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How can we trust logic if it is circular?

Eitan_Zohar
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9/25/2013 1:28:00 AM
Posted: 3 years ago
You can't make an estimate of how "likely" logic is to be true if logic isn't 100% proven, because you need logic itself to do something like that. If you can't be sure that something is certain, but only, say, 90% certain, then what is your estimate of how likely your estimate is to be true? Also 90%? It can keep going. How can this infinite regress be overcome? Has it been addressed by epistemologists? I know that most philosophers are realists.
"It is my ambition to say in ten sentences what others say in a whole book."
FREEDO
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9/25/2013 1:44:42 AM
Posted: 3 years ago
Logic is the least of your problems.

How can you trust your memory?

How can you trust your senses?

These are far more immediate.

Go to yourself and ask what they mean by "trust" and why they are looking for it.

The answer will be nonsense. But that's not the point.
GRAND POOBAH OF DDO

fnord
bossyburrito
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9/25/2013 1:57:40 AM
Posted: 3 years ago
It's based on axioms, and, as such, is not circular.
#UnbanTheMadman

"Some will sell their dreams for small desires
Or lose the race to rats
Get caught in ticking traps
And start to dream of somewhere
To relax their restless flight
Somewhere out of a memory of lighted streets on quiet nights..."

~ Rush
FREEDO
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9/25/2013 2:13:20 AM
Posted: 3 years ago
At 9/25/2013 1:57:40 AM, bossyburrito wrote:
It's based on axioms, and, as such, is not circular.

Once axioms are assumed, yes. But if we are to consider the very foundation for knowledge and understanding, bringing these axioms into context, all things are circular.

This is an inescapable aspect of human thinking. For we do not form thoughts without language. And language has no foundation but definitions, found in dictionaries. Dictionaries are merely written with the very words they describe. With words, humans form thoughts. With thoughts, humans construct organized ideas. All, upon scrutiny, is circular.

In order for logic to be true, it must be logically correct. But logic cannot be used to justify logic. This is circular because we have already made the assumption that logic is true. In order to prove logic, we must do so with a non-logical statement. But this, too, is not permitted by logic's own nature.

We will always run into this wall when we present ourselves with absolutes. An absolute is it's own worst enemy.

There are two types of truths in this world:
Small truths; simply the opposite of what is false
Big truths; true because they are also false.

In western thinking, we shriek and run at the thought of a paradox. The sage finds peace and security. For anything other answer besides a paradox is an answer which only breeds more questions.
GRAND POOBAH OF DDO

fnord
bossyburrito
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9/25/2013 2:43:14 AM
Posted: 3 years ago
At 9/25/2013 2:13:20 AM, FREEDO wrote:
At 9/25/2013 1:57:40 AM, bossyburrito wrote:
It's based on axioms, and, as such, is not circular.

Once axioms are assumed, yes. But if we are to consider the very foundation for knowledge and understanding, bringing these axioms into context, all things are circular.

This is an inescapable aspect of human thinking. For we do not form thoughts without language. And language has no foundation but definitions, found in dictionaries. Dictionaries are merely written with the very words they describe. With words, humans form thoughts. With thoughts, humans construct organized ideas. All, upon scrutiny, is circular.

In order for logic to be true, it must be logically correct. But logic cannot be used to justify logic. This is circular because we have already made the assumption that logic is true. In order to prove logic, we must do so with a non-logical statement. But this, too, is not permitted by logic's own nature.

We will always run into this wall when we present ourselves with absolutes. An absolute is it's own worst enemy.
The only way for logic to be true is for an axiom to be valid and present in reality. As such, axioms need to be logical.
There are two types of truths in this world:
Small truths; simply the opposite of what is false
Big truths; true because they are also false.

In western thinking, we shriek and run at the thought of a paradox. The sage finds peace and security. For anything other answer besides a paradox is an answer which only breeds more questions.

...
#UnbanTheMadman

"Some will sell their dreams for small desires
Or lose the race to rats
Get caught in ticking traps
And start to dream of somewhere
To relax their restless flight
Somewhere out of a memory of lighted streets on quiet nights..."

~ Rush
FREEDO
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9/25/2013 2:46:41 AM
Posted: 3 years ago
At 9/25/2013 2:43:14 AM, bossyburrito wrote:
The only way for logic to be true is for an axiom to be valid and present in reality. As such, axioms need to be logical.

Axioms are ideas. They are not present in reality.

