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Posted

I know this is a science site, but I haven't really read the last few pages of this thread.

 

This will probably get me into a lot of trouble, but how do mathematical equations enter into a discussion of "truth?" Is there anything that can't be reduced to a formula? (That looks like the title of a thread.)

 

Am I completely out of line for thinking the question "Exactly what is 'Truth'?" somehow shouldn't be turned into math? Is it simply the fact that math is a foreign language to me? Do I need to be pulled aside so I can have something discretely explained to me?

 

Is the pursuit of truth, which I thought I had been involved in as an investigative journalist, really something I could have found not by switching to philosophy but by switching to mathematics? Have I been wrong about this all my life?

 

I'll accept a simple "Yes" or "No" answer.

 

Thanks for helping me discover the font of Truth.

 

--lemit

Posted
This will probably get me into a lot of trouble, but how do mathematical equations enter into a discussion of "truth?"
Not too much trouble. B)

 

Somebody had asked about the meaning of truth in the case of "abstract staements such as 2 + 2 = 4". Yup the matter has dragged on a bit too much but I was just trying to clear up that "true" doesn't have the same meaning in math and logic as when talking about material things or what is strictly related to them (such as what a physical person says or believes). Well, some seem to say that even mathematical constructs are based on evidence or experience but I hope the matter is clear enough now.

Posted
I'm in the habit of today's mathematicians, and many others, who use it synonymously with postulate
Cool. I don't know b/c I am not a mathematician. notheless, I do not object as long as we both understand that there is no determination of statement until proven.

 

This is better, but folks typically don't directly prove them consistent

 

I agree. If there is inconsistency, then there is falsity.

 

What I did was not the first thing but test the second.

 

I see it like this. You derived, by design, by plugging it in, the values for A, B, C, from B=A+1, then you replugged them into B=A+1 to prove consistency. That is circular or, as you like to call it, incomplete proof.

 

But, considering what I bolded and that you mean it with statements including the axioms, isn't there a whiff of circularity?

Not if we take axiom to mean self evident statement that follow from definitions. (definitions are statements too.) ( 1+1=2 is true by defintion, 2+2=4 is true by way of definitoin as an axiom, self evident, A+B=C is an axiom from definitions. All are statements consistent with evidence. 3+3+1=0 is not self evident, nor is it a definition, but if proven "not inconsistent," or consistent, then it can be admitted into evidence.)

 

So it appears that your definitions are constrained to the same reality and therefore your evidence is reality. Is that what you understand for abstract statements?
Everything is reality. 3+3+1=0 is in reality, right here, it exists. The only question is whether as a statement, as something that tells us about reality, it is true. And it is true if it is consistent with evidence.

 

What constraint is there, how many fine ladies may/must we define before we (might) posit Mary = the last one of them § Susan?

If Mary = Deborah s. Susan, then Deborah s. Susan s. Susan = Susan; then Deborah = Nadia s. Deborah s. Susan s. Susan. Then Deborah = Nadia s. Mary s. Susan, then Deborah = Nadia s. Susan which is true by defintion, but circular.

 

If Mary = Deborah s. Susan, then Cynthia = Deborah s. Susan s. Susan s. Susan. Then, Nadia = Deborah s. Susan s. Susan s. Susan s. Susan. Then Deborah = Deborah s. Susan s. Susan s. Susan s. Susan s. Susan. Then, Deborah = Mary s. Susan s. Susan s. Susan s. Susan. Then Deborah = Susan s. Susan s. Susan s. Susan = Cynthia s. Susan s. Susan = Nadia s. Susan. True, but circular.

 

If Mary s. Cynthia = Cynthia, then Deborah s Susan s Susan s Susan = Susan s. Susan. then Mary s Susan s Susan = Susan s Susan. then Susan s Susan = Susan s Susan. True, but circular.

 

So the proposition that Mary = Deborah s. Susan, ends in Susan = Susan, and in Susan = 6 Susan (for brevity)[susan s Susan = ((Deborah s Susan) s Susan) s Susan; 2 Susan = 7 Susan; 1 susan = 6 Susan.)

 

So if if anything, we need Susan = 6 Susan definition to prove the statement.

 

Then Cynthia = 7 Susan. Then Deborah = 9 Susan; Then, Mary = 10 Susan; Then, Susan = 11 Susan. And so on and so forth.

 

The proposition does not provide a single answer. The answer diverges through the loop of S = M s S, and C = M s S s S; and N = M s S s S s S; D = M s S s S s S s S; and M = M s S s S s S s S s S; and S = M s S s S s S s S s S s S = M s S; and S = 6 S = 11 S = 16 S = 21 S = 26 S, . . .

