Last edited by snapcap on 11 May 2012, 5:21 pm, edited 1 time in total.

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11 May 2012, 5:18 pm

As someone who just had half a year on logic, I can say that we definitely aren't limiting ourselves with True and False. If it can be both, then you need to qualify it, and if it can't be ether then it's not a proposition.



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12 May 2012, 11:38 am

Chinese philosophy addresses this with the concept of yin and yang. Western philosophy and legal thinking have difficulty understanding that context and relevance matter.



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12 May 2012, 12:35 pm

Every good decision has also bad consequences, and every bad decision has also good consequences.
But a bad decision has more bad consequences than good consequences. And a good decision has more good consequences than bad consequences.

I can not say that something is good, I can only say that it looks good to me, or that I think that it would be good.



Robdemanc
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12 May 2012, 1:16 pm

I am not asking here about what is good or bad. I am talking about our mindset that things have a true or false value.

The reason I ask is because I saw a documentary about infinity. It stated that if we had two infinte sets, can we say they are both equal?

Example:

A = {The set of all numbers}

B = {The set of all even numbers}

Can we say that A > B? If both sets are infinite how can we say one is greater than the other? Perhaps we could say that the statement A > B is neither true nor false, or is both.



abacacus
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12 May 2012, 5:36 pm

A statement can indeed be both true and false. It's a tricky balance, but a skilled liar can weave a tale without ever telling a lie and make you believe whatever he wants you too.


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snapcap
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12 May 2012, 10:35 pm

True and false exists in computer programs.


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edgewaters
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12 May 2012, 10:40 pm

snapcap wrote:
True and false exists in computer programs.


So does fuzzy logic. :wink:

Which more or less deals with exactly this sort of question.



Robdemanc
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13 May 2012, 6:25 am

snapcap wrote:
True and false exists in computer programs.


How does that work?



Declension
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13 May 2012, 7:10 am

Robdemanc wrote:
A = {The set of all numbers}

B = {The set of all even numbers}

Can we say that A > B? If both sets are infinite how can we say one is greater than the other? Perhaps we could say that the statement A > B is neither true nor false, or is both.


The two sets have the same cardinality, and we can write |A| = |B|. We say that two sets have the same cardinality when it is possible to neatly "pair off" each element in A with an element in B. We can do it like this:

A B
1 2
2 4
3 6
4 8
5 10
6 12
... ...
n 2n

However, not all infinite sets have the same cardinality. For example, the set of real numbers, R, has a strictly greater cardinality than the set of natural numbers, N, and we can write |N| < |R|. This means that there is a subset R* of R such that it is possible to neatly "pair off" each element in N with an element in R*, but there is no subset N* of N such that it is possible to neatly "pair off" each element in N* with an element in R.



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13 May 2012, 11:38 am

Robdemanc wrote:
I am not asking here about what is good or bad. I am talking about our mindset that things have a true or false value.

The reason I ask is because I saw a documentary about infinity. It stated that if we had two infinte sets, can we say they are both equal?

Example:

A = {The set of all numbers}

B = {The set of all even numbers}

Can we say that A > B? If both sets are infinite how can we say one is greater than the other? Perhaps we could say that the statement A > B is neither true nor false, or is both.


B is a proper subset of A. B and A have the same cardinality because because a one to one onto map exists between the sets, namely n <-> 2*n

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13 May 2012, 11:41 am

I don't think we're limiting ourselves.

To say that something is both true and false or neither true nor false (which I don't know what criteria would even separate those two), to me just says that the matter being discussed hasn't properly been digested and broken down into its individual factors - hence you have one thing that's true, one thing that's false, its really two things that you're mistaking for one thing.


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Evinceo
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13 May 2012, 12:13 pm

Robdemanc wrote:
snapcap wrote:
True and false exists in computer programs.


How does that work?


Most languages have a Boolean type, and the ones that don't usually treat any integer except zero as True.



Robdemanc
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14 May 2012, 5:02 am

Evinceo wrote:
Robdemanc wrote:
snapcap wrote:
True and false exists in computer programs.


How does that work?


Most languages have a Boolean type, and the ones that don't usually treat any integer except zero as True.


But in programming booleans are treated as either true or false but not both.



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14 May 2012, 5:43 am

Robdemanc wrote:
I am not asking here about what is good or bad. I am talking about our mindset that things have a true or false value.

The reason I ask is because I saw a documentary about infinity. It stated that if we had two infinte sets, can we say they are both equal?

Example:

A = {The set of all numbers}

B = {The set of all even numbers}

Can we say that A > B? If both sets are infinite how can we say one is greater than the other? Perhaps we could say that the statement A > B is neither true nor false, or is both.


The point here is that you do not define what ">" is. When you compare 2 numbers, the meaning of > is clear, the standard greater-than relation. For sets of arbitrary size, however, there are multiple ways to interpret >.

Some other posters in this thread have already mentioned comparing both sets on their "cardinality" (a technical term for size, which is extended for infinite sets). If you look at cardinality, then A = B. If you interpret the > sign as denoting "is a superset of", then A > B is true.

In mathematics, a statement is always either true or false. Not both or neither. But that does require that the statement is very detailed and that all terms are well defined. There is a small branch of math called "fuzzy logic", where a statement can also take on truth-values between the two extremes of true and false (if 0 is false and 1 is true, fuzzy logic allows the truthfulness of a statement to be any real in [0,1], allowing a statement to be "somewhat true"), but this is a sidetrack of mainstream math.

In real life, the question of binary truth is obscured by the fact that many statements are not factual and are polluted with subjective elements. "The weather is nice today" can be both true and false depending on who you ask.