As I explained, axioms can never be proven logically. The best you can do is cop-out and say they're "self-evident". Which they're not.
GRAND POOBAH OF DDO

fnord
bossyburrito
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9/25/2013 2:48:19 AM
Posted: 3 years ago
At 9/25/2013 2:46:41 AM, FREEDO wrote:
At 9/25/2013 2:43:14 AM, bossyburrito wrote:
The only way for logic to be true is for an axiom to be valid and present in reality. As such, axioms need to be logical.

Axioms are ideas. They are not present in reality.

As I explained, axioms can never be proven logically. The best you can do is cop-out and say they're "self-evident". Which they're not.

Axioms have to be proven logically to be proven logically.
#UnbanTheMadman

"Some will sell their dreams for small desires
Or lose the race to rats
Get caught in ticking traps
And start to dream of somewhere
To relax their restless flight
Somewhere out of a memory of lighted streets on quiet nights..."

~ Rush
zmikecuber
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9/26/2013 2:31:33 PM
Posted: 3 years ago
Logic? It works....B!tches.
"Delete your fvcking sig" -1hard

"primal man had the habit, when he came into contact with fire, of satisfying the infantile desire connected with it, by putting it out with a stream of his urine... Putting out the fire by micturating was therefore a kind of sexual act with a male, an enjoyment of sexual potency in a homosexual competition."
dylancatlow
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9/26/2013 2:45:13 PM
Posted: 3 years ago
At 9/25/2013 1:28:00 AM, Eitan_Zohar wrote:
You can't make an estimate of how "likely" logic is to be true if logic isn't 100% proven, because you need logic itself to do something like that. If you can't be sure that something is certain, but only, say, 90% certain, then what is your estimate of how likely your estimate is to be true? Also 90%? It can keep going. How can this infinite regress be overcome? Has it been addressed by epistemologists? I know that most philosophers are realists.

Logic is, by definition, true. Whatever is true is logical. Your error lies in your separation of the two.
dylancatlow
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9/26/2013 2:51:56 PM
Posted: 3 years ago
"Because circular arguments are self-justifying and resistant to falsification, it is frequently assumed that tautology and circular reasoning are absolute theoretical evils. But this is far from the case, for logic and mathematics are almost completely based on circularity. Truth and logical tautology, recursion and iteration, algebraic and topological closure...all involve it to some degree. The problems arise only when circular reasoning is employed without the assurance of full mathematical generality, incorporating false claims of universality on (what may be) non- universal premises....

That is, every tautology is a self-consistent circularity of universal scope, possessing validity by virtue of closure under self-composition, comprehensiveness (non-exclusion of truth), and consistency (freedom from irresolvable paradox). But tautologies are not merely consistent unto themselves; they are mutually consistent under mutual composition, making sentential logic as much a "self-consistent circularity of universal scope" as any one of its tautologies. Thus, sentential logic embodies two levels of tautology, one applying to expressions and one applying to theoretical systems thereof. Predicate logic then extends the tautology concept to cover the specific acts of attribution represented by (formerly anonymous) sentential variables, and model theory goes on to encompass more complex acts of attribution involving more complex relationships.
Reality theory is about the stage of attribution in which two predicates analogous to true and false, namely real and unreal, are ascribed to various statements about the real universe. In this sense, it is closely related to sentential logic. In particular, sentential logic has four main properties to be emulated by reality theory. The first is absolute truth; as the formal definition of truth, it is true by definition.The other properties are closure, comprehensiveness and consistency. I.e., logic is wholly based on, and defined strictly within the bounds of, cognition and perception; it applies to everything that can be coherently perceived or conceived; and it is by its very nature consistent, being designed in a way that precludes inconsistency. It is the basis of mathematics, being the means by which propositions are stated, proved or disproved, and it is the core of science, underwriting the integrity of rational and empirical methodology. Even so- called "nonstandard" logics, e.g. modal, fuzzy and many-valued logics, must be expressed in terms of fundamental two-valued logic to make sense. In short, two-valued logic is something without which reality could not exist. If it were eliminated, then true and false, real and unreal, and existence and nonexistence could not be distinguished, and the merest act of perception or cognition would be utterly impossible." (CTMU)
000ike
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9/26/2013 2:55:19 PM
Posted: 3 years ago
At 9/25/2013 1:57:40 AM, bossyburrito wrote:
It's based on axioms, and, as such, is not circular.

