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Axioms & 'First Principles'

sdavio
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4/8/2015 7:01:45 AM
Posted: 1 year ago
Any philosophical system which claims some kind of totality, must for the most part consist of conditional claims such as derivations of the form 'If / Then', or arguments formed as premises and conclusions. However, in order to avoid these becoming mere castles in the sky, which onlookers might disregard simply by denying the predicates, one major tactic of injecting necessity has been the concept of axioms.

An axiom, we are told, is a statement which we may not deny without also affirming it. Thus, if I say that the statement, "Statements may have truth-value" is false, then I am implying that statements can have truth-values, and we are to conclude that the statement is an axiom. Observing simply the shape of this tactic, we might be reminded of a rat-trap; the opponent is caught within a catch-22: either engage and be caught, or sustain disengagement. The fact that everyone who engages is caught, supposedly proves the veracity of the statement itself.

We see, in conclusion, a kind of closed-circuit of thinking. The paradigm can account for every possibility, and therefore it is valid, true, universal and imperative. G.K. Chesterton discusses this mode of thinking, with reference to madmen:

"If a man says (for instance) that men have a conspiracy against him, you cannot dispute it except by saying that all the men deny that they are conspirators; which is exactly what conspirators would do. His explanation covers the facts as much as yours."

"...his mind moves in a perfect but narrow circle. A small circle is quite as infinite as a large circle; but, though it is quite as infinite, it is not so large. The lunatic's theory explains a large number of things, but it does not explain them in a large way..."

(- G.K. Chesterton, Orthodoxy)

The problem is, that the only possible way of refuting these circuitous arguments, is from outside of their boundaries. Since they insist on categorizing any shade of grey as either black or white - and hence allowing their system to continue flowing smoothly - it is only after denying the logic that we can prove that it is flawed. It is not possible for those inside the loop to even perceive the possibility of an outside. This is why we see a specific kind of argument from delusion, such as the egoist who says that "everyone is an egoist, only they might delude themselves or others toward the idea that they aren't." Even the act of disagreeing with their system is really only seen as a specter.

This is why I see the concepts of 'axioms' and 'first-principles' as in themselves problematic; they immediately signal the tendency toward a closed-in style of thought which is inherently unhealthy, or at the least, somewhat cramped and claustrophobic. We might look forward to a day when, for once, people feel at last free, to allow their premises - the 'circumstances' of their arguments - to float in the vulnerable but free and open fresh air of unsureness; of specificity.

Those of us who end up engaging with these system-builders, are inevitably left being sucked further and further into their trap. On pushing one lever, we only trigger the other side of their argument, and we follow them along in their infinite loop, in a 'ping-pong' backward and forward, each movement triggering the other. Those who simply move on, when challenged by their arguments, might only admit that yes, their system is complete, and no, we cannot refute it. Regardless, it is indeed a very small circle.
"Logic is the money of the mind." - Karl Marx
UndeniableReality
Posts: 1,897
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4/8/2015 7:32:13 AM
Posted: 1 year ago
At 4/8/2015 7:01:45 AM, sdavio wrote:
Any philosophical system which claims some kind of totality, must for the most part consist of conditional claims such as derivations of the form 'If / Then', or arguments formed as premises and conclusions. However, in order to avoid these becoming mere castles in the sky, which onlookers might disregard simply by denying the predicates, one major tactic of injecting necessity has been the concept of axioms.

An axiom, we are told, is a statement which we may not deny without also affirming it. Thus, if I say that the statement, "Statements may have truth-value" is false, then I am implying that statements can have truth-values, and we are to conclude that the statement is an axiom. Observing simply the shape of this tactic, we might be reminded of a rat-trap; the opponent is caught within a catch-22: either engage and be caught, or sustain disengagement. The fact that everyone who engages is caught, supposedly proves the veracity of the statement itself.

We see, in conclusion, a kind of closed-circuit of thinking. The paradigm can account for every possibility, and therefore it is valid, true, universal and imperative. G.K. Chesterton discusses this mode of thinking, with reference to madmen:

"If a man says (for instance) that men have a conspiracy against him, you cannot dispute it except by saying that all the men deny that they are conspirators; which is exactly what conspirators would do. His explanation covers the facts as much as yours."

