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Posted by seagull (Member # 694) on :
 
I believe that "objective truth" is a useful concept regardless of whether it actually exists (I feel the same way about God too).

I do not believe that it is possible for any human to actually know the "objective truth".
Humans who hoenstly claim to know the objective truth are either fools or prophets (or both). One of the tenets of my religion is that these days it is impossible to know the difference between fools and prophets (No offense meant to any Mormons, I do respect your religion and I hope you can respect mine).

I consider people who think that their understanding of "objective truth" is better than that of others to be extremely arrogant and I'll be the first to acknowledge that I can be extremely arrogant about some things.

For many centuries people believed that "the sum of the angles in a triangle is 180 degrees" is an objective truth. Most rational and informed scientists today no longer consider that statement to be an objective truth (it is false in non-Euclidian geometries). Euclidian geometry is such a useful model that it is still tempting to treat it as an "objective truth" even when it is not.

I believe that 1+1=2 in most contexts but I recognize that there are contexts when 1+1=1 or 1+1>2 are much more useful paradigms.
 
Posted by TommySama (Member # 2780) on :
 
WE can't get it. Like what Pete told me, how when we're having sex we're actually masturbating.
 
Posted by kenmeer livermaile (Member # 2243) on :
 
"For many centuries people believed that "the sum of the angles in a triangle is 180 degrees" is an objective truth. Most rational and informed scientists today no longer consider that statement to be an objective truth (it is false in non-Euclidian geometries). Euclidian geometry is such a useful model that it is still tempting to treat it as an "objective truth" even when it is not."

Both Euclidian and non-Euclidian are OBJECTS of human thought. So "the sum of the angles in a triangle is 180 degrees" is objectively true within the object to which it is subject, Euclidian geometry.

I think the philosophers and epistemologists trip over themselves a lot (which is why their tenets change so much in an almost faddish fashion).

I think a much better term for what is called "objective truth" would be 'universal truth': a truth that is true any and everywhere, regardless.

One could see that term and realize that since the human mind is incapable of perceiving the totality of the universe, such a concept remains only a concept.

But in the realm of consensually mediated reality, 1+1=2 in a manner invulnerable to subjective input.

One must change the definition of 'one' to change that axiom. One must alter the object. Altering objects will of course alter those objects' truth correspondingly.

But, for the record:

quote:
In philosophy, an objective fact means a truth that remains true everywhere, independently of human thought or feelings. For instance, it is true always and everywhere that 'in base 10, 2 plus 2 equals 4'. A subjective fact is one that is only true under certain conditions, at certain times, in certain places, or for certain people.
That's a wiki.

"I believe that 1+1=2 in most contexts but I recognize that there are contexts when 1+1=1 or 1+1>2 are much more useful paradigms."

I would call that a subjective belief.
 
Posted by KidB (Member # 3016) on :
 
Kenmeer makes the crucial distinction. An "objective" truth is not an absolute truth - it is contextual, consistent to all observers within a common external referent.
 
Posted by kenmeer livermaile (Member # 2243) on :
 
You know how Injuns have those cool names?

Moon River Shining

Johnny Makes the Fire

Sally Two Guns

I wanna be Kenmeer Makes the Crucial Distinction

(but friends can call me Steps in ****)
 
Posted by yossarian22c (Member # 1779) on :
 
Just because a triangle on a sphere on some other surface doesn't have angles that sum to 180 degrees doesn't mean it isn't an objective truth in euclidean geometry. In mathematics you can clearly define what type of environment you are working in. In mathematics the base assumptions are called axioms and then everything that follows is objective truth based on those minimal assumptions. If you are interested about what can and cannot be determined objectively under different axioms read about Godel's incompleteness theorem.

Working with the natural numbers as normally defined 1+1=2 is an objective truth. Just because there exist systems where the result can be different doesn't make the statement any less objectively true under the normal assumptions/axioms.
 
Posted by Wayward Son (Member # 210) on :
 
As an old buddy of mine once said (who happens to be a math professor at a major university), "mathematics is a system of logic." Given a set of axioms, you can objectively "prove" certain propositions, which simply means the propositions are consistent with the given axioms. Nothing more.

The universe is not that simple. Although it appears to follow rigid rules (which explains why the hard sciences are so successful in predicting outcomes in many circumstances), often times it is not as exact in following the rules we have as we'd like.

For instance, the universe does not follow rules of calculus. Calculus posits that we can divide things into infinitely small segments, and any physicist can tell you that is impossible. You eventually get into quantum wierdness and the mathematics breaks down. But for macroscopic purposes, it works very well, and thus is accepted as "proof."

What this all means is that, as you state, you can't "prove" anything absolutely in this world. But that does not mean you can't "prove" something to an extent that is acceptable to a vast majority of observers. It may not be absolutely "true," but if it is practically true, that is about as good as we can get.

And that is enough for mere mortals. [Smile]
 
Posted by whitefire (Member # 6505) on :
 
"The universe is not that simple."
Really? I'm not sure where to begin with this, but are you suggesting that there are no axioms the universe operates on or are you echoing seagul in:
"I do not believe that it is possible for any human to actually know the "objective truth"."
Frankly, I'm intrigued by the first option. Is it even possible?
I don't think I can express my thoughts on this right now - maybe after I sleep. Hopefully more later.
 
Posted by kenmeer livermaile (Member # 2243) on :
 
Is gthe universe simple? Complex? Who knows, I say. Our minds keep us so busy tracking what they do we scarcely can keep our socks paired.

Pared pairs are the norm.
 
Posted by seagull (Member # 694) on :
 
In mathematical logic, axioms by themselves are not enough. You need to define a formal language before you can state the axioms. You also need to be given rules of inference for constructing true propositions.

For example, a formal logic system with only two axioms:
1. Politician lie.
2. Cast iron sinks.
Is not enough to tell us if "politician lie and cast iron sinks" is a true proposition and how it differs from "politician lie in cast iron sinks". We need inference rules to tell us how manipulating statements using the words "and" and "in" affects their truth. We also need the formal language to resolve the ambiguity between using "sinks" as a noun or as a verb.

The choice of the Formal Language, the Axioms and the Rules of inference can be critical to what can or can not be proved.

When the field of non-Euclidian geometry found its first practical applications there were heated debates about whether the Axiom of parallel lines was an objective (or universal) truth. As time went on it became "obvious" that while Euclidian geometry remains as useful as ever, replacing the Parallel Postulate with "equally valid (though less intuitive)" axioms resulted in elliptic and hyperbolic geometries which are very useful as well. "An implication of Einstein's theory of general relativity is that Euclidean space is a good approximation to the properties of physical space only if the gravitational field is not too strong".