That's completely wrong. As a matter of fact logic designates its own circularity. It is a logical principle that propositions, the truth of which we seek to ascertain, must be contained within another rational arbitration system and adjudicated there, in order to establish their truth or falsity. Where the axioms of logic are the largest containers, they are not themselves contained within anything else, and are not verifiable by anything else. Axioms are definitionally circular, but because they are necessary for the intellect to function, and there are no means with which to make them non-circular, we presuppose their truth and move on.
"A stupid despot may constrain his slaves with iron chains; but a true politician binds them even more strongly with the chain of their own ideas" - Michel Foucault
Cody_Franklin
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9/26/2013 3:02:28 PM
Posted: 3 years ago
I don't really tend to think of logic as something whose truth is evaluable. I think of it as a sophisticated, crystalline table of inputs and outputs. Put in X, do the derivations, get Y. Consider a simple binary system, defined by the following table:

If A, ~X;
If ~A, X.
A v ~A.

You could put this into a table in which you have two possible outputs based on your input--on this view, it doesn't really make sense to ask whether one actually gets, if A, not-X, because it's a function, not a proposition (the latter of which coincides with its inputs, not its structure)--so, we could ask "Do we actually have A, and not not-A?", but not "Do we actually get X if not-A?". Insofar as it may be modeled as a really sophisticated function, one asks the wrong question when one inquires whether logic is "true" or "trustworthy", because it's merely a defined set of joined algorithms with discrete outputs, like a big system of equations. Certainly, you can eliminate some possible choices of rules of inference, e.g., "A --> (X v ~X)", but this is a question not of truth as much as of internal consistency. The entire system could have zero correspondence to reality (we could, for instance, imagine some system of derivation the rules of which are alien to our own formal logic and which, though completely consistent, seems to have nothing to do with reality; consider a simple trinary system without determinate truth-values: "[(A v ~B --> Red) v (~A v B --> Green) v (A v B --> Blue)] & ~(~A & ~B).)

In this system, the table would be modeled in such a way that it is never "true" that A "implies" red; rather, it's just that, given A as an input, the table spits out red as an output. Formal logic, in a similar move, is defined with certain stipulations and rules such that, given an input, you just *get* an output for which "truth" is, at least deductively, only a way of assessing whether it is actually a product of the algorithms. As far as the system itself is concerned, we have reason neither to trust it nor to regard it as true; however, we can say of it that it is well-defined, by which we mean consistent. I think, as a consequence, that our only possible practical disposition toward it should be one of use, in which sense we are neither appropriating it as our own natural inheritance nor revering it as a truth-bearing formula. The moment it ceases to serve our purposes, supposing we find it unmistakeably consistent, by which we mean that it demonstrates an irreconcilable noncorrespondence with states of affairs, we are free to relegate it to the same status as the RGB algorithm.
Eitan_Zohar
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9/26/2013 3:07:21 PM
Posted: 3 years ago
At 9/26/2013 3:02:28 PM, Cody_Franklin wrote:
I don't really tend to think of logic as something whose truth is evaluable. I think of it as a sophisticated, crystalline table of inputs and outputs. Put in X, do the derivations, get Y. Consider a simple binary system, defined by the following table:

If A, ~X;
If ~A, X.
A v ~A.

You could put this into a table in which you have two possible outputs based on your input--on this view, it doesn't really make sense to ask whether one actually gets, if A, not-X, because it's a function, not a proposition (the latter of which coincides with its inputs, not its structure)--so, we could ask "Do we actually have A, and not not-A?", but not "Do we actually get X if not-A?". Insofar as it may be modeled as a really sophisticated function, one asks the wrong question when one inquires whether logic is "true" or "trustworthy", because it's merely a defined set of joined algorithms with discrete outputs, like a big system of equations. Certainly, you can eliminate some possible choices of rules of inference, e.g., "A --> (X v ~X)", but this is a question not of truth as much as of internal consistency. The entire system could have zero correspondence to reality (we could, for instance, imagine some system of derivation the rules of which are alien to our own formal logic and which, though completely consistent, seems to have nothing to do with reality; consider a simple trinary system without determinate truth-values: "[(A v ~B --> Red) v (~A v B --> Green) v (A v B --> Blue)] & ~(~A & ~B).)