 

To limit it we need to eliminate S = M s S. We can not define S in terms of M. S just is as a fundamental element.

 

Or, if you want to keep looping then define Susan in terms of some notation such as Susan = nSusan, for all n such that n = 1 + 5m, where m = (0,1,2,3,...); and nSusan denotes Susan s Susan s Susan . . . You need more for the looping series.

 

( I don't have routine in this. I may have missed something. Feel free to point out a mistake.)

 

Is the notion of a sewing circle necessary as evidence for this to be possible?
No. (only to the extent that it is a some kind of relationship as defined).

 

Is it sufficient to know we can (somehow) find enough elements?
yes. We have all the elements defined, mary being fundamental, and presuming not defined as D s S.

 

Are the definitions really sufficient "evidence" to decide which element the ring is closed after?
Yes. Definitions are both necessary and sufficient, based on the closed problem you present; Mary is fundamental, and Deborah is final.. If you mean A to be an infinite combination of names, then we may need more. If you want looping series then we need more definitions.

 

All propositions are compared against evidence (definitions). We can not plug in blindly and and replug to test for truth. We must compare against the evidence for consistency to say whether a proposition is true or false. in this case, when we derive Susan = 6 Susan, we have nothing in evidence to compare it against. It is indeterminable. Since propositions must be consistent with evidence, then this proposition has an effect of being false; it is not admissibile in evidence.

Posted
This will probably get me into a lot of trouble, but how do mathematical equations enter into a discussion of "truth?" Is there anything that can't be reduced to a formula? (That looks like the title of a thread.)

 

Am I completely out of line for thinking the question "Exactly what is 'Truth'?" somehow shouldn't be turned into math? Is it simply the fact that math is a foreign language to me? Do I need to be pulled aside so I can have something discretely explained to me?

 

Is the pursuit of truth, which I thought I had been involved in as an investigative journalist, really something I could have found not by switching to philosophy but by switching to mathematics? Have I been wrong about this all my life?

 

philosophizing, thinking, doing math are all mental processes that strives to create a "perfect image" of the fact of existence. truth is the principle used to do so. imo

Posted

This will probably get me into a lot of trouble, but how do mathematical equations enter into a discussion of "truth?"

 

I think there are many different ways of defining truth. You could look at it in a purely scientific viewpoint: "Truth is the opposite of falsehood."

 

However, in real practice I don't think math can explain truth because truth is influenced by people's perceptions and beliefs.

Posted
We can not define S in terms of M. S just is as a fundamental element.
I did not define it, I chose Susan as a new symbol and that relation just means Mary is the neutral element of the operator.

 

Well, I can see you aren't a modern mathematician, I give up. Mathematical postulates don't care about evidence nor need to be self evident.

Posted
I did not define it, I chose Susan as a new symbol and that relation just means Mary is the neutral element of the operator.

I meant to say there, susan is fundamental if M= DsS stands, or Mary is fundamental if S=MsS stands.

 

Well, I can see you aren't a modern mathematician, I give up.
Thank you for giving me more credit than I gave myself. I am not any kind of mathematician.
Mathematical postulates don't care about evidence nor need to be self evident.
Sure, if you understand a postulate to be a definition or a fundamental assumption itself.
  • 9 months later...
Posted

Is it true that the sun will rise tomorrow?

How do you know?

How many times do you have to see the sun rise before you know it will rise tomorrow?

Obviously no matter how many times you see it rise you will never be able to be certain that it will rise tomorrow.

On the otherhand, if you know 'why' it rises then you can know whether it will or not.

 

error correction:

http://en.wikipedia.org/wiki/Multidimensional_parity-check_code

Posted
Is it true that the sun will rise tomorrow? How do you know? On the other hand, if you know 'why' it rises then you can know whether it will or not.

 

Yes, it is true that the sun will rise tomorrow. By definition, what is true is derived from facts of reality (such as the movement of the sun in the universe), and some facts (such as whether or not sun will rise yet another day to an observer on the earth) are true in the future to that observer with less than 100% certainty. By definition, science itself is "uncertain knowledge". Some facts may change over time, with time being that which is intermediate between two moments (the before and the after). Thus, you know that the sun will rise tomorrow, with less than 100% certainty, when you apply the logic of science to the question at hand (Is it true the sun will rise tomorrow ?).

 

Now, some facts are known with 100% certainty (they never change between the before and the after moments), and they are types of facts not related directly to science. One such non-scientific fact is that the next triangle you will observe (or imagine) will have 3 and only 3 angles. There is absolutely nothing uncertain about the proposition (not in present, past, or future as relates to time), thus the truth of the proposition can never be explained by science, unlike the movement of the sun in space-time.

