Is All Human Reasoning Circular?

[GTdan]

Is all logic/reasoning circular?

Consider this: Science uses experimentation and physical evidence (logic, reasoning, and the senses) to prove or disprove a hypothesis, theory, or judgment. The hypothesis/theory/judgment, however, was made by using logic/reasoning/senses.

We essentially "created" human logic and reasoning. By using logic and reasoning to prove theories that were created by our own logic and reasoning, are we really proving anything at all?

 

[christianjb]

Let's take mathematics, which doesn't depend on external reality (though it can be guided by needs in physics).

There's no possible algorithm given a list of axioms that generates all possible proofs or proves the truth or falsity of all possible statements in that axiomatic set.

The discovery of proofs therefore adds fundamentally new information to our system of knowledge. Without proof, we would have no way of knowing whether (e.g.) the Pythagorean theorem were true no matter how many triangles we tested.

Even 'experimental mathematics' in which we use computers to find results we couldn't feasibly do by hand adds evidence that was not previously available to us.

I'm sure others will chirp in with better examples.

 

[AsianSensationK]

If it turned out that logic was circular, would you stop using it?

If you answered yes, then please explain why. See if your reason stands up to public scrutiny.

If you answered no, then think about what that means. Even if you can't ground your use of logic in some stable, proven set of matter of fact claims, and you're still compelled to use it. That should give you a hint as to how logic is grounded.

Edit: I actually see a thread that's really, really similar on this page. Perhaps reading what's there may help.

https://www.physicsforums.com/showthread.php?t=154450

 

[Gelsamel Epsilon]

How would you go about proving that all logic/reasoning is circular without committing the fallacy of circular logic?Bar axioms, logic/reasoning is not circular.

 

[GTdan]

I would probably still use logic but only because we have seen how it is useful for us. It's practical. I'm not sure if that actually answers the question though.

Maybe I'm not explaining myself correctly: Continuing with mathematics for example. I create a system of numbers and say that I have 2 apples. From that point on everyone says and believes that I have 2 apples. Do I really have 2 apples? Or is it just that I have defined my set of fruit as being 2 apples and in reality this statement means nothing because I could be holding any amount of anything?

 

[Hurkyl]

Do I really have 2 apples?

Does it matter? A rose by any other name would smell as sweet.

 

[christianjb]

I would probably still use logic but only because we have seen how it is useful for us. It's practical. I'm not sure if that actually answers the question though.

Maybe I'm not explaining myself correctly: Continuing with mathematics for example. I create a system of numbers and say that I have 2 apples. From that point on everyone says and believes that I have 2 apples. Do I really have 2 apples? Or is it just that I have defined my set of fruit as being 2 apples and in reality this statement means nothing because I could be holding any amount of anything?

You could define the dollar in your pocket as 'a million bucks' too. However, try buying a car with redefined currency and you'll find that you won't get too far.

 

[GTdan]

You could define the dollar in your pocket as 'a million bucks' too. However, try buying a car with redefined currency and you'll find that you won't get too far.

And that's exactly why I said I would still use logic because it is practical. The entire way we live is made off of this system. But can we really say anything about "reality" or that something is a "fact." Do we really "know" anything?

Maybe I am asking about truth. Can we really find truth using the system of logic we have created?

Hurkyl:

It only smells sweet because that's the word we decided to use to describe the smell.

 

[Hurkyl]

Maybe I am asking about truth. Can we really find truth using the system of logic we have created?

Of course -- because we decided to use the word "truth" to describe what we can find with logic.

 

[GTdan]

Of course -- because we decided to use the word "truth" to describe what we can find with logic.

Your right. What is it that we find with logic though?

 

[JonF]

We essentially "created" human logic and reasoning.

this is not true

 

[GTdan]

this is not true

Why isn't it true?

 

[AsianSensationK]

It doesn't seem true to say that we created it.

It really seems as though we're just formalizing what was already there in our language. Or better yet, formalizing certain thought processes in people.

Even Aristotle agreed that you couldn't "prove" certain fundamental ideas in logic like the principle of non-contradiction. What he did do was give arguments which show everyone is committed to using the principle of non-contradiction.