I have heard heated debates between mathematicians about whether the Axiom of Choice is true or not. Some of the them believed in the axiom of choice with a deep almost religious convictions and treated those who wanted to spend their time studying (and teaching) other formal systems as blasphemous heretics that were wasting the time and resources of their community. My impression was that alternate systems that do not include the axiom of choice do not yet have enough practical applications to earn the respect (and funding) that non-Euclidian geometry has but that it is possible (and according to some even likely) than it will do so in the future.

quote:
in the realm of consensually mediated reality, 1+1=2 in a manner invulnerable to subjective input
I prefer the more accurate phrasing that "1+1=2" can be proved to be true for Natural numbers as defined by the Peano axioms augmented with the operation of addition and using a decimal notation.

Obviously if binary notation was used the same statement would be expressed as 1+1=10 but changing notation would have no effect on the truth of the statement. The following four statements:
* 1+1=10 (in binary notation)
* 1+1=2 (in any base greater than two).
* one plus one equal two (in English)
* uno más uno es igual a dos (in Spanish)
All express the same concept which can be proved if you accept the peano axioms and the common definition for addition regardless of what language we choose to express them in.

But, no matter what language we write it in, the concept that "one plus one equals two" is not an objective truth in a world where the axioms of number theory are not true.

For a long time, even after I studied formal logic and understood the improtance of Non-Euclidian geometry, I still could not imagine a world in which those axioms would not be true. I was open to the idea that such models could exist but I could not concieve of one that had any meaning to me and at the time I would have agreed that 1+1=2 was an objective truth.

Then I mentioned this to someone who said these two simple sentences:

"One cloud plus One clound equals one cloud"
"One man plus one Woman equals more than two people"

If you translate these two sentences back into mathematical notation we get: 1+1=1 and 1+1>2.

Since that day, I no longer consider 1+1=2 to be an absolute/universal/objective truth.

Don't get me wrong, I still love number theory and use it in the appropriate context. But I do not believe in it religiously and I think that my world is richer for being able to see other perspectives as well.

[ November 13, 2009, 07:57 PM: Message edited by: seagull ]
 
Posted by yossarian22c (Member # 1779) on :
 
quote:
Originally posted by seagull:

I do not believe that it is possible for any human to actually know the "objective truth".

That statement is a version of the liar's paradox. The liar's paradox being a statement like; "This statement is false."

If it is impossible for us to know objective truth then how can you be sure that it is impossible.
 
Posted by yossarian22c (Member # 1779) on :
 
quote:
Originally posted by seagull:

Then I mentioned this to someone who said these two simple sentences:

"One cloud plus One clound equals one cloud"
"One man plus one Woman equals more than two people"

If you translate these two sentences back into mathematical notation we get: 1+1=1 and 1+1>2.

Since that day, I no longer consider 1+1=2 to be an absolute/universal/objective truth.

Don't get me wrong, I still love number theory and use it in the appropriate context. But I do not believe in it religiously and I think that my world is richer for being able to see other perspectives as well.

The translation back to mathematical notation is wrong. A cloud is a collection of water particles. Meaning that to think about clouds in a mathematical setting you would need to think about a cloud as a set made up of all its particles. Then "adding" the two clouds would be taking the union of the two sets that make up each cloud.

The second statement is also difficult to translate back into a formal mathematical language. Words are a difficult thing to transform into logic. There is also a bit left out from the statement that makes the logical translation seem almost reasonable but it is really saying one man plus one woman plus a sperm meeting an egg is more than two people. So if you want to try to define what you mean by plus and how you want to count embryos then maybe you could take another shot.

It's fine to discuss philosophy in the vagaries of those two statements but it is meaningless and misleading pretend like there is some formal mathematical meaning in how you interpreted either one.

To respond specifically to your last statement number theory is a tool. If you have read about Godel you know that the theory of natural numbers is inherently incomplete. I'm not sure what is gained by making vague statements in English and "translating" them into the language of mathematics in an imprecise way. Mathematics is about precision and logic. I think your for your statements to have any meaning it should be viewed from a philosophical point of view not a mathematical one.
 
Posted by yossarian22c (Member # 1779) on :
 
quote:
Originally posted by Wayward Son:

For instance, the universe does not follow rules of calculus. Calculus posits that we can divide things into infinitely small segments, and any physicist can tell you that is impossible.

Very interesting things happen when things can be broken up into infinitely small pieces. For example a ball can be cut into 5 pieces and reassembled into two balls of the same size or one ball with larger volume. It's the banach-tarski paradox if you're interested.
 
Posted by seagull (Member # 694) on :
 
quote:
how can you be sure that it is impossible?
I am human and I do not think I am either a prophet or a fool. So I can not be sure.

I believe that it is impossible (as an axiom) but I have no proof that the axiom is true.
 
Posted by seagull (Member # 694) on :
 
I have also thought of the water particles and embryos but they are only specific models that represent the basic concepts expressed by 1+1=1 and 1+1>2. Thinking about these abstract concepts in terms of specific models is like thinking about axiomatic Number theory in terms of apples and oranges. It has a meaning but it misses the point.

quote:
I'm not sure what is gained by making vague statements in English and "translating" them into the language of mathematics in an imprecise way.
I am not sure either.

Frankly, I can't come up with a precise formal system that would reflect the behavior of clouds and families. All I have been able to come up with in the years since I started thinking about it is specific models that do not have the aesthetic beauty that I enjoy so much when I think of Number theory, Euclidian geometry or Spherical geometry.

A spherical triangle with one corner at the north pole, a second corner on the equator at zero longitude and a third corner on the equator at 90 degrees longitude, has three right angles. People have known intuitively that the sum of the angles in that triangle is 270 degrees well before spherical geometry was defined formally with axioms. The seeming "contradiction" with the Euclidian theorem that the sum of the angles in a triangle must be 180 degrees never bothered them as long as they kept track of the context. But it was much harder to express concepts, prove theorems and make useful calculations with spherical trigonometry using an imprecise language like English.

I know intuitively that the expressions 1+1=1 and 1+1>2 have a meaning in contexts that are different from number theory. The alternate formal logic system that would allow us to express that meaning in a precise way using a small number of axioms may not have been invented yet, but I like to believe that it is possible for humans to invent such a system.
 
Posted by Viking_Longship (Member # 3358) on :
 
You're exploring facts, and really just countering them with more facts.

We can talk about Truth, ultimate Truth

quote:
37 Therefore Pilate said to Him, “So You are a king?” Jesus answered, “You say correctly that I am a king. For this I have been born, and for this I have come into the world, to testify to the truth. Everyone who is of the truth hears My voice.” 38 Pilate said to Him, “What is truth?”

Which has a certain philosophic flexibility.

We can also talk about facts. Now you can try to refuse to admit something occured or exists despite tangible evidence in a sort of "you have your reality, I have mine" manner. You waon't get far with that in a court of law, but you can get away with it in the court of public opinion with some people. Or you can argue that facts are concrete and have evidence. This is the way we usually think.