In this system, the table would be modeled in such a way that it is never "true" that A "implies" red; rather, it's just that, given A as an input, the table spits out red as an output. Formal logic, in a similar move, is defined with certain stipulations and rules such that, given an input, you just *get* an output for which "truth" is, at least deductively, only a way of assessing whether it is actually a product of the algorithms. As far as the system itself is concerned, we have reason neither to trust it nor to regard it as true; however, we can say of it that it is well-defined, by which we mean consistent. I think, as a consequence, that our only possible practical disposition toward it should be one of use, in which sense we are neither appropriating it as our own natural inheritance nor revering it as a truth-bearing formula. The moment it ceases to serve our purposes, supposing we find it unmistakeably consistent, by which we mean that it demonstrates an irreconcilable noncorrespondence with states of affairs, we are free to relegate it to the same status as the RGB algorithm.

I understand this, but is there any way to get an estimate of truth? Are solutions like falsificationism workable?
"It is my ambition to say in ten sentences what others say in a whole book."
000ike
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9/26/2013 3:08:34 PM
Posted: 3 years ago
At 9/26/2013 2:45:13 PM, dylancatlow wrote:
At 9/25/2013 1:28:00 AM, Eitan_Zohar wrote:
You can't make an estimate of how "likely" logic is to be true if logic isn't 100% proven, because you need logic itself to do something like that. If you can't be sure that something is certain, but only, say, 90% certain, then what is your estimate of how likely your estimate is to be true? Also 90%? It can keep going. How can this infinite regress be overcome? Has it been addressed by epistemologists? I know that most philosophers are realists.

Logic is, by definition, true. Whatever is true is logical. Your error lies in your separation of the two.

Truth is a comparative juxtaposition of proposal within one system, and actuality within another. To judge the truth of proposals forwarded by the eyes, we touch.... to verify a deductive conclusion, we see. No one source of information is considered absolute, but rather we judge truth (as far as we can possibly do so) by seeking coherence between them. A rational thing that senses nothing knows not the meaning of what he reasons - and so because there is no coherence to appeal to and no verification within another system, the axioms of logic remain unquestionable to him, but yet he lacks the confidence with which to call them truth....that is only arrived with coherence between 2 or more sources of information. And then, we should keep in mind that what we're calling truth is still very relative to our senses; we have no reason to assume its persistence in our absence.
"A stupid despot may constrain his slaves with iron chains; but a true politician binds them even more strongly with the chain of their own ideas" - Michel Foucault
Cody_Franklin
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9/26/2013 3:15:54 PM
Posted: 3 years ago
I certainly can't think of any. Falsificationism seems somewhat workable in the local sense, by which I mean it has its uses in human affairs--consider in medicine the use of differential diagnosis--but even this is predicated on the correspondence to our observations of the functions we use. The only sense in which we get "closer" to what's the case is that in which we view the world from the set, of infinite cardinality, of possibilities of what is the case. Once we have eliminated in some way even one of those possibilities (the elimination of which is constrained, naturally, by these same mentioned limits), n - 1 possibilities remain. What is decisive, however, is that this is only a qualitative proposition insofar as we have no meaningful means of approximation. We could therefore claim to be closer to the truth, but this is not meaningful relative to the goal of evaluating our absolute proximity to it.
wrichcirw
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9/26/2013 5:34:51 PM
Posted: 3 years ago
Perhaps a good way of summarizing this thread is to ask:

"How can we trust what we trust?"
At 8/9/2013 9:41:24 AM, wrichcirw wrote:
If you are civil with me, I will be civil to you. If you decide to bring unreasonable animosity to bear in a reasonable discussion, then what would you expect other than to get flustered?
FREEDO
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9/26/2013 11:39:24 PM
Posted: 3 years ago
At 9/26/2013 2:45:13 PM, dylancatlow wrote:
Logic is, by definition, true.

There are a million books in this statement.
GRAND POOBAH OF DDO

fnord
Eitan_Zohar
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9/27/2013 12:06:46 AM
Posted: 3 years ago
At 9/26/2013 3:15:54 PM, Cody_Franklin wrote:
I certainly can't think of any. Falsificationism seems somewhat workable in the local sense, by which I mean it has its uses in human affairs--consider in medicine the use of differential diagnosis--but even this is predicated on the correspondence to our observations of the functions we use. The only sense in which we get "closer" to what's the case is that in which we view the world from the set, of infinite cardinality, of possibilities of what is the case. Once we have eliminated in some way even one of those possibilities (the elimination of which is constrained, naturally, by these same mentioned limits), n - 1 possibilities remain. What is decisive, however, is that this is only a qualitative proposition insofar as we have no meaningful means of approximation. We could therefore claim to be closer to the truth, but this is not meaningful relative to the goal of evaluating our absolute proximity to it.