I like the wikipedia article here
http://en.wikipedia.org/wiki/Principle_of_non-contradiction

Certainly an important principle like non-contradiction is undeniable, but is it demonstrable? If it isn't demonstrable, then how can you say we created it?

Can we really find truth using the system of logic we have created?

I think we preserve it with our systems of logic. Logic doesn't actually tell me much about the world (physics and chem help more with that), so how am I supposed to find truth with logic?

 

[GTdan]

It doesn't seem true to say that we created it.

It really seems as though we're just formalizing what was already there in our language. Or better yet, formalizing certain thought processes in people.

Even Aristotle agreed that you couldn't "prove" certain fundamental ideas in logic like the principle of non-contradiction. What he did do was give arguments which show everyone is committed to using the principle of non-contradiction.

I like the wikipedia article here
http://en.wikipedia.org/wiki/Principle_of_non-contradiction

Certainly an important principle like non-contradiction is undeniable, but is it demonstrable? If it isn't demonstrable, then how can you say we created it?



I think we preserve it with our systems of logic. Logic doesn't actually tell me much about the world (physics and chem help more with that), so how am I supposed to find truth with logic?

I suppose you are right about not creating it.

Physics and Chem (along with all science) uses logic/reason. If Physics tells about the world then so does the use of logic/reason.

 

[JonF]

Why isn't it true?

Because abstract concepts aren't "created". For X to be created by Y, Y needs to be the cause of X existence. This is not true about logic and humans.

 

[out of whack]

Because abstract concepts aren't "created". For X to be created by Y, Y needs to be the cause of X existence. This is not true about logic and humans.

The word "created" is commonly applied to material things instead of mental constructs. A better word may be "formulated" with regards to the latter.

Can we not say that logic was formulated by humans? Since it takes mental abilities to formulate abstract concepts, the conclusion seems to be that logic as we know it was formulated by humans.

 

[JonF]

The word "created" is commonly applied to material things instead of mental constructs. A better word may be "formulated" with regards to the latter.

He used the word "made", so it's pretty clear he doesn't mean "formulated". Also if you substitute "formulated" for "made" in the original statement it becomes non sequitur.

 

[out of whack]

He used the word "made", so it's pretty clear he doesn't mean "formulated".

I don't think it's all that clear so we should ask. GTdan?

My take: since as you said you cannot really "make" an abstract concept, yet we use it, then it must exist in some form. I assume we formulate it because I don't know how logic can be used without being formulated.

Also if you substitute "formulated" for "made" in the original statement it becomes non sequitur.

Replacing terms, the statement summarizes into something like this:

Science uses logic/reasoning/senses as proof, i.e. what we try to prove was formulated using logic/reasoning/senses. Since we also formulated logic/reasoning and we use logic/reasoning for proof of our own logic/reasoning-based claims, are we really proving anything at all?

Given this point of view, the answer to "Is all logic/reasoning circular?" would be yes.

 

[GTdan]

I don't think it's all that clear so we should ask. GTdan?

My take: since as you said you cannot really "make" an abstract concept, yet we use it, then it must exist in some form. I assume we formulate it because I don't know how logic can be used without being formulated.
Replacing terms, the statement summarizes into something like this:
Given this point of view, the answer to "Is all logic/reasoning circular?" would be yes.

I think the word formulated falls in line better with what I was thinking at the time. Note in my first post I put quotations around the word, create.

After JonF and AsianSensationK explained that you can't really create logic, I was kind of left at odds on how to explain what I was trying to say. So yeah, "formulated" definitely fits the bill.

 

[AsianSensationK]

Yes. If you mean we the way we've formulated logic makes it circular, then it seems that you're right.

Even if we didn't create some of the fundamental ideas of logic, we certainly have to try and justify our definitions to ourselves, and the only way we can do that is by appealing to and utilizing the ideas we're trying to describe.

 

[kmarinas86]

Is all logic/reasoning circular?

Consider this: Science uses experimentation and physical evidence (logic, reasoning, and the senses) to prove or disprove a hypothesis, theory, or judgment. The hypothesis/theory/judgment, however, was made by using logic/reasoning/senses.