"...his mind moves in a perfect but narrow circle. A small circle is quite as infinite as a large circle; but, though it is quite as infinite, it is not so large. The lunatic's theory explains a large number of things, but it does not explain them in a large way..."

(- G.K. Chesterton, Orthodoxy)

The problem is, that the only possible way of refuting these circuitous arguments, is from outside of their boundaries. Since they insist on categorizing any shade of grey as either black or white - and hence allowing their system to continue flowing smoothly - it is only after denying the logic that we can prove that it is flawed. It is not possible for those inside the loop to even perceive the possibility of an outside. This is why we see a specific kind of argument from delusion, such as the egoist who says that "everyone is an egoist, only they might delude themselves or others toward the idea that they aren't." Even the act of disagreeing with their system is really only seen as a specter.

This is why I see the concepts of 'axioms' and 'first-principles' as in themselves problematic; they immediately signal the tendency toward a closed-in style of thought which is inherently unhealthy, or at the least, somewhat cramped and claustrophobic. We might look forward to a day when, for once, people feel at last free, to allow their premises - the 'circumstances' of their arguments - to float in the vulnerable but free and open fresh air of unsureness; of specificity.

Those of us who end up engaging with these system-builders, are inevitably left being sucked further and further into their trap. On pushing one lever, we only trigger the other side of their argument, and we follow them along in their infinite loop, in a 'ping-pong' backward and forward, each movement triggering the other. Those who simply move on, when challenged by their arguments, might only admit that yes, their system is complete, and no, we cannot refute it. Regardless, it is indeed a very small circle.

It seems to me that "axiom" and "premise" are incorrectly being used interchangeably here. Please correct me if I'm wrong.
sdavio
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4/8/2015 7:35:02 AM
Posted: 1 year ago
At 4/8/2015 7:32:13 AM, UndeniableReality wrote:
It seems to me that "axiom" and "premise" are incorrectly being used interchangeably here. Please correct me if I'm wrong.

I would see a premise as simply the presumed first part of an argument, where it's like, if you don't agree with the premise then the argument doesn't apply. Whereas an axiom applies to everyone. I'd see my main argument as promoting the use of premises as opposed to axioms.
"Logic is the money of the mind." - Karl Marx
UndeniableReality
Posts: 1,897
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4/8/2015 8:10:34 AM
Posted: 1 year ago
At 4/8/2015 7:35:02 AM, sdavio wrote:
At 4/8/2015 7:32:13 AM, UndeniableReality wrote:
It seems to me that "axiom" and "premise" are incorrectly being used interchangeably here. Please correct me if I'm wrong.

I would see a premise as simply the presumed first part of an argument, where it's like, if you don't agree with the premise then the argument doesn't apply. Whereas an axiom applies to everyone. I'd see my main argument as promoting the use of premises as opposed to axioms.

But reading your post, what I see is the suggestion that the use of axioms is problematic because they cannot be rejected from within the confines of the argument. Yet you define "axiom" as a statement which cannot be denied generally. In the second to last paragraph, the switch from "axiom" to "premise" takes place.

The point being made makes sense when talking about premises. But by the very definition of "axiom" being used here, it does not apply to axioms. Premises are already open to debate, making the point somewhat moot anyway. In contrast, axioms are by definition effectively not subject to debate.

The rejection of axioms would result in a kind of 'intellectual anarchy', if I can use my terms loosely. We could say that all of math is wrong because I reject the notion that X + 0 = X, or that (A) + (B) = (A+B). Is this being philosophically open and brave, or is this just being silly? It really depends on the basis for such a rejection, I think.
sdavio
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4/8/2015 8:32:40 AM
Posted: 1 year ago
At 4/8/2015 8:10:34 AM, UndeniableReality wrote:
At 4/8/2015 7:35:02 AM, sdavio wrote:
At 4/8/2015 7:32:13 AM, UndeniableReality wrote:
It seems to me that "axiom" and "premise" are incorrectly being used interchangeably here. Please correct me if I'm wrong.

