View Full Version : Can a thing be both true and false at the same time?

B. de Corbin

10 Jul 2016, 05:31

In Western logic, a fundamental principle is that a thing can be either true or false, but not both.

Basic principles like: If A = B and B = C then A = C fall apart if this principle is false because then A could equal C, but also not equal C (If A = B and B = C then A may or may not = C).

In more concrete terms, If 6+4=10 and 15-5=10 then 6+4=15-5 becomes If 6+4=10 and 15-5=10 then 6+4 may or may not = 15-5.

Here's a video describing the problem:

http://youtu.be/-3-eGiSVCks

So - is it possible for a thing to be both true and false at the same time?

(I realize that this seems to be a highly abstract problem, but it has huge aplications in real-world thinking. Instead of being forced to say "yes" or "no" in responding to a simple question it becomes intellectually valid - i.e. Not a copout or mealy-mouthed - to say "yes and no.")

MaskedOne

10 Jul 2016, 06:18

Can you take the square root of a negative number?

That's the closest scenario I can think of atm where "yes and no" becomes valid.

B. de Corbin

10 Jul 2016, 06:25

Can you take the square root of a negative number?

That's the closest scenario I can think of atm where "yes and no" becomes valid.

Much simpler: This statement is false. Is the preceeding sentence true?

Also, if you want to find a plethora of examples, change abstractions into concretes...

anunitu

10 Jul 2016, 06:31

The square root of -1 is defined as I(Imaginary number) I had to work with this while studying electronics. It is a bit hard to wrap your mind around it at first.

Imaginary Number. (http://mathbitsnotebook.com/Algebra1/Radicals/RADNegativeUnder.html)

also Boolean algebra... (https://en.wikipedia.org/wiki/Boolean_algebra)

DragonsFriend

10 Jul 2016, 08:37

The sun is a good thing. The sun is a bad thing. Both statements are true but they are also contradictory. In reality the sun is. it exists as a system and not a single thing. (similar to the square root of a negative number) the square root of -4 is 2 and -2, a system and not an absolute.

When operating with absolute values they can be true or not but not both. There is only a single value. When operating with systems there can be properties that are true and false.

I like numbers, they have absolute values but can be used in systems that don't have absolute values. Zero has no value, yet you can multiply with it, add it and subtract it but you can't divide by it. Logically any number divided by itself is 1. If you could divide by zero the zero divided by zero would be 1. If you divide any number by zero you get infinity and why not multiplying any number by zero gives you zero. True or not many statement have degrees of each.

thalassa

10 Jul 2016, 08:39

How are we defining "truth"?

B. de Corbin

10 Jul 2016, 08:45

How are we defining "truth"?

Matching reality :).

I.e.: a thing is true (in this context) if it can be demonstrated to accurately reflect reality.

"Truth" is the quality possessed by a true statement.

DragonsFriend

10 Jul 2016, 08:45

It seemed from the first post that we were using true as an adjective while "TRUTH" infers a noun. The TRUE statement -> The TRUTH is.

I don't know how anyone else has defined it but it seemed to me the usage was self evident.

anunitu

10 Jul 2016, 08:57

In reality there are also things that violate the "Laws" of physics The whole string theory idea,and the idea( I believe recorded) where the mere observation of something can change the outcome. The idea that a subatomic partial can exist in more than one place at the same time. The attempt to explain these things..oh and Schrödinger's cat(poor kitty does not know if it is coming or going).

And the question if true and false can describe the same object(Perhaps or perhaps not) or true and false. Welcome to the rabbit hole...

B. de Corbin

10 Jul 2016, 09:05

The sun is a good thing. The sun is a bad thing. Both statements are true but they are also contradictory. In reality the sun is. it exists as a system and not a single thing. (similar to the square root of a negative number) the square root of -4 is 2 and -2, a system and not an absolute.

When operating with absolute values they can be true or not but not both. There is only a single value. When operating with systems there can be properties that are true and false.

The value of Western bolar logic is that it forces "large grain" questions to be rephrased as "small grained" questions, increasing exactitude.

