Circular logic the logic of life.

[Eric0728]

I do not understand why people always say that circular logic is invalid. After all linear logic requires that the logic has to be based on something before it, and something before that, and something before that, and on forever. Unless you assume that there is an infinite chain of logic supporting whatever logical happenstance is occuring, then the only way for logic to work is if it is circular. Or maybe square, or any other connected shape.

 

I have no pineapple. I buy pineapple.

 

 

 

I eat pineapple.

 

 

 

Triangular logic!!!!

Yea I originally actually thought I might have been right but then I realized

that maybe logic doesn't apply at all, after all maybe the universe just did poof out of thin void and didn't do that whole circular expanding contracting thing. Hell if I know the answers to the universe.

[Klaynos]

Circular logic is invald because it rarely adds anything.

 

Why is the earth round?

 

The earth is round because it is the earth. (not a great example)

 

The earth is round because gravity is spherically symmetric. this adds something to the discussion, and we can go down investigating gravity...

[iNow]

I have no pineapple.

I buy pineapple.

I eat pineapple.

 

 

 

Triangular logic!!!!

Actually, that's linear logic (or, more appropriately, chronological).

[Kyrisch]

I am God. How do you know? Ask me, I will tell you so.

 

Circular logic. Did I really just prove that I am God? You seem to have a misconception as to the definition of "circular logic". What you're referring to is the fact that we must, in order for any argument to be valid, make some assumptions. An excellent example of this is "What The Tortoise Said To Achilles" by Lewis Carroll.

 

The basic gist is as follows. Consider:

 

A: Things that are equal to the same thing are equal to each other.

B: The two sides of this triangle are equal to the same thing.

Z (conclusion): The two sides of this triangle are equal to each other.

 

The tortoise comments on the relationship between A, B, and Z. Anyone versed in logic in any sense will tell you that if A and B, therefore Z. However, the tortoise challenges, what if someone refused to agree to such a relationship? We can add an assumption:

 

C: If A and B are true, then Z is true.

 

But does this help? If the individual refuses to recognize the logic of A and B leading to Z, then why should this change anything? He could just as easily say, "but who says that if A, B, and C are true, Z is true?"

 

Therefore we must add a fourth assumption:

 

D: If A, B, and C are true, then Z is also true.

 

And on and on. There must always be an initial assumption, but it does not render the logic that follows invalid.

[Reaper]

It's basically shorthand for "Begging the Question"; you are already assuming some proposition to be true though you are trying to prove it. It doesn't add any real insight to the discussion, or to mathematical proofs.

[granpa]

self consistency and consistency with observed facts is the ultimate basis for all of science.

 

linear logic requires that the logic has to be based on something before it, and something before that, and something before that, and on forever.

 

thats very much like multidimensional parity error correction. after you perform the error correction you can ask yoursef how you know any one bit and the answer will be because I know these other 10 things. but how do you know each of those 10 things. you know them because of 100 other things which in turn are based on 1000 other things. it goes on and on and around and around. yet it works.

[swansont]

self consistency and consistency with observed facts is the ultimate basis for all of science.

 

 

This would appear to be beside the point of the OP, which is about logic alone and not the connection to science. So let's stay on topic.

[granpa]

science isnt logic? whats the difference? he asked for the logical basis of any given statement. the only possible basis that I know of is consistency. thats on topic.

 

After all linear logic requires that the logic has to be based on something before it, and something before that, and something before that, and on forever. Unless you assume that there is an infinite chain of logic supporting whatever logical happenstance is occurring, then the only way for logic to work is if it is circular.

 

each field of science/logic is based on a small set of axioms (definitions) which are based on a simpler field of science/logic. ultimately the simplest field, the one that all others ultimately reduce to, is based on a set of axioms that are basically just a set of definitions. logic could therefore be said to be 'by definition'. however that doesnt explain how we actually discover it or how we know how it applies to the real world.

Edited December 24, 2008 by granpa

[D H]

Science uses logic, but that doesn't mean science is logic. Science also abuses logic. In particular, the cornerstone of science, "proof" by experimentation, is not logically valid. Scientists of course know this. That is why scientific theories are deemed to be at best provisionally correct.

[granpa]

since some of you dont seem to know what I'm talking about here is a link on two dimensional parity.

http://www.iu.hio.no/data/QIC/info2/node10.html

 

Suppose we arrange the stream of bits we want to send in a two dimensional MxN array.

 

N

---------------------

| 1 1 0 1 0 | 1

| 0 0 0 1 1 | 0

| 0 0 0 0 0 | 0

| 0 0 0 0 0 | 0

| 0 0 0 0 0 | 0

------------------------

| 1 1 0 0 1 |

 

We make the same assumption as before, namely that errors are rare, so that the chance of two errors occurring the same row or column is extremely low. In this scheme, we add a parity sum for each row and column. Now, if an error occurs, we detect a parity error in both a row and a column. This allows us to localize the bit which is in error, using far fewer bits. Since it is only a bit which is in error, we can simply flip the bit to correct the error.

 

multidimensional parity is exactly like it except that it can have more than 2 dimensions.

 

now correcting one error in a mere 2 dimensional scheme isnt very relevant but if we think in terms of 100 dimensions and many many errors (the limit is 50% error=100% noise) then it becomes very educational.