We essentially "created" human logic and reasoning. By using logic and reasoning to prove theories that were created by our own logic and reasoning, are we really proving anything at all?

Everything that is controvertible is essentially circular.

 

[JonF]

"we use logic/reasoning for proof of our own logic/reasoning-based claims"

While this is true, this is not the only way we derive logic.

 

[baywax]

Could we say that we recognize logic in a sequence or set rather than make a formula out of a sequence or set?

If we do not recognize logic in a sequence or set is it still possible that there is a logic existing in the same?

 

[JonF]

Could we say that we recognize logic in a sequence or set rather than make a formula out of a sequence or set?

If we do not recognize logic in a sequence or set is it still possible that there is a logic existing in the same?

i have no idea what you are intending to say by this.

 

[baywax]

i have no idea what you are intending to say by this.

Yeah, I said it wrong.

I mean that it takes conditioning to find a logic in anything. As an infant we do not see a pattern or have any experience with shapes or sequence so, we don't recognize them as such.

I guess that the logic a bush tribal elder applies to an experience is going to sometimes be very different from the logic applied to the same experience by a rocket scientist.

The logic applied by the tribesman will involve parameters like "does it stop me from being hungry?" or "can I drink it?" and "why does it fall up?". Where as the rocket scientist will have a completely different set of parameters that formulate their logic about the experience.

So, is logic relative to the observer? Or, is it absolute?

Edit:
"Recognizing" logic (in a situation) suggests that the logic is an intrinsic part of what we observe.

"Formulating" a logic (out of a situation) suggests that the logic is extracted from the situation and is relative to who does the extracting and formulating.

 

[JonF]

Not all reasoning is logic. Logic, by virtue of what it is is universal.

 

[raolduke]

See if your reason stands up to public scrutiny

Of course if you went on about logic not existing and you imposed your thoughts about how nothing should have structure and how things are flawed you will of course receive criticism of some sort. It’s when you make your thoughts into actions when you will be struck down. I agree with you - nothing in life makes sense at all – but because of 1000s of years of vices that smarter and stronger human beings created the word "civilized" has now been imposed on your being. It doesn’t seem fair that you have to be involved in their justice system but you are. You can do anything you put your mind to but you'll have to deal with others imperfections when you mess with their business.

 

[baywax]

Not all reasoning is logic. Logic, by virtue of what it is is universal.

I tend to agree until personal logic enters the picture. It may seem to be based on universal princibles yet, in the end, it is based on emotion and what makes the person feel good.

 

[JonF]

I tend to agree until personal logic enters the picture. It may seem to be based on universal princibles yet, in the end, it is based on emotion and what makes the person feel good.

If it is based on emotion it is no longer logic, but rather an entirely different mode of reasoning.

 

[LightbulbSun]

I tend to agree until personal logic enters the picture. It may seem to be based on universal princibles yet, in the end, it is based on emotion and what makes the person feel good.

Emotions do not coincide with logic.

 

[Smurf]

There's no such thing as "false knowledge", it's simply not knowledge.

Similarly, there's no such thing as "False Logic" by virtue of it being emotional, it's simply not logic.

 

[honestrosewater]

Is all logic/reasoning circular?

Consider this: Science uses experimentation and physical evidence (logic, reasoning, and the senses) to prove or disprove a hypothesis, theory, or judgment. The hypothesis/theory/judgment, however, was made by using logic/reasoning/senses.

What do you take proving something to mean? It sounds like you are saying that if you walk from X to Y, you have walked in a circle because there was a time at which you were not walking.

You learned how to reason just like you learned how to walk. (You might have learned to reason in a large part by learning your native language(s) as a child.) Do you assume that reasoning is anything more than just pushing things around, be they abstract symbols, electrons in a circuit, or ions in your brain?

Following some set of rules to get from one sentence (or thought) to another sentence is not necessarily circular just because the rules themselves might happen to be sentences.

You can find two rocks on a path and beat them together to make one a chisel and then use the chisel to make the other into a chisel and then break the first chisel into two pieces and use the second chisel to make chisels out of the pieces, and so on. That doesn't change the fact that you started with two rocks.

