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The Nature of Truth
#1
How do you view truth? Is truth absolute in your mind, relative or subjective?
What theory do you identify with and why?
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#2
Truth is absolute, just like logic. But just as we humans make mistakes in Math calculations, we may also not grasp the truth entirely and be mislead into fallacy.


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#3
I used to believe in correspondence theory but ever since I encountered Jordan B Peterson his pragmatic approach to the question leaves me refreshed its just so radically different from what i'm used to hearing and I can't help but to entertain the idea.

tldr; its only true if its useful to its survival



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#4
Truth is reality,
Conformity to fact,A statement of truth that corresponds reality.
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#5
What options are there?

I've never deeply studied the topic, but as far as i am concerned, right now, there is an absolute truth that can only be view from "God perspective" (or "3rd person perspective"). As long as you are part of some truth, you can't comprehend it.
What i am trying to say is that, we, humans, live in universe (we are part of it) so we can't fully comprehend truth about it, we can't put it in persepctive so to speak.
You can't comprehend your own existance so absolute truth is unreachable to individual creatures like us.

Having that said, i don't think this topic is any relevant to our existance, just like possiblity of some God out there somewhere.
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#6
It is relevant to our existence because people claim they know the truth and start wars over it.
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#7
What's true to me is what convinces me it is (with sufficient "proof").

(without getting very philosophical)

The word "proof" is different in different contexts. I like to think there's a hierarchy of classes of "proofs".
  • My mother is suddenly yelling at me for stealing the cookies. I see from the corner of my eye my an evil grin on my brother's face. That's "proof" he stole the cookies. That's (probably) reasonable. But not absolutely correct, as this kind would fail me if my brother was grinning for some other unrelated reason.
  • In a court of law, in a reasonably small list of possibilities, you being the only suspect without an alibi is "proof" you committed the crime; say court learns the committer was wearing a  red shirt, and you happen to be the only one who was wearing a red shirt that day. That's reasonable. But not absolutely correct, as this kind would fail if you're a victim of a plan to incriminate you/police did a sloppy work/unlucky/..etc.
  • In science, getting positive results for a theory in an experiment again and again is "proof" (appropriately, evidence) the theory is correct (works). That's reasonable, but note absolutely correct. There's the known quote by Einstein: "No amount of experimentation can ever prove me right; a single experiment can prove me wrong."
  • In formal mathematics and logic, proofs rely on solid foundation that's the closest to "the metal" as you can get. Reasonable of course, and people tend to think you can't go wrong here. But that's not absolutely correct either. There's a lot to say about this.

I feel bad for making a list like that, because there are always things in between. Even in mathematics, sometimes certain proofs are favoured over the others.

So, sometimes in maths, if you are familiar with the context, you can allow semi-correctness.
For example, the probability that a 2x2 matrix with randomly generated real coordinates has a determinant that's exactly zero is 0%. But this doesn't mean that there is no matrix with determinant zero (in fact, there are infinitely many. Just let three of the coordinates be zero, and the last can be anything you like). What you can do in regard the matrices with zero determinant as "a degenerate case", and allow the assumption that all matrices have non-zero determinants.

Another example is if you pick a random real number between 0 and 1, then the probability that this number is rational is 0% (so if you want to integrate a function that is not defined for all rational numbers, you can just dismiss all the undefined values as "having measure 0" and proceed with integration).

Now, for a long time, mathematicians accepted this, because it was all "under their watch". Moreover beneath all of this, mathematicians had to agree on  a set of "axioms" or "truths" that they'd just believe in and work upon. But it's no big deal. Until you learn that the foundation is not really that solid.

So we talk a little bit about Mathematical logic. One would imagine that the foundation of mathematics would be consistent (non-contradictory); it would be contradictory if you can prove that A is true, and B is true, but (A and B) is not true, or if you can prove that A is true and that A is not true. You would also want the system to be complete (anything true in the system should be provable within the system).
For example, natural languages like English is a system that is not consistent; suppose A said "I'm lying". If you prove A is saying the truth, then he's lying, but then if he's lying, then he's telling the truth => inconsistent. Hodgepodge. (I think English would also be considered incomplete since it doesn't describe everything it should; you need to update the language to add new words ..etc after every number of years/decades/centuries).

So the goal of mathematicians was to ensure that the axiom system that underlies mathematics is both consistent (you can't construct sentences like "I'm lying") and complete (everything true is provable). They thought they had done so (most popularly with the ZFC axioms). But soon their bubbles would be popped when a guy called Godel proved that any axiom system that allows us to do basic arithmetic, for example, make statements like "After every natural number is another natural number", is incomplete. Such system would also necessarily be unable to prove its own consistency (Godel's Incompleteness theorems ). So now we just accept the incomplete, semi-consistent ZFC axioms as a set of axioms that can prove almost everything in maths (intuitionism).

So yes, logic in its current state is not absolute for even relatively unsophisticated systems, and so is the nature of truth if you look at it as a set of all provable true statements. That's why we need intuition to make some calls. The thing is that the moment we allow intuition to participate in the judgement, things get fuzzy, and different people will have different "thresholds" to what's convincing enough. While that makes things blurry, having a very big threshold as to considering very weak evidence makes you gullible, while having a very small threshold to not consider relatively strong evidence makes you ignorant. In both cases, your judgement would be unreasonable.