The problem is when people try to play both sides. A politician is on record saying something embarassing. He can deny he said it. Even when it's on the record some people will support him. Those same people would call a politician from the other side a liar for saying something that appears false and even when the evidence supports the politician from the other side will continue to call this person a liar. (And when confronted will play the "what evidence? huh? ....Well what about this other thing he said?")

Its not that facts don't exist or that Truth is relative, it's that we want them to be that way.
 
Posted by kenmeer livermaile (Member # 2243) on :
 
To the best of my recollection, I do not remember having such a conversation (insert into countless government interrogations, including interviews with Cheney regarding the Plame affair)

We have conclusive evidence that Saddam has WMD (as read in innumerable media accounts)

Your assignment, sophomore class, is to epistemologically categorize these two statements.

I will be in the teacher's lounge snorting brandy in my coffee and trying to get a peek up Ms. Boniface's legs.

[ November 14, 2009, 08:19 AM: Message edited by: kenmeer livermaile ]
 
Posted by seagull (Member # 694) on :
 
Viking:
According to at least two major religions Jesus was a prophet. Can you elaborate on how you think your quote relates to my original post?

KL:
Was Cheney quoting Clinton when he said "I do not remember" or did they both have the same teacher in sophomore epistemology?

In a rational discussion, we should allow for more than just two possibilities and recognize that the word "or" is not necessarily exclusive.
 
Posted by yossarian22c (Member # 1779) on :
 
quote:
I am human and I do not think I am either a prophet or a fool. So I can not be sure.

I believe that it is impossible (as an axiom) but I have no proof that the axiom is true.

Fair enough. That as an axiom is strange in that you can prove nothing from it. So the system is the axiom. That has a nice aesthetic in a way but lacks any practicality.


quote:
I know intuitively that the expressions 1+1=1 and 1+1>2 have a meaning in contexts that are different from number theory. The alternate formal logic system that would allow us to express that meaning in a precise way using a small number of axioms may not have been invented yet, but I like to believe that it is possible for humans to invent such a system.
The statements are probably better left in philosophical terms rather than mathematical terms since there is no precise translation from one to the other. It detracts from your point to dress it in the language of mathematics without a precise formal logic and definitions.

Philosophically however I think the concepts can be captured by language like the whole is greater than the sum of the parts. Language has a flexibility that allows these statements to engage the mind without a contradiction.
 
Posted by seagull (Member # 694) on :
 
quote:
That as an axiom is strange in that you can prove nothing from it.
It may feel strange, but it is an inevitable consequence of Godel's incompleteness theorem that statements of this type (or it's negation) can be added as an axiom to any formal system that is powerful enough to be interesting.

Axioms and rules of inference can not be proved! They are taken for granted because people are willing to believe in them. Willingness to believe is not a rational process, the rational process begins only after the axioms and the rules of inference are accepted.

In dealing with a statement like: "it is possible for a human to know the objective truth". I see three mutually exclusive choices (please let me know if I missed something):
Trying to prove that the statement is either true or false runs into epistemological problems due to Godel's incompleteness theorem so I did not include it as a fourth option.

In a context where someone argues that they have some knowledge of an "OBJECTIVE TRUTH" that I do not accept, I prefer to add that premise as an explicit axiom just to make it clear that their argument is not rational. So if/when I am forced to choose between the following two axioms:
I prefer to choose the later because I find it much more practical that the alternative (especially in the middle of an online debate).

In most other contexts, I am perfectly happy accepting that neither of these statements can be proved.
 
Posted by Viking_Longship (Member # 3358) on :
 
quote:
Viking:
According to at least two major religions Jesus was a prophet. Can you elaborate on how you think your quote relates to my original post?

Yes I can.
 
Posted by Viking_Longship (Member # 3358) on :
 
Jesus is not the only one quoted there. Jesus seems to believe in an objective truth. Pilate seems not to.
 
Posted by threads (Member # 5091) on :
 
quote:
Originally posted by seagull:
In a context where someone argues that they have some knowledge of an "OBJECTIVE TRUTH" that I do not accept, I prefer to add that premise as an explicit axiom just to make it clear that their argument is not rational. So if/when I am forced to choose between the following two axioms:
I prefer to choose the later because I find it much more practical that the alternative (especially in the middle of an online debate).
At this point we should probably define what we mean by an "objective truth". If we go by the definition that KL posted earlier:
quote:
In philosophy, an objective fact means a truth that remains true everywhere, independently of human thought or feelings. For instance, it is true always and everywhere that 'in base 10, 2 plus 2 equals 4'. A subjective fact is one that is only true under certain conditions, at certain times, in certain places, or for certain people.
Then objective truths clearly exist but aren't very interesting for people who don't accept the first principles from which the truths are derived from. I'm not sure if it's possible to come up with a definition of objective truth that is independent of first principles.

One of the main problems I encounter when debating people over objective morality is that while many people have a clear source for their morality (ex: God's word, utilitarianism, etc.) they act as if their moral claims reach beyond this starting source. For example, even if I don't accept that God's word defines morality then I am still somehow "objectively" wrong when my moral beliefs differ from God's word. The only way that this could be the case is if their moral beliefs were derivable from my starting premises (or, trivially, if you redefine what "objective" means). Essentially, people want the claim "that's morally wrong" to have argumentative force for all people regardless of first principles. It's not clear to me how that's possible.
 
Posted by seagull (Member # 694) on :
 
quote:
it is true always and everywhere that in base 10, 2 plus 2 equals 4
As I explained above, I used to agree with this statement before I was convinced that "in base 10, 2 plus 2 equals 4" is not "true always and everywhere".

For example, in the context of a formal system for describing population growth in a world where men and women are equally likely to be born (p=q=0.5) and each woman has exactly four children (r=4) the expression 2+2=4 would be false because starting with two men and two women the next generation would have 8 children. Note that all of these calculations are using base 10 but I chose to use axioms that assign a different meaning to the operator "plus" that makes sense in a specific context.

Saying "That's a wiki" as if that made it more believable was a really good joke.

Threads,
Your last paragraph is a terrific example that the concept of "objective truth" can be used to confuse a discussion.

I believe in God as an axiom.
My personal belief that "objective truth" exists is also an axiom.

By saying that these are axioms, I am explicitly stating that these are things that I believe but can not prove.
I will not expect you to agree with me on "facts" that I derive from axioms that you do not believe in.

I expect the same courtesy from others who want to engage in a rational discussion.

[ November 15, 2009, 02:53 PM: Message edited by: seagull ]
 
Posted by PSRT (Member # 6454) on :
 
quote:
As I explained above, I used to agree with this statement before I was convinced that "in base 10, 2 plus 2 equals 4" is not "true always and everywhere".
It is true, always and everywhere, once we've defined what the terms mean, though.