Maybe you are wondering where logic and reasoning originate.

If your point was more about the relationship between a language and its metalanguage, that can be cleared up as well, but it takes a bit more work.

We essentially "created" human logic and reasoning. By using logic and reasoning to prove theories that were created by our own logic and reasoning, are we really proving anything at all?

So you are disturbed by the fact that your conclusion follows from premises? That is what a conclusion is. Perhaps you are expecting a conclusion to be absolute in some way. If so, you are expecting too much from it. You have to start somewhere, or yes, you cannot get anywhere, not even in circles.

 

[yougene]

Gödel's incompleteness theorems states

"For any consistent formal, computably enumerable theory that proves basic arithmetical truths, an arithmetical statement that is true but not provable in the theory can be constructed. That is, any effectively generated theory capable of expressing elementary arithmetic cannot be both consistent and complete. 1"

While the theorem deals with math it applies to all rational constructs. All rational constructs ultimately rest on axioms and as such these constructs cannot prove their own axioms/themselves. These constructs are said to be consistent with themselves but are incomplete in that they cannot prove themselves.

My understanding is a logical system can be made complete if it's situated within a context of other system(s). For example, the scientific method heavily depends on mathematics(which depends on other constructs, which also depend on other constructs, etc...) and vice versa. The issue here is it becomes an infinite regression of constructs. So which do you prefer? Circular but consistent or Infinitely regressing but complete?

 

[Hurkyl]

While the theorem deals with math it applies to all rational constructs.

No it doesn't. It only applies to

consistent formal, computably enumerable theories that prove basic integer arithmetical truths.​

Those are the hypotheses of the theorem, and thus are the only things that this theorem can prove incomplete.

The elementary theory of Euclidean geometry and the elementary theory of real number arithmetic are notable examples of consistent formal, computably enumerable, complete theories. (In fact, they are essentially the same theory)

Furthermore, I'm fairly certain that there exist consistent formal theories that can prove their own consistency. (which, of course, requires that the theory fails to include integer arithmetic, or that it fails to be computably enumerable)

These constructs are said to be consistent with themselves but are incomplete in that they cannot prove themselves.

No, they are said to be incomplete in the sense that there exists a statement in its language that it can neither prove nor disprove.

 

[Cane_Toad]

Gödel's incompleteness theorems states
...

IMHO, the main contribution of this theorem is that such a thing can be done, so it's worth seeing what else might be incomplete, not that it says anything about anything else.

My understanding is a logical system can be made complete if it's situated within a context of other system(s). For example, the scientific method heavily depends on mathematics(which depends on other constructs, which also depend on other constructs, etc...) and vice versa. The issue here is it becomes an infinite regression of constructs. So which do you prefer? Circular but consistent or Infinitely regressing but complete?

At some point, you have to reach axioms. I don't know of any such infinite regression. If you try to force it, you'll just end up restating stuff.

 

[yougene]

No it doesn't. It only applies to

consistent formal, computably enumerable theories that prove basic integer arithmetical truths.​

Those are the hypotheses of the theorem, and thus are the only things that this theorem can prove incomplete.

True enough, however the nature of axioms are universal regardless of what construct they are used in.

The elementary theory of Euclidean geometry and the elementary theory of real number arithmetic are notable examples of consistent formal, computably enumerable, complete theories. (In fact, they are essentially the same theory)

I'm just an armchair thinker here so you'll have to forgive my lack of in depth experience with either one of those. My understanding is it's impossible to have a construct be both simultaneously complete AND consistent due to the fact that all constructs rest on axioms. It's just the nature of the relationship we have with reality. We can clearly see that 1 + 1 = 2, and use that as an axiom to build up the construct consistently however you can't use that construct to prove that 1 + 1 = 2, since the construct assumes that it's true already. In the end it would be like saying 1 + 1 = 2 therefore 1 + 1 = 2.

Furthermore, I'm fairly certain that there exist consistent formal theories that can prove their own consistency. (which, of course, requires that the theory fails to include integer arithmetic, or that it fails to be computably enumerable)

A theory can prove it's own consistency, it just can't be complete at the same time.