Without further complication, what's true to me is what has got what has fallen within my threshold of sufficient evidence. Or just, "what makes sense".
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#8
(04-17-2017, 11:55 PM)A-Man Wrote:  
  • My mother is suddenly yelling at me for stealing the cookies. I see from the corner of my eye my an evil grin on my brother's face. That's "proof" he stole the cookies. That's (probably) reasonable. But not absolutely correct, as this kind would fail me if my brother was grinning for some other unrelated reason.
  • In a court of law, in a reasonably small list of possibilities, you being the only suspect without an alibi is "proof" you committed the crime; say court learns the committer was wearing a  red shirt, and you happen to be the only one who was wearing a red shirt that day. That's reasonable. But not absolutely correct, as this kind would fail if you're a victim of a plan to incriminate you/police did a sloppy work/unlucky/..etc.
  • In science, getting positive results for a theory in an experiment again and again is "proof" (appropriately, evidence) the theory is correct (works). That's reasonable, but note absolutely correct. There's the known quote by Einstein: "No amount of experimentation can ever prove me right; a single experiment can prove me wrong."
  • In formal mathematics and logic, proofs rely on solid foundation that's the closest to "the metal" as you can get. Reasonable of course, and people tend to think you can't go wrong here. But that's not absolutely correct either. There's a lot to say about this.
While I agree with the overall statement I would like to make a few nitpicks:
  • The cookie and court example are actually kind of similar: The term commonly used is "proof beyond a reasonable doubt", which notes that it is not definitively true. The term used for the grin on your brother's face and wearing a red shirt is "evidence" to support a claim. A court will typically use these terms correctly, your mother (unless she is a lawyer/judge) probably won't.
  • In science the term "proof" is rarely ever used. Scientists generally prefer (as you noted) "evidence", or typically "sufficient evidence" to "support a given theory". You can't even really prove something wrong because there is always uncertainty in your measurements, so you can find evidence against it.
  • For mathematics (including formal logic) a proof is a set of statements that, given a a set of assumptions, tries to convince others of a conclusion. Those assumptions don't necessarily have to be axioms (close to "the metal") but they are simply assumptions where, if you agree with them, you have to accept the conclusion. The funny thing to note here is the statements in the middle are never necessary for the proof to be sound, and they are essentially like comments in programming, in that they help other people follow along. Here the proof is absolutely correct, if the assumptions are.
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#9
I think truth is what is "free of opinions".

As an example, if you see a fire is burning, "Fire is burning" is a fact.
I assume everyone that can sense a fire nearby will agree that "A fire is burning".

Opinions are what humans derive from sensation and experience.
Some people are scared by fire while some are enjoying the fire, probably because they made a living involving fires.

If you are placing a virtual fire, someone might be fooled into thinking "A fire is burning".
But there is a level of fact where you only see what you can reach.
If you don't understand the fire is virtual, "A fire is burning" is conceived as a truth.
Notice that the fire is conceived from a fact into a truth.
If you find out that fire is virtual, you don't dismiss that fire, you instead conceive new truth and amend the property of involved fact:

"A fire is burning" -> "Something looks like a burning fire is here" "It's virtual fire that may deceive people"

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To apply the concept of "free-of-opinions truth" into the society is to view common sense as a mere social norm.

For instance "you are benefited by being less probable to be hit by car if you obey the traffic rules" is actually a piece of rule imposed by societal education to civilians.

To magnify the effect of rule, A fine is imposed to anyone who is caught crossing the road improperly.

There exists large portion of people who don't follow the traffic rules for their benefits, if they think neither "Being less probable to be hit by car" or "Being fined" is apparent to them.

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tl;dr:

Truth is what is "free of opinions".
However we can only accept something as truth if we have an opinion that that is free of opinion,
that is, truth is actually always relative in regards of each man's view.

Human usually attachs facts into truths to comprehend his surroundings, if he doesn't understand a fact he generally won't accept it as something new, but conceives that as a part of his knowledge.

Opinions are what a human feels about a fact. It is the only thing that a human thinks is biased.

P.S.

However, if a human acknowledges facts as biased, he would become either mentally unstable or loses willpower. One who doesn't exhibit either of symptoms will be very stubborn.

For religion:
The societal norm and politics are already too messy (and interesting) to tackle with, I don't need to accept another norm and conceive there is something "free-of-opinion" that is mind-controlling while my mind is already biased.
Also I am not that stupid to need someone else to tell me I'm faithful.
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#10
(04-18-2017, 06:00 PM)Someone else Wrote:  While I agree with the overall statement I would like to make a few nitpicks:
  • The cookie and court example are actually kind of similar: The term commonly used is "proof beyond a reasonable doubt", which notes that it is not definitively true. The term used for the grin on your brother's face and wearing a red shirt is "evidence" to support a claim. A court will typically use these terms correctly, your mother (unless she is a lawyer/judge) probably won't.
  • In science the term "proof" is rarely ever used. Scientists generally prefer (as you noted) "evidence", or typically "sufficient evidence" to "support a given theory". You can't even really prove something wrong because there is always uncertainty in your measurements, so you can find evidence against it.
  • For mathematics (including formal logic) a proof is a set of statements that, given a a set of assumptions, tries to convince others of a conclusion. Those assumptions don't necessarily have to be axioms (close to "the metal") but they are simply assumptions where, if you agree with them, you have to accept the conclusion. The funny thing to note here is the statements in the middle are never necessary for the proof to be sound, and they are essentially like comments in programming, in that they help other people follow along. Here the proof is absolutely correct, if the assumptions are.
I did use the term "proof" rather loosely in the examples. I'm aware evidence is preferable, but I do hear "experimental proof" being tossed more often (also, "experimental proof" on google has 93,700,000 results, while "experimental evidence" has 12,200,000). "Sufficient evidence" I hear a lot in a law court setting too.

I like the definition of proof that you gave. In essence, a theorem you give being contained in the system makes is all needed to make it valid with respect to the system, but the middle statements are necessary to convince a reader that it is so.
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