"Is the sun a good thing?" Is a large grained question because it is indefinite, leading to a "yes and no" response as the only possible response. Since binary logic can not accept "yes and no" as an answer, the question would be tossed back as malformed, and would have to be revised (made small grained) by including specific details of context (i.e: is the sun good for photosynthesis?").

With absolute values, I wonder if 10 always equals 10. This is where the question actually gets interesting...

anunitu

10 Jul 2016, 09:12

And again a question comes to mind..a certain man,who will remain nameless,who just happens to have a tiny little square mustache. If he tries to take over the world,is it because we wishes to destroy the world,or is he trying to rebuild it in a better form(at least in his mind and vision of what is better) Or,is he just as crazy as an excrement eating flying rodent?

MaskedOne

10 Jul 2016, 09:12

Nope sometimes 10 = 2 or 10 = 8 or 10 = 7....

Ok, I'll stop playing with different bases now. Especially since the prereq of absolute values might negate that ploy anyway.

anunitu

10 Jul 2016, 09:23

Have you found the truth and joy of Octal??? Hands pamphlet while singing the Octal song.

- - - Updated - - -

Also context is always a factor,except when it is not.

B. de Corbin

10 Jul 2016, 09:36

Nope sometimes 10 = 2 or 10 = 8 or 10 = 7....

Ok, I'll stop playing with different bases now. Especially since the prereq of absolute values might negate that ploy anyway.

LOL - sticking to base 10, I'm going to make the illogical statement that "while 10 always ='s 10, not all 10's are =."

- - - Updated - - -

...because:

...context is always a factor,except when it is not.

thalassa

10 Jul 2016, 10:40

Something can be true in multiple ways, some of those ways are seemingly contradictory. This does not mean that those contradictions are false, rather (as anu said), context is everything...except when its not.

Also, one must consider value-laden, opinion-based statements...there's no way for them to be "true" in the sense of a universally-accepted multiply-shared reality.

Denarius

10 Jul 2016, 14:00

48÷2(9+3) = 2

48÷2(9+3) = 288

One is true and the other false, which one is which depends on the order of operations used. (http://knowyourmeme.com/memes/48293) Meaning that saying one is true and the other false is just as valid either way. However, no matter how you solve it, one is true and one is false.

Sort of an algebraic superposition, Schrodinger's equation. Meaning that it is only both true and false at the same time as long as it is unsolved, as it can't be solved to be both at the same time.

Hawkfeathers

10 Jul 2016, 15:41

Sure, why not?

4912

B. de Corbin

12 Jul 2016, 05:03

Here's how I think about it - context... are we talking about abstractions, or are we talking about real things?

If 6+4=10 and 15-5=10 then 6+4=15-5, as long as you are talking about pure abstractions (numbers) that are not tied to real-world "things."

However, as soon as those abstractions relate to "things" in the real world, 6+4 is not = 15-5, because one represents an increase, while the other represents a decrease, and an increase is not the same as a decrease.

For example, if you have $6, and you find $4 laying on the ground, you now have more money, but if you have $15, and you lose $5, you now have less money, even though in both cases you have (in the end) $10.

DragonsFriend

12 Jul 2016, 09:43

Again, the process is not the same but the resultant values are the same. 10 = 10 no matter what process is used to get there.

You need to define whether you are comparing values or processes.

In math:

48÷2(9+3) = 2 is false because the parenthesis are calculated first so you have 48÷2x12 and the rest of the operation is performed left to right. 24x12=288

48÷2(9+3) = 288 is true.

The definitions of procedure are as important in this case as is the definitions of the values. to make the answer 2 you need to add another set of parenthesis: 48÷(2(9+3))=2

Hawkfeathers

12 Jul 2016, 09:50

I had a boss once who proved that 1+1 does not =2. We got our new sales quotas, and they were double the previous ones. He quoted some formula they used to create the goals, using run rates, economic indicators, etc., and 45 minutes of related gobbledy-gook, and they weren't doubled, they were "adjusted". I told him he should call Harvard and tell them he has changed mathematics. The little weasel never liked me.

anunitu

12 Jul 2016, 09:56

From the little weasel description,I imagine you were not a fan of him also...

DragonsFriend

12 Jul 2016, 10:00

There are times when algebra doesn't work:

If A = B then A+B = 2A = 2B is correct in all situations but under the same hypothesis A/B = 1 is not correct in at least one case.