As kenmeer talked about early in the thread, objectively true is more about whether or not a particular statement is valid, not whether or not the statement is true in all circumstances.

When discussing a particular event, there is an objective truth to that event. Regardless of the observer who is describing the event, the event happened in the same way. The observers might report it differently, though, depending on the view points of the observers.
 
Posted by seagull (Member # 694) on :
 
quote:
there is an objective truth to that event. Regardless of the observer who is describing the event
That is so two centuries ago.

If you accept the premise of theories of relativity, observation is the only way to access "the objective truth". There are objective truths that we will never be able to access and even the truths that are theoretically accessible to a hypothetical omniscient observer can never be known by a finite observer.

Still, AFAIK, the concept of an "objective truth to that event" still means something in a relativistic world. Then you get to Quantum Theory and even that breaks down: What is the objective truth about Schroedinger's cat? Is it alive or dead? Is it even meaningful to ask that question?

quote:
always and everywhere, once we've defined what the terms mean
I see an incosistency between "always and everywhere" and the use of the word once to qualify it. Would you care to clarify how you interpret the terms "always", "everywhere" and "once" without leading to a contradiction?

[ November 15, 2009, 09:21 PM: Message edited by: seagull ]
 
Posted by PSRT (Member # 6454) on :
 
quote:
Still, AFAIK, the concept of an "objective truth to that event" still means something in a relativistic world. Then you get to Quantum Theory and even that breaks down: What is the objective truth about Schroedinger's cat? Is it alive or dead?
Both. That's the whole point of the thought experiment.

quote:
I see an incosistency between "always and everywhere" and the use of the word once to qualify it. Would you care to clarify how you interpret the terms "always", "everywhere" and "once" without leading to a contradiction?
For a given set of definitions of the terms involved, 2+2=4 is true. If you and I sit down and agree on how we are using the terms, then for every situation where the definitions were are using apply, 2+2=4 would be true.
 
Posted by JWatts (Member # 6523) on :
 
In engineering classes, we were always told to follow the 99% rule. Essentially, if you can get within 1% of the "correct" answer it's good enough.
 
Posted by seagull (Member # 694) on :
 
quote:
If you and I sit down and agree on how we are using the terms, then ...
I agree, but that is not the issue. If 2+2=4 was true always and everywhere, there would be no need for the cumbersome "If ... then ..." preamble. The fact that we have to use the word "If" implies (to me) that 2+2=4 is not true "always and everywhere".

JWatts,
I took similar classes and I agree that in SOME contexts that is the right thing to do. But in other contexts ...

My work as an Engineer is used directly in designing the safety procedures for air traffic control and airport approach procedures. Do you think that if we can get 99% of the planes to land safely, that would be "good enough"?

[ November 16, 2009, 03:21 AM: Message edited by: seagull ]
 
Posted by JWatts (Member # 6523) on :
 
quote:
Originally posted by seagull:
JWatts,
I took similar classes and I agree that in SOME contexts that is the right thing to do. But in other contexts ...

My work as an Engineer is used directly in designing the safety procedures for air traffic control and airport approach procedures. Do you think that if we can get 99% of the planes to land safely, that would be "good enough"? [/QB]

I know that if you try and ensure that 100% of the planes land safely, that none will ever take off, because you will never be able to reach that magical 100% success rate.

That was kind of my point. The talk of objective truth, of 100% verifiability is just talk. Those that do must actually do.

The actual number of 9's you need for your job is just the details. Certainly 99% would be less than the current standard, however 99.999% would be 7 times greater than the current standard. And far less than 100%.

Math:
8 fatal accidents per 100 million miles Link
866 miles average distance flown Link
12.5 million miles/866 miles = 1 fatal accident per 14,400 flights (99.993% success)
 
Posted by Pyrtolin (Member # 2638) on :
 
Having dipped my fingers into the code that generates payroll confirmation reports, I've definitely found some of those large values of two for which 2+2=5. And when you move to multiplication, you vastly increase the margin by which a little rounding at the wrong time can skew your results.
 
Posted by seagull (Member # 694) on :
 
JWatts, Thanks for the math links (the first one is really great).

Actually there is work being done on increasing safety standards (for commercial airline traffic) from 99.99999% to 99.999996%
 
Posted by seagull (Member # 694) on :
 
quote:
I've definitely found some of those large values of two for which 2+2=5.
I know about roundoff.
Also for a signed byte: 127+127=-2
But how exactly do you get 2+2=5?

unless it comes from the classic:
quote:
Kid: Dad how much is 2+2?
Dad: That depends on whether you are buying or selling.


 
Posted by seagull (Member # 694) on :
 
Different proofs that all odd numbers are prime:

Math major:
1 is prime, 3 is prime, 5 is prime, 7 is prime,
so by induction we can see that odd numbers are prime.

Physics major:
1 is prime, 3 is prime, 5 is prime, 7 is prime,
9 is a measurement error
11 is prime, 13 is prime
That's good enough for me.

Humanities major: 1 is prime, 3 is prime, 5 is prime, 7 is prime, 9 is prime ...

Computer science major:
1 is prime, 3 is prime, 5 is prime, 7 is prime,
1 is prime, 3 is prime, 5 is prime, 7 is prime,
1 is prime, 3 is prime, 5 is prime, 7 is prime ...
 
Posted by Pyrtolin (Member # 2638) on :
 
quote:
Originally posted by seagull:
quote:
I've definitely found some of those large values of two for which 2+2=5.
I know about roundoff.
Also for a signed byte: 127+127=-2
But how exactly do you get 2+2=5?

[/QUOTE]

As I said, large values of two:

2.3+2.3=4.6 => 2+2=5

When one system adds then rounds, another rounds then adds, (or for more fund, if one does all the addition, then just rounds off what it displays) you get all kinds of interesting math.
 
Posted by seagull (Member # 694) on :
 
I was talking to my 8 year old son today and he said that the temperature in the pottery oven in his class was 1800 degrees which is 18 times 100 degrees. I replied by explaining to him that multiplication for a temperature is most naturally done in Kelvin rather than Celsius or Fahrenheit.

So twice of 0 degrees celsius is 273.15 degrees Celsius and twice of 100 degrees Celsius is 473.30 degrees Celsius.

[ November 19, 2009, 07:06 AM: Message edited by: seagull ]
 
Posted by TomDavidson (Member # 99) on :
 
Oh, man. Now you've messed up his brain.
 
Posted by seagull (Member # 694) on :
 
Tom, I assume that was a joke.

My son loves Chemistry and I don't want him to grow up believing in objectively false statements like "1800 degrees is 18 times 100 degrees".

I can't even think of a context where that statement would be both meaningful and true. But I am keeping an open mind, any suggestions would be appreciated.
 
Posted by OpsanusTau (Member # 2350) on :
 
0 degrees Celsius = 273.15 Kelvin
2*273.15 K = 546.30 K
546.30 K = 273.15 degrees C

So that's okay.