If we can trust the validity of mathematics, however, doesn't it follow that we can gain a reasonably accurate picture of reality, not by proceeding step by step in falsifying propositions, but by apprehending the limit?
"It is my ambition to say in ten sentences what others say in a whole book."
RoyLatham
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9/27/2013 12:58:37 AM
Posted: 3 years ago
At 9/25/2013 2:13:20 AM, FREEDO wrote:
At 9/25/2013 1:57:40 AM, bossyburrito wrote:
It's based on axioms, and, as such, is not circular.

Once axioms are assumed, yes. But if we are to consider the very foundation for knowledge and understanding, bringing these axioms into context, all things are circular.

Logic is correct as a consequence of the axioms. The axioms are either (a) self-evident and therefore do not need to be proved or (b) impossible to prove, in which case you will use them anyway, but feel good about knowing they are not proved. I'm inclined to go with (b), but I really don't know. Could be (a).

This is an inescapable aspect of human thinking. For we do not form thoughts without language. And language has no foundation but definitions, found in dictionaries.

Thoughts are possible without language. Many people, myself included, remember having thoughts before having learned any language. Language associates symbols with objects and concepts. That can be done with each word independent of the rest of language. The first word a child learns cannot depend upon knowing other words. Also, think of Helen Keller learning language word by word.
Cody_Franklin
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9/27/2013 2:04:42 AM
Posted: 3 years ago
At 9/27/2013 12:06:46 AM, Eitan_Zohar wrote:
At 9/26/2013 3:15:54 PM, Cody_Franklin wrote:
I certainly can't think of any. Falsificationism seems somewhat workable in the local sense, by which I mean it has its uses in human affairs--consider in medicine the use of differential diagnosis--but even this is predicated on the correspondence to our observations of the functions we use. The only sense in which we get "closer" to what's the case is that in which we view the world from the set, of infinite cardinality, of possibilities of what is the case. Once we have eliminated in some way even one of those possibilities (the elimination of which is constrained, naturally, by these same mentioned limits), n - 1 possibilities remain. What is decisive, however, is that this is only a qualitative proposition insofar as we have no meaningful means of approximation. We could therefore claim to be closer to the truth, but this is not meaningful relative to the goal of evaluating our absolute proximity to it.

If we can trust the validity of mathematics, however, doesn't it follow that we can gain a reasonably accurate picture of reality, not by proceeding step by step in falsifying propositions, but by apprehending the limit?

I don't understand what you mean. I am sure what you mean neither by "the validity of mathematics" nor by "apprehending the limit".
Cody_Franklin
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9/27/2013 2:14:46 AM
Posted: 3 years ago
At 9/27/2013 2:04:42 AM, Cody_Franklin wrote:
At 9/27/2013 12:06:46 AM, Eitan_Zohar wrote:
At 9/26/2013 3:15:54 PM, Cody_Franklin wrote:
I certainly can't think of any. Falsificationism seems somewhat workable in the local sense, by which I mean it has its uses in human affairs--consider in medicine the use of differential diagnosis--but even this is predicated on the correspondence to our observations of the functions we use. The only sense in which we get "closer" to what's the case is that in which we view the world from the set, of infinite cardinality, of possibilities of what is the case. Once we have eliminated in some way even one of those possibilities (the elimination of which is constrained, naturally, by these same mentioned limits), n - 1 possibilities remain. What is decisive, however, is that this is only a qualitative proposition insofar as we have no meaningful means of approximation. We could therefore claim to be closer to the truth, but this is not meaningful relative to the goal of evaluating our absolute proximity to it.

If we can trust the validity of mathematics, however, doesn't it follow that we can gain a reasonably accurate picture of reality, not by proceeding step by step in falsifying propositions, but by apprehending the limit?

I don't understand what you mean. I am sure what you mean neither by "the validity of mathematics" nor by "apprehending the limit".