This is an example of math is not always logical. If A=0...

I can be both awake and not alert at all. :p

Denarius

12 Jul 2016, 14:03

In math:

48÷2(9+3) = 2 is false because the parenthesis are calculated first so you have 48÷2x12 and the rest of the operation is performed left to right. 24x12=288

Actually, there is the argument that using an obelus instead of a solidus implies that everything before it is the numerator and everything after it is the denominator. Making it a complex fraction, which you would simplify to two.

There are other arguments as well. You'd know that if you followed my link.

DragonsFriend

12 Jul 2016, 17:04

Actually, there is the argument that using an obelus instead of a solidus implies that everything before it is the numerator and everything after it is the denominator. Making it a complex fraction, which you would simplify to two.

There are other arguments as well. You'd know that if you followed my link.

If you had taken the time to view the note on the statement you would have found exactly what I stated. The parenthesis make that part of the operation first instead of last and division and multiplication are taken in order left to right.

There is a reason for standards.

As a hobbyist programmer I use notations like that a lot and I have to be aware of the order of operations in order to get an accurate answer. such as this:

deflexn = (velrot*pow(ranj,2)*sin(all.latitude))/(ranj/tt);

Denarius

12 Jul 2016, 17:16

There is a reason for standards.

There are always exceptions and differing interpretations. Order_of_operations#Exceptions (https://en.wikipedia.org/wiki/Order_of_operations#Exceptions)

What we are talking about are conventions, not hard and fast rules. There is no one universal standard.

DragonsFriend

12 Jul 2016, 17:49

There are always exceptions and differing interpretations. Order_of_operations#Exceptions (https://en.wikipedia.org/wiki/Order_of_operations#Exceptions)

What we are talking about are conventions, not hard and fast rules. There is no one universal standard.

You are correct which is why it is important to use some means of forcing the process that you use or intend to be used to solve the notation.

Even in language we use notation to force the understanding:

Let's eat grandma. and Let's eat, grandma. Same letters with different meanings.

thalassa

13 Jul 2016, 01:45

Sometimes people get bogged down in minutia.

Scale is often an area where this are the are true/false become the opposite.

Familiarity often does the same thing--many times to someone with a basic knowledge or understanding, a subject seems inflexible and rule-bound...but to someone with a greater understanding it's quite bendy.

And so, it (once again) comes down to context.

The answer, Corbin, is probably what I tell people at work all the time--It depends. There are too many variables to ever give an answer without exceptions and nuances. In the real world, there is only one absolute--there are no absolutes.

B. de Corbin

13 Jul 2016, 02:08

The answer, Corbin, is probably what I tell people at work all the time--It depends. There are too many variables to ever give an answer without exceptions and nuances. In the real world, there is only one absolute--there are no absolutes.

When I started reading Neitsczhe I was bothered when he said something to the effect that science does not give a accurate depiction of reality (something along those lines).

Since you know I have an amature's love of science, and nobody can seriously refute the successes of the scientific method, I didn't know what to make if it - was he gonna give me some anti-intellectual gobbledygook?

Eventually I came to understand what he was saying - context matters. That's the actual meaning of the imfamous title Beyond Good and Evil; there are no absolutes, everything depends on context. In science, theories and experiments remove variables - it's actually required, and a large part of the reason to do an experiement.

But by doing that, one creates an abstraction - something that is no longer real because in the real world their are infinite variables.

As long as the person doing the thinking remembers this, it isn't much of a problem. Scientists do drug trials and monitor long term effects, even when in vitro tests suggest that the drug is perfect because you need to test it where all the variables go back in, i.e.: the real world.

Physical science has become pretty good at this, but other "sciences," maybe not so much - political science, economic science, often the social sciences and psychology (although they are getting better) get a fail here. They are still so in love with abstract theory that they have lost touch with reality.

Context - the variables - matters.

Raphaeline

13 Jul 2016, 10:00

Not precisely on topic, but I was listening to someone talk about The Fourth Way and mentioned something about true/not true vs. useful/not useful and it was something I've held on to as a way to describe my religious beliefs, which usually make me sound like an atheist in denial.

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