No, they are said to be incomplete in the sense that there exists a statement in its language that it can neither prove nor disprove.

True enough

 

[yougene]

IMHO, the main contribution of this theorem is that such a thing can be done, so it's worth seeing what else might be incomplete, not that it says anything about anything else.

True, the thing is it applies to all axiomic systems. Basically everything.

At some point, you have to reach axioms. I don't know of any such infinite regression. If you try to force it, you'll just end up restating stuff.

In a consistent system you end up where you started. What can be done is the axioms can be pawned off to another construct to test it's provability(out of the box so to speak). The problem with this is the other construct itself rests on axioms(whose own axioms can be pawned off to another construct that rests on axioms to infinity).

I don't have any experience with this however an earlier conversations noted to me that the infinite nature of number set theory illustrates this as well.

 

[Hurkyl]

My understanding is it's impossible to have a construct be both simultaneously complete AND consistent due to the fact that all constructs rest on axioms.

And I'm telling you that your understanding is incorrect.

The content of Tarski's theorem¹ is that the elementary theory of real arithmetic², or equivalently the elementary theory of Euclidean geometry, is simultaneously consistent complete, consistent, and computably enumerable.


An easier theorem is to prove that any consistent theory can be extended to become a complete, consistent theory. From this it follows that there does exist a consistent and complete theory of integer arithmetic. (so, by Gödel's theorem, the completion must not be computably enumerable)

In the end it would be like saying 1 + 1 = 2 therefore 1 + 1 = 2.

And that's a perfectly valid proof.

A theory can prove it's own consistency, it just can't be complete at the same time.

Do you have a reference for that? I can't seem to find one.


1: alas, there are a few that go by this name, and Wikipedia doesn't have an entry for the one I'm talking about

2: if you want a buzzword to start investigating, try real closed field.

 

[yougene]

And I'm telling you that your understanding is incorrect.

The content of Tarski's theorem¹ is that the elementary theory of real arithmetic², or equivalently the elementary theory of Euclidean geometry, is simultaneously consistent complete, consistent, and computably enumerable.

I fail to see how this doesn't rest on unproveable axioms(e.g 1 + 1 = 2).

Maybe I'm not interpreting the Godel's incompleteness theory correctly but all math is essentially sitting on unproveable givens(as apparent as they can be).

And that's a perfectly valid proof.

It's a perfectly valid observation, a perfectly valid observation but you can't "prove" its validity by using mathematics(since mathematics simply assumes it's true). You can only observe it. As such it's proof lays outside of the formal system in direct observation.

Do you have a reference for that? I can't seem to find one.

It's just Kantian philosophy. It's not specific to mathematics.

1: alas, there are a few that go by this name, and Wikipedia doesn't have an entry for the one I'm talking about

2: if you want a buzzword to start investigating, try real closed field.

Interesting stuff, I just may have to try and wrap my head around it.

 

[honestrosewater]

It seems like "proof" is being used in more than one way. To some people, an axiom is a proof of itself, so there is no such thing as an "unproveable axiom".

What do you take "proof" to mean? Logic and mathematics have defined the term for themselves already. You seem to be using a different meaning.

Also, a deductive system doesn't even need to have any axioms. You can have rules that allow you to deduce sentences from "nothing" (or the empty set).

 

[yougene]

It seems like "proof" is being used in more than one way. To some people, an axiom is a proof of itself, so there is no such thing as an "unproveable axiom".

What do you take "proof" to mean? Logic and mathematics have defined the term for themselves already. You seem to be using a different meaning.

I'm talking about proving somethings existence using a formal system without being circular.

Also, a deductive system doesn't even need to have any axioms. You can have rules that allow you to deduce sentences from "nothing" (or the empty set).

The process of deduction introduces givens that aren't neccasarily proven. Assumptions about our relationship to reality, logic, etc...

 

[honestrosewater]

I'm talking about proving somethings existence using a formal system without being circular.

So you are talking about a formal proof, then? How about the following definition?