100 degrees Celsius = 373.15 Kelvin
2*373.15 K = 746.30 K
746.30 K - 273.15 = 473.15 degrees C

So that's almost okay.

You want to be careful, however, when discussing temperature, heat, and energy.
 
Posted by TomDavidson (Member # 99) on :
 
*grin* Yes, it was a joke.
 
Posted by seagull (Member # 694) on :
 
On page 5 of the Rational, informed and conservative thread. seekingprometheus writes:
quote:
I found your posts on the linked thread about objective truth to be keenly interesting and indicative of a deep grasp of logic as well as nuance, but it seemed that the point of it all within a greater context was to find ways to discount the importance of conclusions derived from relatively sound and well structured logic through the use of an interesting distraction--instead of acknowledging that an interlocutor has a compelling point that appears to be as sound as 1+1=2, you seem to think it better to simply undermine the point by discussing the discursive impossibility of translating arguments about issues into perfect formal logic.
I think seekingprometheus is missing the point.

"sound and well structured logic" can be the basis for a rational discussion only when the premises are shared. Rational people can agree to disagree about which premises they accept and when they do that they move beyond the realm of rational discussion.

I have no problem acknowledging that an interlocutor has a compelling point that appears sound (within their own context) but I don't see a point in going out of my way to do so. My problem is with people who refuse to acknowledge that their premises exist and then claim that making a compelling point or rational argument is enough to prove that people who do not accept their premises (and reach different conclusions) can not be rational.

Claiming that something is "as obvious as 2+2=4" is not a rational argument (if anything it is meta-Rational). Trying to analyze the logic of an argument before the context is defined is meaningless. Demostrating that even a statement that sounds "as obvious as 1+1=2" depends on context makes that point.

When the premise that it is possible to be rational and conservative is challenged on a thread titled "Rational, informed and conservative" defining the context is on topic and the specific arguments and compelling points (as interesting as they might be) are the distractions.
 
Posted by seagull (Member # 694) on :
 
quote:
746.30 K - 273.15 = 473.15 degrees C
So that's almost okay.

OOPS, my mistake. Thanks for the correction.
 
Posted by seekingprometheus (Member # 3043) on :
 
quote:
I think seekingprometheus is missing the point.
I disagree.
quote:
"sound and well structured logic" can be the basis for a rational discussion only when the premises are shared.
How to respond to this?

This doesn't seem to fully grasp the nature of "sound and well-structured logic" or "rational discussion." Premises can be subjected to the same examination that conclusions can.

To use as an example the specific argument which occasioned this thread:

originally by velcro:
quote:
1)Cheney said there was classified evidence
2a)Trusted people checked ALL the evidence and found none
2b)Cheney was capable of showing the alleged evidence to certain people, but never did.
3)Cheney lied

You responded by rejecting one of the premises:

originally by seagull:
quote:
I do not trust any of the people you refer to in 2a.
But you don't seem to grasp that this premise can be re-framed as a conclusion and examined. You seem to think that once a premise has been disagreed with, the argument stalls.

Instead of questioning velcro regarding his reasoning for why these individuals should be trusted, or providing reasons that rational individuals should distrust them, you took the occasion to create an diversionary argument as to why the difficulties in translating arguments to logical form precludes the possibility of obtaining valid results through logic. (Which doesn't follow, by the way).
quote:
When the premise that it is possible to be rational and conservative is challenged on a thread titled "Rational, informed and conservative" defining the context is on topic and the specific arguments and compelling points (as interesting as they might be) are the distractions.
If you'll recall, I objected to velcro's framing of that issue in the initial thread, some three thread-bounces ago.

Nonetheless, engaging in the arguments themselves affords the opportunity to present rational and informed opinions on the topic.
 
Posted by seagull (Member # 694) on :
 
quote:
you don't seem to grasp that this premise can be re-framed as a conclusion and examined. You seem to think that once a premise has been disagreed with, the argument stalls.
I think I can see where the confusion is coming from so let me clarify.

I agree that SOME premises can be re-framed as a conclusion and examined. In formal logic statements that can be proved from other axioms are classified as theorems rather than axioms. For many centuries, people tried to prove that the Euclidian axiom of parallel lines is a theorem rather than an axiom but no one ever succeeded. Stating that something is a premise (or an axiom) places it beyond the realm of rational discussion. You can try to rationally prove to me that there is a contradiction between the axiom I stated and some of MY other axioms and that would force me to revise my belief system and concede the point. There is also room for interesting meta-rational discussions about the practicality of believing or not believing in some premises.

But trying to prove the opposite of my axiom based on premises that I did not accept is as futile as trying to prove the Euclidian axiom of parallel lines in spherical geomery (which postulates different axioms that contradict the Euclidian one). It is a non starter.

quote:
Instead of questioning velcro regarding his reasoning for why these individuals should be trusted, or providing reasons that rational individuals should distrust them, you took the occasion to create an diversionary argument as to why the difficulties in translating arguments to logical form precludes the possibility of obtaining valid results through logic. (Which doesn't follow, by the way).
It seems that you are still missing the point.
My position in this discussion is that "politician lie" is an axiom. At the meta-Rational level I am willing to concede that not all politicians lie all the time but if you want to take that approach the burden of proof that any specific politician is not lying would be on you.

"I do not trust politicians" is my premise. You can trust them if you want but that does not make my position irrational. To show that my position is irrational velcro would have to show a contradiction between that premise and other premises that I accept.

Can you see that this argument is independent of the distraction/diversion about what can or can not be translated into formal logic?

[ November 20, 2009, 06:57 AM: Message edited by: seagull ]
 
Posted by TomDavidson (Member # 99) on :
 
quote:
You can trust them if you want but that does not make my position irrational.
No. But it makes your position redundant, in that the argument becomes unnecessary. If you assume from the beginning that all politicians lie all the time, the rest of this conversation is pointless.
 
Posted by kenmeer livermaile (Member # 2243) on :
 
Especially since Cheney is, you know, um, a politician. Seagull's argument perspective is then not only redundant but absurd, a hoary non sequitur.
 
Posted by kenmeer livermaile (Member # 2243) on :
 
Well, not really a non seq. Not sure what you;d call the logic whereby one defends a politician from pert near overwhelming evidence that he's lying because some of the evidence comes from politicians, and one believes politicians are liars.
 
Posted by seagull (Member # 694) on :
 
Funny,
The Non Sequitur here is the claim that I defend Cheney.

Seagull: (on page 3 of the Rational, informed and conservative thread):
quote:
Why bother with all the heaping steaming (and cursing). You don't need all that to convince me that he lied.

1. Politicians lie.
2. Cheney is a politiciam
3. From 1 and 2 we can conclude that Cheney lied.

This rational argument is enough to convince me that Cheney lied but I find it rather trivial.
I also think it is irrelevant to the question of whether I should think of myself as a conservative.

