Is all logic/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.