Definition. If L is a formal language and F is a set of L-formulas, a proof of an L-formula f_n from F is a non-empty finite sequence of formulas f₁, f₂, ... f_n such that, for each f_i, at least one of the following is true:
1) f_i is an axiom
2) f_i is in F
3) f_i follows by your rules from some combination of L-formulas occurring earlier in the sequence.

There's no point in continuing to use words whose meanings aren't agreed on, yes?

The process of deduction introduces givens that aren't neccasarily proven. Assumptions about our relationship to reality, logic, etc...

What is "the process of deduction"? A proof? What is a given? An axiom? Are you again claiming, with different words, that there exist unprovable axioms?

What formal deductive system says anything about reality? Formal deductive systems don't actually "say" anything in the usual sense. If you want to interpret them as making promises that they cannot keep, that sounds like it's not their problem.

And how is that a response to my comment? You seemed to have problems with axioms, so I thought it might be helpful to point out that you don't necessarily need them.

I suppose this thread might be on the way back to "but how do you know that your deductive system(/your rules/your car/the key to a lock) works?".And by the bye, what exactly is wrong with being circular in the sense of having your conclusion be one of your premises, besides perhaps usually being a waste of time?

 

[yougene]

So you are talking about a formal proof, then? How about the following definition?

Definition. If L is a formal language and F is a set of L-formulas, a proof of an L-formula f_n from F is a non-empty finite sequence of formulas f₁, f₂, ... f_n such that, for each f_i, at least one of the following is true:
1) f_i is an axiom
2) f_i is in F
3) f_i follows by your rules from some combination of L-formulas occurring earlier in the sequence.

There's no point in continuing to use words whose meanings aren't agreed on, yes?

I'm not talking about a proof. I'm talking about proof as in being able to prove it.

I agree, it was probably a mistake to bring Godel's theorem into this. What I'm talking about here isn't particular to Math.

What is "the process of deduction"? A proof? What is a given? An axiom? Are you again claiming, with different words, that there exist unprovable axioms?

A given is something that seems to be readily apparent and is assumed to be true. An axiom is considered a given yes.

What formal deductive system says anything about reality? Formal deductive systems don't actually "say" anything in the usual sense. If you want to interpret them as making promises that they cannot keep, that sounds like it's not their problem.

And how is that a response to my comment? You seemed to have problems with axioms, so I thought it might be helpful to point out that you don't necessarily need them.

I assumed people would be ok with me using the term axioms outside of mathematics. Myth of the given seems to be the more appropriate phrase when talking generally. A deduction begins with a premise which is the given. We can split hairs here but it's essentiallly the same thing.

And by the bye, what exactly is wrong with being circular in the sense of having your conclusion be one of your premises, besides perhaps usually being a waste of time?

There's nothing wrong with it, I was just pointing out that it's not neccasarily circular because the givens can then be validated from another perspective(which also rest on givens)

 

[Hurkyl]

I'm not talking about a proof. I'm talking about proof as in being able to prove it.

What do you mean by "to prove" if you don't mean "to provide a proof"?

 

[yougene]

What do you mean?

 

[kmarinas86]

What do you mean?

=P

Look, all logic relies on definitions. A logical statement must have defined components. They are "defined", therefore they rest on axioms. You cannot have logic without conventional methods of reasoning. Nevertheless, reasoning doesn't have to be circular.

claim 1: A therefore B
claim 2: B therefore C
result: A therefore C

A, B, and C

But just because A, B, and C are true, does that really mean that A therefore B, and B therefore C?

Suppose we know these:

fact 1: A therefore B
fact 2: B therefore C
result: A therefore C

Then by knowing that A is true, then we can know that B and C are true. But knowing A, B, and C is not the clincher that establishes A therefore B, and B therefore C. Ways to make this estabilished (in the sciences) involve making it acceptable by the (scientific) parties involved with the subject. This is done groupwise.

An example of circular reasoning is this:

I don't have a job because I don't have any skills.
I don't have any skills because I didn't go to school.
I didn't go to school because I didn't have any money.
I didn't have money because I didn't have a job.

Circular reasoning can be used to describe viscious and virtous circles. They are valid arguments and can describe our natural world, yet they are circular.

So don't think of circular reasoning so negatively. They can and do make logical descriptions of reality. On the other hand, is all reasoning circular?