Kenmeer, if you are making a point, I must have missed it, care to clarify?
 
Posted by seekingprometheus (Member # 3043) on :
 
quote:
It seems that you are still missing the point.
As I've said, I don't believe I'm failing to understand to your point. I do seem to be responding to what you're saying in a way that leaves you unconvinced that I grasp what you want to convey.
quote:
"I do not trust politicians" is my premise. You can trust them if you want but that does not make my position irrational. To show that my position is irrational velcro would have to show a contradiction between that premise and other premises that I accept.

I'm relatively disinterested in your argument with velcro per se. I think that demanding a comprehensive defense of cherry-picked issues framed in a biased way is likely to generate little more than a showcasing of spectacularly biased opinions whistling impactlessly past each other.

I am interested in how and why you choose to respond to such a conversation-opener, and how you respond to the flow of the conversation.

I've understood your solipsistic pose from the beginning, and I can appreciate it for what it is. (Personally, I love solipsists--I've been trying to find a suitable club to join for some time now).
quote:

Can you see that this argument is independent of the distraction/diversion about what can or can not be translated into formal logic?

Yup. But my interest and how I've responded is not concerned with the exclusivity of these issues. I've been talking about how they are related--why one should follow from the other in the flow of your responses, in the context of the conversation.

One may start a new thread in order to create the impression of a new topic whose framework has yet to be determined, but if such threads are clearly responsive to a conversation already in progress, changing venues doesn't obliterate the context in which the new "statement" is also a response.

p.s. The paragraph immediately above refers more specifically to the thread from which this one sprang than it does to this particular thread.

p.p.s. De-railing tangents may be frowned upon, but I think that they are less confusing than title-bouncing-conversations. [Smile]

[ November 21, 2009, 01:51 AM: Message edited by: seekingprometheus ]
 
Posted by velcro (Member # 1216) on :
 
Seagull,

All the mental gymnastics are very interesting, but when you say 1+1 does not equal 2, it is because you are using non-standard assumptions, like base 2 instead of base 10.

With agreed upon assumptions, and agreed upon rules of reasoning, there is a "right" conclusion.

In the real world (do you agree to the assumption of a real world, if only for purposes of argument?), the assumptions are fairly standard, for example when you hit your hand with a hammer, it hurts. Now I might have to difine "hit", "your", "hand", and "hurt" for you if you are trying to play a game of avoiding the truth, and I would have to stipulate that you hit it hard, without anesthesia, you have no neurological damage, ad nauseum to counter all the exceptions you would come up with. But when all the assumptions are covered, it would indeed hurt.

That is objective truth.
 
Posted by kenmeer livermaile (Member # 2243) on :
 
I recommend you just slap me preemptively, seekprom, for I am about to meddle:

"I think that demanding a comprehensive defense of cherry-picked issues framed in a biased way is likely to generate little more than a showcasing of spectacularly biased opinions whistling impactlessly past each other."

shows all the qualities needed for a whizbang sentence, but they are not fully integrated. 3 things:

a) the opening ending in "biased way" is of itself superb

b) "whistingly impactlessly" WANTS to be terrific trope but "impactlessly" lacks adequate, um, impact even though it is the properly correct word (that's language for ye)

c) the "showcasing" bridge uses both the proper word that also will work just swell, but the fittings need adjusting.

Your mission, should you choose to accept it, is to rewrite this hummer so that we can hear those "spectacularly biased opinions" whistling past each other and register their lack of meaningful impact without being told to.

The *other* cheek, too? Damn Xtian!
 
Posted by seagull (Member # 694) on :
 
quote:
you are using non-standard assumptions, like base 2 instead of base 10
Kenmeer, as the above quote demonstrates, velcro did not bother to read my earlier posts on this thread. As a result, his "spectacularly biased opinions" are "whistling impactlessly past" the discussion between seekprom and me, thus completing your mission preemptively. [Smile]

quote:
a comprehensive defense of cherry-picked issues framed in a biased way
ROTFL [Big Grin]
But seriously, the indirect reference to cherrypoptart's informative post on the third page of the Rational, informed and conservative thread is extremely relevant (even if it was unintentional) to both to the rational argument on that thread and the meta rational argument on this thread.

I can't figure out if the reference was:
1. Unintentional
2. Humorous
3. Serious
4. Any combination of the above.

I'll try to respond on the other thread (where it belongs).

I'll respond to the solipsism argument later.

[ November 21, 2009, 11:06 AM: Message edited by: seagull ]
 
Posted by kenmeer livermaile (Member # 2243) on :
 
The mission is to achieve this sensorial/logical concept ("comprehensive defense of cherry-picked issues framed in a biased way...(in) ...a showcasing of spectacularly biased opinions whistling impactlessly past each other" in words that do their job so well one scarcely sees the words for the impressions and ideas emanating from them.

I confess I grew bored with the abstract logics awhile back.

Metaphysics are, in my realm, for two purposes: to crack real physical mysteries and pry from their shells principles of physics that engineers can then apply to make me a real true flying carpet afore I die, and to provide conceptual space for mystery of a highly aesthetic nature, in which aspect I join with the metaphysicians of Tlön:

"The metaphysicians of Tlön do not seek for the truth or even for verisimilitude, but rather for the astounding. They judge that metaphysics is a branch of fantastic literature. They know that a system is nothing more than the subordination of all aspects of the universe to any one such aspect. Even the phrase "all aspects" is rejectable, for it supposes the impossible addition of the present and of all past moments. Neither is it licit to use the plural "past moments," since it supposes another operation... One of the schools of Tlön goes so far as to negate time: it reasons that the present is indefinite, that the future has no reality other than as a present memory. Another school declares that all time has already transpired and that our life is only the crepuscular and no doubt falsified and mutilated memory or reflection of an irrecoverable process. Another, that the history of the universe - and in it our lives and the most tenuous detail of our lives - is the scripture produced by a subordinate god in order to communicate with a demon. Another, that the universe is comparable to those cryptographs in which not all the symbols are valid and that only what happens every three hundred nights is true. Another, that while we sleep here, we are awake elsewhere and that in this way every man is two men."

For me, these disquisitions of whether 2=2+4 or not are just so many null integers. [Wink]

[ November 21, 2009, 10:58 AM: Message edited by: kenmeer livermaile ]
 
Posted by kenmeer livermaile (Member # 2243) on :
 
Crepuscular is such an ugly word for the thing it connotes, so it rarely achieves its aim but instead serves as embellishment that really only works when one wants a touch of the ungainly or grotesque in one's twilight depictions, but here its use is apt:

"Another school declares that all time has already transpired and that our life is only the crepuscular and no doubt falsified and mutilated memory or reflection of an irrecoverable process."