 

Both of the above (i.e., sun, triangles) are examples of the truth of the statement: "the future is what you know". What you know comes in different degrees of probability as relates to future observation of facts of reality (the sun rising---the number of angles in triangle--etc.).

 

Finally, is it true you know why the sun rises ? It would appear to be a correct assumption that the event has to do with motion--but--does anyone know exactly "why" the motion of the sun is as observed ? I would suggest that claims of knowing "why" an event has such a large degree of uncertainty that such claims are of little use to knowing whether an event "will or will not" occur. We know that the sun will rise tomorrow in the future, not because we know the physics of why the sun rises, but because we know the uncertain fact that the sun has risen in the past.

Posted

Truth = reality

 

From my perspective this is good "starting point" and reflects how we are limited with our thinking, language, logic, concepts and mathematics.

I would go beyond this definition Truth=reality to following;

 

"Truth is all what is and what is not, absolutely"

 

This allows all what is to be reality and the again accepts all what is not into this definition also.

One might say that absolute nothing cannot be logical conclusion. It is impossible. That is exactly why definition should include absolute nothing/impossible due it has to "include" absolute all and absolute nothing.

 

If you want to define the truth it has to be first viewed "beyond human truth"

 

Now if we come closer to our realm of "understanding things" then "Truth = Reality" where we are part of it exist, regardless if we consciously know it or not. So called d subconscious is also included to this "reduced category" of truth definition.

 

Now again moving closer to human life and tools what we are using, namely, to define things/truths whatever we need to define to make definitions more "lifelike"

No here comes from my perspective concerning the key point we normally mix definition of something as "real it".

From my perspective all definitions done with words/language, mathematics, concepts and theories are mere reflection of the reality due these reflections do not interact with reality, as exist is all at once and continuously changing. If we have mathematical formula to reflect reality all should comprehend that is reflection of assumed phenomenon but due it is not alive within that exist, mathematical formula cannot experience truth or reality. Thinking, language, logic, concepts and mathematics cannot link "itself" any other way as mere reflection of "All what is and all what is not, absolutely" via our conscious thought.

 

So it is important to decide on what level we want to define the truth itself.

Posted (edited)
Is it true that the sun will rise tomorrow?
During the night, the rotation of Planet Earth will come to a grinding halt. Waters will go surging over eastern shores, getting some people soaked through, many tall things will topple over, on your half of the planet the sun will not rise and the other half will get baked through. This will happen the night following March the 31st and, when peoples alarm clocks start to go off, God will say: "April Fool!"

 

Sure, if you understand a postulate to be a definition or a fundamental assumption itself.
Modern mathematicians don't consider it an assumption, they consider it a choice. Yes, in many cases postulates are, explicitly or implicitly, the way some things are defined.

 

For instance, let's define morning (or morrow) as being when the sun rises. From this clearly follows the truth that the sun rises every morning and also that the sun will rise tomorrow (unless the next morrow will never come).

Edited by Qfwfq
dumb mistake!
Posted

Truth is synonymous with fact, or so it seems to me. The separation of the terms is due to the odds at which theology and philosophy have found themselves.

 

Theologians feel that truth is divine, capitial T Truth. They use the term in statements such as "the truth will set you free," which implies that truth can take action and has authority over an individual. These sorts of statements also imply that the conveyors of the divine truth also hold authority, since they hold the proverbial key to the cell in which the uneducated resides.

 

Western philosophy tends to view truth in an analytical way...thus the above debate over tautologies.

 

Those who's opinions are somewhere in between the two are those who I feel are on the fence about origins, and thus divinity.

 

But that's just my two cents.

Posted

I didn't really have time to read all seven pages, so I apologize if this has already been said, I would like to expound on the statement "truth=reality." An example of this would be to say that on a street surrounded by people, a car wreck were to occur. There is an absolute truth about the car wreck, how and moreso that that happened actually happened, even to the most minute detail.

 

Now from where I am standing, I see part of the truth, this is my perspective of the truth. My perspective may be highly similar to that of another person perhaps one standing next to me. However, my perspective may vary more from someone standing across the street. Possible from my angle I could see that Car A swerved to avoid an old lady in the street when it ran into Car B. However from the guy across the street's point of view Car A swerved and hit Car B for a malicious purpose.

 

The point of view doesn't at all change the actual event, and if we work together and attempt to understand how others saw what happened, we can peice together how the event occured, and thus attain an accurate account of absolute truth. Just because we do not see things the way other people may see them, doesn't make their view any less valid, simply a different angle.