 

when we begin we dont know which bits/statements are right and which are wrong. a soft in/soft out decoder assigns a confidence value to each bit depending on how many other bits support or argue against it. on the second pass through the decoder it does the same thing except that it then takes into account the confidence value of each of the bits that supports or argues against it. after many passes through the soft in/soft out decoder it becomes clear which are correct and which are wrong. (unless the errors are too extensive).

 

each bit in our example can be thought of as being equivalent to some scientific statement that we have reason to believe. just as each bit is connected (vertically and horizontally) to many other bits (which it either supports or argues against) so our statement is connected to many other statements some of which it supports and some of which it argues against. everything we know about everything forms a vast interconnected web of statements. each statement supports some others and argues against some others. at first we dont know which statements are right and which are wrong. but after extensive error correction we finally decide which ones are right. (unless the errors are too extensive)

 

but then we are left asking ourselves 'what is the basis for believing X'. where X is some bit/statement. this is why it is relevant to this thread. it seems circular (though in reality there is a firm basis for believing X is correct)

Edited December 26, 2008 by Mokele
Removing private PM

[Eric0728]

Yea...Apparently I misunderstood the meaning of what circular logic was, multidimensional parity was more of what I imagined.My problem is not that the facts support eachother in the web of facts, its more of where did the facts originate.

[granpa]

before they were facts they were [bayesian] expectations. after error correction, presumably, they become facts.

 

at first I 'expect' that the sun will rise tomorrow because I saw it rise 1000 times before. after connecting the rising of the sun with the rotation of the earth, the orbit of the earth around the sun, and many other things which support it, it becomes a fact.

Edited January 5, 2009 by granpa

[padren]

Granpa, I think you are basically saying while we may compile more information that works and is consistent with yet more data, that eventually you end up finding you are relying on axioms at some point. If I understand you correctly, you pretty much mean knowledge is a "pyramid scheme" but I don't know if that is the same as circular.

 

I think scientific knowledge though, is about trying to create working theories that describe what we see, and can make reliable predictions. There is never a guarantee that a theory is fact, or that it will always produce reliable predictions, just a level of "strength" based on all available data.

 

Also, the mandatory:

[granpa]

knowledge is a "pyramid scheme"? I dont even know what that would mean.

[swansont]

before they were facts they were [bayesian] expectations. after error correction, presumably, they become facts.

 

at first I 'expect' that the sun will rise tomorrow because I saw it rise 1000 times before. after connecting the rising of the sun with the rotation of the earth, the orbit of the earth around the sun, and many other things which support it, it becomes a fact.

 

 

You can discuss circular reasoning within syllogistic logic — the premise and the conclusion are the same thing, or equivalent to each other. This has nothing to do with error correction.

[granpa]

what if both premises and conclusions are not known for certain? that is the question. what if all you have is a vast body of interconnected truth statements/hypothesis none of which are known for certain, some of which may contradict each other? how do you proceed? how do you determine which statements are more probable? can you ever know anything for certain or are you doomed to eternal uncertainty? that is what I believe the op is asking.

Edited January 5, 2009 by granpa

[swansont]

what if both premises and conclusions are not known for certain? that is the question. what if all you have is a vast body of interconnected truth statements none of which are known for certain, some of which may contradict each other? how do you proceed? how do you determine which statements are more probable? can you ever know anything for certain or are you doomed to eternal uncertainty? that is what I believe the op is asking.

 

I think one can determine for sure if one has purchased a pineapple. Determining the veracity of the premise isn't germane if you state it as a conditional, i.e. "IF A is true, then A is true" is still circular logic, and does not depend on the truth of A.

 

Error correction is tangential to the arguments. Make a new thread to discuss them, if you wish

[Sisyphus]

what if both premises and conclusions are not known for certain? that is the question. what if all you have is a vast body of interconnected truth statements/hypothesis none of which are known for certain, some of which may contradict each other? how do you proceed? how do you determine which statements are more probable? can you ever know anything for certain or are you doomed to eternal uncertainty? that is what I believe the op is asking.

 

Yup, eternal uncertainty. Ultimately almost every statement is conditional, and traceable back to unprovable axioms. From a practical standpoint, all you can really do is reduce those axioms to the point where you're satisfied they can't really be denied. This is one of the central ideas of Cartesian philosopy, which goes back to the famous proclamation, "Cognito, ergo sum." That is, "I think, therefore I am." The supposedly undoubtable and irreducible axioms being that there is thought, and that in order to do something (think), something has to exist (you). Sadly, later philosophers ably demonstrated that there is quite a bit of assumption going on even in those statements, but such is life.

[granpa]

I totally agree that nothing is ever known beyond a doubt. but I wonder whether some things might be knowable beyond a reasonable doubt?

[Sisyphus]

but I wonder whether some things might be knowable beyond a reasonable doubt?

 

Well yeah, that is the goal, and I think you certainly can. The only hitch is that some doubts that seem very unreasonable when first proposed end up being confirmed by reason and observation. It's a common pattern that mainstream but counterintuitive scientific theories are unknowingly predicted (sometimes centuries in advance) by what are at the time considered to be purely academic exercises in philosophy or mathematics.