Borges makes the Alzheimerian word search, that most of us do when confronted with the word crepuscular ('is that about blood? fabric? oh, wait, I remember: twilight!'), serve the story's aims by linking it to a memory of an already transpired reality now fading in our "mutilated memory".

Well, Borges' translator does. I don't read Spanish.
 
Posted by seagull (Member # 694) on :
 
quote:
Personally, I love solipsists--I've been trying to find a suitable club to join for some time now
Solipsism has its limitations [Wink]
My meager attempts to define a "formal language" in which "1+1=2" is not obvious are also too limited to be practical for most applications. I presented them in order to demonstrate that even that seemingly obvious statement depends on the context.

quote:
I am interested in how and why you choose to respond to such a conversation-opener, and how you respond to the flow of the conversation.
I started the "Rational informed and conservative" thread to call velcro's bluff. The rational discussions by other people on that thread turned out to be much more interesting than I anticipated based on velcro's initial taunt.

I started this thread to address the meta-rational issues that would (in my opinion) have been a distraction from the interesting rational discussions on the original thread.

I believe that when a discussion boils down to:
Person A: "I trust X"
Person B: "I do not trust X"
Where both people honestly believe in their own statement, they are obviously operating in different contexts (Euclidian and Spherical geometries serve as a good analogy) and that both people can be rational within their own context. At that point the discussion could deteriorate into Solipsism but it does not have to. There is still much room for an interesting meta-rational discussion about why each side chooses to adopt their axiom and why adopting each axiom can lead to useful and meaningful models of reality.

I believe that the axiom "politicians lie" is realistic enough to be shared by more than a few isolated solipsists. I believe that it can form a basis for a useful and rational model of reality that explains real world events without resorting to unfounded and untestable assumptions about motivation. Models based on this axiom may not be able to reflect everything in the real world (just like Newton's laws), but they are good enough for many practical purposes.

I acknowledge that other models of reality exist which are inconsistent with the axiom "politicians lie" and that other people may find those models more useful than mine. I see nothing inherently wrong with switching to another context. I do prefer to be informed about what the context is and why it may be better suited to a specific topic before I enter such a discussion.
 
Posted by TomDavidson (Member # 99) on :
 
quote:
I believe that the axiom "politicians lie" is realistic enough to be shared by more than a few isolated solipsists. I believe that it can form a basis for a useful and rational model of reality that explains real world events...
I think it's hysterical that you'd consider that axiomatic, though, knowing as you apparently do what "axiom" means.
 
Posted by kenmeer livermaile (Member # 2243) on :
 
I liked the combination of "few" and "isolated" and "solipsists".

I imagine two of them bumping into each other on the street and realizing with shock that They Are Not Alone...
 
Posted by seagull (Member # 694) on :
 
Thanks Kenmeer, [Wink] It is not intentional but the image you present is indeed funny.

Tom, why exactly do you find it hysterical?
 
Posted by kenmeer livermaile (Member # 2243) on :
 
Solipsism is perhaps my fave paradox. I like this guy's perspective on some of the issues surround solipsism:
Wittgenstein and Private Language
 
Posted by TomDavidson (Member # 99) on :
 
quote:
why exactly do you find it hysterical?
Because as an axiom, it's exactly as useful as "I am always right."
 
Posted by threads (Member # 5091) on :
 
quote:
Originally posted by seagull:
"I do not trust politicians" is my premise. You can trust them if you want but that does not make my position irrational. To show that my position is irrational velcro would have to show a contradiction between that premise and other premises that I accept.

Can you see that this argument is independent of the distraction/diversion about what can or can not be translated into formal logic?

If making a consistent argument were your goal then you would get an A but presumably you also want your argument to be convincing. Concluding that Cheney lied because politicians lie is a pretty lame argument since you take the only part of your argument that requires actual substance and shove it into a premise.

As a rule of thumb, if we have the capabilities to evaluate the truth of a claim then the claim should probably not be taken as a premise.

[ November 22, 2009, 02:40 PM: Message edited by: threads ]
 
Posted by seagull (Member # 694) on :
 
quote:
Cheney lied because politicians lie is a pretty lame argument
As lame as it is, it satifies Occum's razor much better than arguments that try to second guess someone else's motivation or assume access to classified information.

quote:
presumably you also want your argument to be convincing
The argument that "Cheney lied" was not my argument and I could not care less if it was convincing. My point was that if you want to prove to me that Cheney lied, you do not need to make unnecessary assumptions that violate Occum's razor. I am willing to accept that "Cheney lied" based on the much simpler axiom that politician lie.

I like "politicians lie" as a starting premise because it is not biased. It is also representative of the real world because:
People who want to trust some politicians and vilify others find it much harder to argue their cause without a set of biased axioms to support their agenda.

quote:
if we have the capabilities to evaluate the truth of a claim then the claim should probably not be taken as a premise
The truth of a claim depends on the context (that's the whole point of this thread). If something as basic and formally defined as the axiom of parallel lines can be true in one context and false in another context, what makes you think that the claim "Cheney lied" can be evaluated without clearly defining our premises.

If your "capability to evaluate the truth" relies on any of the following premises:
You are willing to take a much larger "leap of faith" than I am with the simple premise that "politicians lie" and we are clearly operating in different contexts.

It really doesn't matter what we think of each other's premises (unless one of us is trying to convince the other to accept a premise). We can agree on the truth of the statement "Cheney lied" but let's not pretend that we got to it in the same way.
 
Posted by threads (Member # 5091) on :
 
quote:
Originally posted by seagull:
quote:
Cheney lied because politicians lie is a pretty lame argument
As lame as it is, it satifies Occum's razor much better than arguments that try to second guess someone else's motivation or assume access to classified information.
Without going in to whether it does or doesn't, I don't see why it matters. The opposite argument (politicians never lie -> Cheney never lied) satisfies all of the same criteria. Clearly we're looking for more than just a sound argument.

quote:
Originally posted by seagull:
quote:
presumably you also want your argument to be convincing
The argument that "Cheney lied" was not my argument and I could not care less if it was convincing. My point was that if you want to prove to me that Cheney lied, you do not need to make unnecessary assumptions that violate Occum's razor. I am willing to accept that "Cheney lied" based on the much simpler axiom that politician lie.

I like "politicians lie" as a starting premise because it is not biased. It is also representative of the real world because:
People who want to trust some politicians and vilify others find it much harder to argue their cause without a set of biased axioms to support their agenda.

This is fine but I think your terminology is muddled. If you've concluded that politicians lie then it isn't an axiom. You can use it as a premise for other arguments but premises need to be defended so I don't have an issue with that.

That said...
quote:
Originally posted by threads:
if we have the capabilities to evaluate the truth of a claim then the claim should probably not be taken as a premise

I'm guilty of muddling terminology as well. I should have said "axiom" in place of "premise".
 