Toward the former, I mean that I am unsure what you mean by suggesting we "trust the validity of mathematics". If, as I suggest, all these kinds of systems are invoked, not on the basis of some criterion like truth or trustworthiness, but, rather, on the basis purely of usefulness (understood only as correspondence between outputs and observed states of affairs), we are confronted with the question, not of whether we trust mathematics, but of whether we find ourselves able to use it. The closest thing I can imagine to that to which you're referring are mathematical (in the sense of computational mathematics, rather than abstract mathematics) evaluations--as in Bayesian analysis--of the truth, in which case I have certain reservations I would be happy to share.
Eitan_Zohar
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9/27/2013 2:23:34 AM
Posted: 3 years ago
At 9/27/2013 2:14:46 AM, Cody_Franklin wrote:
At 9/27/2013 2:04:42 AM, Cody_Franklin wrote:
At 9/27/2013 12:06:46 AM, Eitan_Zohar wrote:
At 9/26/2013 3:15:54 PM, Cody_Franklin wrote:
I certainly can't think of any. Falsificationism seems somewhat workable in the local sense, by which I mean it has its uses in human affairs--consider in medicine the use of differential diagnosis--but even this is predicated on the correspondence to our observations of the functions we use. The only sense in which we get "closer" to what's the case is that in which we view the world from the set, of infinite cardinality, of possibilities of what is the case. Once we have eliminated in some way even one of those possibilities (the elimination of which is constrained, naturally, by these same mentioned limits), n - 1 possibilities remain. What is decisive, however, is that this is only a qualitative proposition insofar as we have no meaningful means of approximation. We could therefore claim to be closer to the truth, but this is not meaningful relative to the goal of evaluating our absolute proximity to it.

If we can trust the validity of mathematics, however, doesn't it follow that we can gain a reasonably accurate picture of reality, not by proceeding step by step in falsifying propositions, but by apprehending the limit?

I don't understand what you mean. I am sure what you mean neither by "the validity of mathematics" nor by "apprehending the limit".

Toward the former, I mean that I am unsure what you mean by suggesting we "trust the validity of mathematics". If, as I suggest, all these kinds of systems are invoked, not on the basis of some criterion like truth or trustworthiness, but, rather, on the basis purely of usefulness (understood only as correspondence between outputs and observed states of affairs), we are confronted with the question, not of whether we trust mathematics, but of whether we find ourselves able to use it. The closest thing I can imagine to that to which you're referring are mathematical (in the sense of computational mathematics, rather than abstract mathematics) evaluations--as in Bayesian analysis--of the truth, in which case I have certain reservations I would be happy to share.

Go ahead.
"It is my ambition to say in ten sentences what others say in a whole book."
Eitan_Zohar
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9/27/2013 2:24:40 AM
Posted: 3 years ago
Also, you know what limits are, correct? It's me that may be confused here.
"It is my ambition to say in ten sentences what others say in a whole book."
dylancatlow
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9/27/2013 9:19:32 AM
Posted: 3 years ago
Think about it this way: if logic weren't circular, it would necessarily need to be informed by chaos, which, by definition, does not have order and thus cannot give rise to it. When you ask the question: "How can we trust logic if it is circular?" you are asking the question "How can we trust logic if its only true by truth's standard." The point is that logic is truth's standard, and that standard is reality.
Cody_Franklin
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9/27/2013 10:24:21 AM
Posted: 3 years ago
At 9/27/2013 9:19:32 AM, dylancatlow wrote:
Think about it this way: if logic weren't circular, it would necessarily need to be informed by chaos, which, by definition, does not have order and thus cannot give rise to it. When you ask the question: "How can we trust logic if it is circular?" you are asking the question "How can we trust logic if its only true by truth's standard." The point is that logic is truth's standard, and that standard is reality.

Two things:

First, what's at stake for me is whether logic is actually circular. I claim it isn't, precisely because circularity, like the question of "truth", is not applicable at the level at which formal logic is articulated. Propositions inside the system, e.g., "X, because X" can be circular because their proofs are recursive, but I don't think this is true for logic, which never regards itself as proven. As a consequence, I think it's a fundamental error to try to attest to the truth of logic--particularly insofar as truth-values are internally assigned to products of the function--on the basis of self-evidence. It just is defined such that, given some variable input and a set of rules, you get a determinate outcome, much the same as, if I define some function with arbitrary operators, where a colon signifies the input/output relation, [X # Y] : Z; [X # Z] : Y; [Y # Z] : X, and vice versa for singular inputs, the system can be completely consistent without the question of truth being relevant. It is in this sense we can say the logical operation of implication, in modus ponens, for instance, isn't something true or false--it's just a rule of the system, which system may or may not correspond in its operation to observations. Indeed, it is owing to this insight that, in categorical and predicate logic, the Aristotelian tradition of existential assumption could be abandoned for the hypothetical view, one representation of the stakes of such an adjustment their divergent relation to the question of whether a unicorn is a horse with one horn; though this may be true according to the hypothetical view, classical logic, with its existential assumption, would call this false on account of the nonexistence of unicorns.