 

So in short, I believe that there is absolute truth, that that truth is not relative, and that the only way to grasp that absolute truth is to consider all vantage points and assemble the pieces.

Posted

Truth is a word used quite often with little thought as to exactly what is meant when we use it. In a rough sense, it is nothing more than a category to which we assign specific ideas, statements or explanations. What qualifies a particular specific idea for that assignment? Well first, I think we could get almost universal agreement that the idea must be consistent with all other ideas already assigned to that category. It is pretty well accepted that, if any idea is inconsistent with something already regarded as true, there is a major problem. So the first thing one can say is that everything held as true must be consistent with everything else held as true.

 

I agree absolutely with your first two sentences. But I think that the following statements in the paragraph reflect a fundamental difference in our opinions, or definitions, of the term Truth.

 

You seem to start from the assumption there is some absolute, over-arching, all-encompassing, "thing" that ties together with all other such "things". In fact you make your definition dependent on the interconnectedness of various truths.

 

In my view Truth is a convenient, conversational fiction. Or, if not fiction, then a forever unattainable goal. Science is characterized by the primary concept that Fact is based on repeatable and public observation. It is understood that the inherent accuracy of our sensory impressions can only be assumed, never confirmed. But those sensory impressions are all we have to work with. The strength of observable fact is that we can achieve high degrees of concurrence from objective observers. That concurrence of observations constitutes our reality, but not the REALITY (whatever that might be).

 

The facts of science depend solely on concurrence of observations, not on conformity to other observations. Apparent conformity, or disconformity, simply tells us something about the presence or absence of relevant facts. A fact is "real" to the limits of our sensory systems, the conditions of observation, and the degree of concurrence. That is the origin of uncertainty.

 

That brings us to another leg of my contention that there is no useful concept of Truth. Truth implies certainty. But the only path open to Science is through limited means of observation, and observation can only reduce uncertainty - never achieve certainty.

 

We are thus lead to assign the concept "truth" to a assemblage of ideas or concepts which are totally consistent with one another. Now clearly, this is not the total definition of truth as it implies a collection of ideas totally consistent with one another could be called truth. I can easily come up with a collection of ideas which are totally consistent with one another which no one here would accept as truth. What is missing from this definition?

What is missing is the idea that there is only one truth. That is, the truth must be consistent with every idea assigned the title "true". It cannot be a simple collection, it must be all encompassing. Thus it becomes evident that we are talking about a single complete structure. Well, I am of the opinion that our subconscious minds are already aware of this fact and have assigned a label to refer to it. That label is "reality"; reality is what is truly real. Reality must be totally consistent with itself (or rather, any explanation of reality, if it is to be regarded as true, must be totally consistent with itself).

 

We are thus led to the idea that the "truth" is what is totally consistent with reality. But, what is reality? Isn't it what we consider to be absolutely true? It seems we are going in circles here; but are we? I think we can break out of that circle by realizing that our experiences are the fundamental issue of truth.

 

Most people will add to the concept of "truth" the idea that if something is really true, one will never come to learn it is false. If that idea is "true" then the truth can never change. If the truth can never change, then it is impossible to know as the possibility, no matter how slim, always exists that what you thought was true might be proved wrong. Most modern philosophers use that fact to curtail the search for truth as something unachievable. Thus implying the concept is useless.

 

Let me suggest that the concept is still useful. Instead of holding that the truth cannot change, let me instead put forth the idea that the truth must be totally consistent with what is known. If what is known changes, then the truth can change. Under this constraint, the truth becomes merely an accurate representation of what is known and need not be unchangeable.

 

This leads me to the rather strange definition that the truth is exactly what you believe to be true. I am fairly confident that the definition fulfills all usage common to any philosophical discussion. I would challenge anyone to prove that what he believes to be true is not true. The issue is, once he has proved something he believed to be true is not true, does he still think it is true?

 

There is a very important issue buried in that last observation. That is the fact that no one has any control at all over what he believes is true. That is why we have the word convinced. It follows that, if you wish to learn the truth, your only option is to search for flaws in the consistency of what you believe. When you find inconsistencies in your beliefs, it opens your mind to the fact that something you believe to be true must be false. If you never look for inconsistencies, you will never find them and thus, learning the truth will be absolutely beyond possibility.

 

Again, I agree with most of your argument but take issue with the notion implicit in your final conclusion. I agree truth is unattainable but I do so based on my own belief that there is no such animal as Truth. What we're dealing with is one of the few fundamental beliefs of faith extent in Science, that we can only reduce uncertainty by focusing on the observable.

 

I'll leave the question of subconscious for another thread elsewhere. B)

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