Posted by seagull (Member # 694) on :
 
quote:
If you've concluded that politicians lie then it isn't an axiom.
There is a world of difference between adopting a statement as an axiom and concluding (or proving) that it is true in a specific context. Axioms like Newton's laws, the five axioms of Euclidian Geometry and Peano's axioms are accepted as a premise because we believe that the models generated from them are useful even if the axioms are NOT true in all contexts.

Newton's laws are false in a universe that follows Einstein's theories. Euclid's postulate of parallel lines is false on the surface of a sphere. But that does not make the models based on those axioms any less useful.

Accepting an axiom does not make it true, all it means is that I find it to be a useful premise for a rational discussion. Concluding that a statement is true requires proof based on axioms and rules of inference already accepted in the context of the discussion.

I have not "concluded that politicians lie". Saying that I believe it as an axiom or premise is a weaker statement than claiming that I can prove it.

quote:
I'm guilty of muddling terminology as well.
In the context of this thread I have been using premise and axiom almost interchangably as well so you have no reason to geel guilty. This kind of muddling terminology is bound to happen in a meta-rational discussion where we discuss the merits of the premise/axiom rather than our ability to prove it.

I have been trying to use "axiom" to refer to a premise in the context of a "formal language" that includes clear definitions of "well formed" statements and rules of inference. I use "premise" when the context is not clear but the conventional meaning in English is (hopefully) enough for both sides to understand the concept even if they do not agree on its truth.

[ November 23, 2009, 06:29 AM: Message edited by: seagull ]
 
Posted by seagull (Member # 694) on :
 
quote:
if we have the capabilities to evaluate the truth of a claim then the claim should probably not be taken as [an axiom]
The axioms of set theory can be used to construct a model for which the axioms of number theory can be proved.

There are other useful models that can be constructed in which the axioms of number theory are either unprovable or false. There are also useful models that do not originate in set theory where the axioms of number theory are accepted on faith rather than proved.

Our ability "to evaluate the truth" of the number theory axioms in a specific model does not detract from their status as one of the most useful axiomatic systems in mathematics.
 
Posted by kenmeer livermaile (Member # 2243) on :
 
"Peano's axioms"

I thank you deeply for this. Never heard of Peano before, and if ever a name was delightfully hilarious in possession of a set of axioms, Peano it was.

I also rather enjoyed your explication of your sense of the word 'axiom'.
 
Posted by seagull (Member # 694) on :
 
quote:
I thank you deeply for this.
You are very welcome.
quote:
Never heard of Peano before
The Peano axioms were mentioned (with a link) in the first page of this thread to explain the context in which "1+1=2" can be proved to be true.
 
Posted by threads (Member # 5091) on :
 
seagull, I don't disagree with you on the usefulness of different axioms in different contexts. My point is that "axiom" and "premise" should not be used interchangeably. An axiom can be a premise but not vice versa. I tried typing up a technical explanation of the difference but I'm not confident enough in my abilities to do so without accidentally making a statement that's either too broad or too narrow so I'll try to illustrate the difference through an example.

Here's a very simple argument:
Premise: If a person has never lied then they are not a politician
Conclusion: If a person is a politician then they have lied

To get from the premise to the conclusion I used an axiom of propositional logic* ((-q -> -p) -> (p -> q)) (in english: (not q implies not p) implies (p implies q)). However, the premise is not an axiom. For my argument to be convincing to anyone who accepts the same logical axioms that I do, I need to be able to show that the premise is derivable from those axioms. In practice, political arguments are relatively informal since we are reasoning using objects and concepts that are so far abstracted away from basic logical axioms that any attempt to make them purely formal would likely fail.

I suspect the difference between an axiom and a premise is what prompted Tom's comment that "Because as an axiom, ['politicians lie' is] exactly as useful as 'I am always right.'" "Politicians lie" is certainly not an axiom in any serious logic system though it can be used a premise provided that it is well-supported.

Overall I think we agree on most of the points in this thread.

* Technically there are different equivalent sets of axioms for propositional logic but the axiom I used is commonly used as an axiom.

[ November 23, 2009, 02:17 PM: Message edited by: threads ]
 
Posted by seagull (Member # 694) on :
 
"An axiom can be a premise" is somewhat of an understandment. In the context of a specific formal language, only axioms (or theorems derived from them) can be used as a premise for deriving a proof.

"A premise can not be an Axiom" is not necessarily true. There is nothing preventing a premise from just happening to be an axiom in some formal language.

But that's not the point. The point is that when we construct a context (a meta rational process) any premise can be chosen as an axiom as long as there is no contradiction between the set of axioms that are chosen.

There are too many ways to choose axioms that have no meaning and even if we choose axioms that do mean something, there are too many combinations of axioms that are practically useless. What makes it all interesting (and worthy of study and discussion, at least for me) is when we choose a set of axioms that can help us better understand the world that we live in.
 
Posted by TomDavidson (Member # 99) on :
 
I submit that the axiom "politicians lie" is not useful in a world in which politicians may or may not lie.
 
Posted by velcro (Member # 1216) on :
 
I just came across a very relevant quote from Richard Feynman.
quote:

We can not define anything precisely! If we attempt to, we get into that paralysis of thought that comes to philosophers, who sit opposite each other, one saying to the other, "You don't know what you are talking about!" The second one says, "What do you mean by know? What do you mean by talking? What do you mean by you? and so on. In order to be able to talk constructively, we just have to agree that we are talking about roughly the same thing.

I apologize if some of my posts were too confrontational. But I agree with Feynman, that in order to talk constructively, you just have to agree that we are talking about the same thing. Denying 2+2=4 because we don't agree on the definition of 2 is just a way to weasel out of a conclusion that you can not find a way to accept.
 
Posted by PSRT (Member # 6454) on :
 
In order to practice what I preach a little bit:

Velcro, I agree with you about objective truth, but you are speculating on seagull's motives. That can't go anywhere good, aside from being against site rules.
 
Posted by seagull (Member # 694) on :
 
PSRT, I happen to agree with Feynman too.

The issue I tried to raise in thread is that when people do not "agree that we are talking about roughly the same thing" it is pointless to try to get through the paralysis by convincing the other party to talk about the same thing that you want to talk about.

People can accept some disagreement and identify where there is common ground about "roughly the same thing". In those situations discussions can be interesting and meaningful. But when one side (and it takes only one) tries to force their axioms on the other, discussion become a waste of time.

The Feynman quote just highlights that fact.

Tom,
I find the axiom "politician lie" to be useful (in some contexts) but I can see your point as well and willingly concede it in some contexts. I have no wish to force you to accept my axiom and I am sure that when we want to we can still find common ground on other matters.

[ December 07, 2009, 01:07 AM: Message edited by: seagull ]
 
Posted by kenmeer livermaile (Member # 2243) on :
 
We cannot define precisely whether or not we can define anything precisely.
 


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