Well if there is a strict uni-directional casuality between A and B, then the system can be described without circular reasoning; actually it must not involve circular reasoning. For example:

fact 1: There are only two one pound balls on a given weight scale.
result: There are two pounds on this weight scale.

However, you cannot determine that there are two one pound balls simply by knowing the weight on the scale. Therefore sound circular reasoning concerning this is impossible. Circular reasoning is avoided when one reasons from the specific material to the general material, since you cannot logically deduce something specific (e.g. the two balls each weighing a pound on the scale) from a generality of what exists (e.g. the two pounds on the scale).

I can assure you that not all logic is circular. Also, we do not necessarily arrive a definition of words through deductive reasoning but often through trial an error (e.g. discovering what is a "cow"). Begging the question can be certainly avoided by avoiding deductive reasoning and sticking with inductive reasoning.

 

[yougene]

Then by knowing that A is true, then we can know that B and C are true. But knowing A, B, and C is not the clincher that establishes A therefore B, and B therefore C. Ways to make this estabilished (in the sciences) involve making it acceptable by the (scientific) parties involved with the subject. This is done groupwise.

Turn A, B, and C into a real statement, digg down deep enough, and you'll end up where you started.

An example of circular reasoning is this:

I don't have a job because I don't have any skills.
I don't have any skills because I didn't go to school.
I didn't go to school because I didn't have any money.
I didn't have money because I didn't have a job.

Circular reasoning can be used to describe viscious and virtous circles. They are valid arguments and can describe our natural world, yet they are circular.

So don't think of circular reasoning so negatively. They can and do make logical descriptions of reality. On the other hand, is all reasoning circular?

I have nothing against circular reasoning I find it rather useful.

Well if there is a strict uni-directional casuality between A and B, then the system can be described without circular reasoning; actually it must not involve circular reasoning. For example:

fact 1: There are only two one pound balls on a given weight scale.
result: There are two pounds on this weight scale.

However, you cannot determine that there are two one pound balls simply by knowing the weight on the scale. Therefore sound circular reasoning concerning this is impossible. Circular reasoning is avoided when one reasons from the specific material to the general material, since you cannot logically deduce something specific (e.g. the two balls each weighing a pound on the scale) from a generality of what exists (e.g. the two pounds on the scale).

The problem with that is we never ever directly experience the two balls or the scale. Our experience of the other is always mediated through the mind(culture, constructs, etc..). As such all similar thinking is laid down on assumptions that we hold about our relationship to the outside world. Once you start digging deep enough in the foundations of your reasoning, you start running in circles.

 

[honestrosewater]

I'm still confused about why you consider the axioms to be any more or less "provable" than the other theorems that you derive from them. All that a proof of Q from P says is that Q follows from P by your rules. From outside, a proof of Q from P doesn't give you Q. It gives you a proof of Q from P.

And why this relation (you can view syntactic and semantic consequence as relations just like any other relations) should bother someone more than other relations (does anyone have a problem with equality?) also escapes me.

 

[yougene]

I'm still confused about why you consider the axioms to be any more or less "provable" than the other theorems that you derive from them. All that a proof of Q from P says is that Q follows from P by your rules. From outside, a proof of Q from P doesn't give you Q. It gives you a proof of Q from P.

I consider them on equal footing.

How do we get P? And how did we get that? and so on?

And why this relation (you can view syntactic and semantic consequence as relations just like any other relations) should bother someone more than other relations (does anyone have a problem with equality?) also escapes me.

I don't have a problem with it. I was just discussing the limitations of only being able to observe reality through mediated constructs. That's not saying the rational pov is a mediating construct and the pre-rational pov is not. All of our experience of the outside world is mediated.

 

[honestrosewater]

How do we get P? And how did we get that? and so on?

Well, outside of the system, you don't get P. You can get a proof of P from P (and so on).

I don't have a problem with it. I was just discussing the limitations of only being able to observe reality through mediated constructs. That's not saying the rational pov is a mediating construct and the pre-rational pov is not. All of our experience of the outside world is mediated.

Oh. Roger.

Well, that is perception for you, I guess.