So, it is true that reality, in the sense of the external world, is our standard; however, I take this not as a standard of truth, but as one of usefulness to which a system of derivation may more or less conform, and it is here that the impossibilities of knowledge and systemic completeness coincide. What's finally at stake, then, especially respecting the seeming impossibility of escaping logic, is the possibility of a use of logic which is never substantiated into an appropriation in apophantic discourse.

Second, what do you mean by "chaos", especially in the context of "informing" logic?
dylancatlow
Posts: 12,245
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9/27/2013 10:32:39 AM
Posted: 3 years ago
At 9/27/2013 10:24:21 AM, Cody_Franklin wrote:
At 9/27/2013 9:19:32 AM, dylancatlow wrote:
Think about it this way: if logic weren't circular, it would necessarily need to be informed by chaos, which, by definition, does not have order and thus cannot give rise to it. When you ask the question: "How can we trust logic if it is circular?" you are asking the question "How can we trust logic if its only true by truth's standard." The point is that logic is truth's standard, and that standard is reality.

Two things:

First, what's at stake for me is whether logic is actually circular. I claim it isn't, precisely because circularity, like the question of "truth", is not applicable at the level at which formal logic is articulated. Propositions inside the system, e.g., "X, because X" can be circular because their proofs are recursive, but I don't think this is true for logic, which never regards itself as proven. As a consequence, I think it's a fundamental error to try to attest to the truth of logic--particularly insofar as truth-values are internally assigned to products of the function--on the basis of self-evidence. It just is defined such that, given some variable input and a set of rules, you get a determinate outcome, much the same as, if I define some function with arbitrary operators, where a colon signifies the input/output relation, [X # Y] : Z; [X # Z] : Y; [Y # Z] : X, and vice versa for singular inputs, the system can be completely consistent without the question of truth being relevant. It is in this sense we can say the logical operation of implication, in modus ponens, for instance, isn't something true or false--it's just a rule of the system, which system may or may not correspond in its operation to observations. Indeed, it is owing to this insight that, in categorical and predicate logic, the Aristotelian tradition of existential assumption could be abandoned for the hypothetical view, one representation of the stakes of such an adjustment their divergent relation to the question of whether a unicorn is a horse with one horn; though this may be true according to the hypothetical view, classical logic, with its existential assumption, would call this false on account of the nonexistence of unicorns.

So, it is true that reality, in the sense of the external world, is our standard; however, I take this not as a standard of truth, but as one of usefulness to which a system of derivation may more or less conform, and it is here that the impossibilities of knowledge and systemic completeness coincide. What's finally at stake, then, especially respecting the seeming impossibility of escaping logic, is the possibility of a use of logic which is never substantiated into an appropriation in apophantic discourse.

Second, what do you mean by "chaos", especially in the context of "informing" logic?

By chaos I mean lack of order (non-existence). I'm in school atm so I'll address the rest later.
Cody_Franklin
Posts: 9,483
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9/27/2013 10:41:26 AM
Posted: 3 years ago
At 9/27/2013 10:32:39 AM, dylancatlow wrote:
By chaos I mean lack of order (non-existence). I'm in school atm so I'll address the rest later.

Fair enough; preliminarily, though, I think you could do better, either definitionally or terminologically, because the two notions of chaos with which I'm familiar--on the one hand, the Chaos Theory sense, which defines chaos as sensitivity of the outputs of a system (for Lorenz, the paradigm was a weather-prediction algorithm) to changes in initial conditions, and, on the other hand, the colloquial understanding of entropy as chaos, which, in thermodynamics, is defined in terms of change in energy (heat) over temperature, and which, in statistical mechanics, describes the number of possible microstates which could correspond to a given macrostate--entail that chaos not only exists inescapably, but that, in the case of entropy, the universe, as a closed system, always becomes more chaotic (hence the prediction in cosmology of the universe's eventual heat death). On this view, it's not just that disorder doesn't correspond 1:1 with nonexistence; rather, the two ideas are absolutely exclusive.