I would see a premise as simply the presumed first part of an argument, where it's like, if you don't agree with the premise then the argument doesn't apply. Whereas an axiom applies to everyone. I'd see my main argument as promoting the use of premises as opposed to axioms.

But reading your post, what I see is the suggestion that the use of axioms is problematic because they cannot be rejected from within the confines of the argument. Yet you define "axiom" as a statement which cannot be denied generally. In the second to last paragraph, the switch from "axiom" to "premise" takes place.

The point being made makes sense when talking about premises. But by the very definition of "axiom" being used here, it does not apply to axioms. Premises are already open to debate, making the point somewhat moot anyway. In contrast, axioms are by definition effectively not subject to debate.

It's the fact that they're not open to debate that is what I'm addressing. It seems like you've assumed that, since I'm making a point that you regard as impossible, you conclude that I must be making a mistake or not communicating my position clearly. However, it is just that impossibility which is the subject; what does it consist in? In my view, it is nothing but a disposition on the part of the 'holder' of the axiom.

I might put it in simple terms like this: If what we hold as an 'axiom' is really so convincing, then one could just use it as a premise and nobody would find occasion to take issue with it. If we need to call it an axiom, this indicates that someone might find reason to take issue with it; and it is in these cases that we get stuck in the kind of mental circuitry, going around in circles because you will always interpret any criticism within the confines of your own paradigm, which has a kind of rat-trap system going on.

The rejection of axioms would result in a kind of 'intellectual anarchy', if I can use my terms loosely.

That is actually quite a good description. As an anarchist, I'd regard what I'm getting at as a translation of anarchist principles into philosophy.

We could say that all of math is wrong because I reject the notion that X + 0 = X, or that (A) + (B) = (A+B). Is this being philosophically open and brave, or is this just being silly? It really depends on the basis for such a rejection, I think.

I wouldn't find the above example as silly whatsoever. It would be an interesting argument, certainly. Of course, it would require additional argumentation beyond that rejection - the rejection itself is not sufficient reason for math being invalid - but neither does it automatically invalidate the argument.

However, we should also see the much more common example where it's not that I want to necessarily say that something is 'wrong', but that I reject the terms of the statement itself. This somewhat even applies to your math example, actually, because people sometimes use the fact that maths 'has axioms' to therefore justify seeing everything in mathematical terms. See for instance, the egoist example I gave in the OP. The egoist sees everything as binary, either egoist / altruist; and says "all preferences are my own preferences, therefore they are egoic." Now, I don't want to want to say that all action is altruistic; but simply I want to reject the terms themselves. However, whenever I try to do so, the egoist will interpret my arguments as arguments for altruism and now I'm trapped in their little game.

The same for your math thing; it is very different from claiming that math is "wrong", to claiming that "math equally applies for all people at all times." However, the two are conflated under the 'axiomatic' mode of thinking.
"Logic is the money of the mind." - Karl Marx
zmikecuber
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4/8/2015 9:22:41 AM
Posted: 1 year ago
At 4/8/2015 7:01:45 AM, sdavio wrote:
Any philosophical system which claims some kind of totality, must for the most part consist of conditional claims such as derivations of the form 'If / Then', or arguments formed as premises and conclusions. However, in order to avoid these becoming mere castles in the sky, which onlookers might disregard simply by denying the predicates, one major tactic of injecting necessity has been the concept of axioms.

An axiom, we are told, is a statement which we may not deny without also affirming it. Thus, if I say that the statement, "Statements may have truth-value" is false, then I am implying that statements can have truth-values, and we are to conclude that the statement is an axiom. Observing simply the shape of this tactic, we might be reminded of a rat-trap; the opponent is caught within a catch-22: either engage and be caught, or sustain disengagement. The fact that everyone who engages is caught, supposedly proves the veracity of the statement itself.

We see, in conclusion, a kind of closed-circuit of thinking. The paradigm can account for every possibility, and therefore it is valid, true, universal and imperative. G.K. Chesterton discusses this mode of thinking, with reference to madmen:

"If a man says (for instance) that men have a conspiracy against him, you cannot dispute it except by saying that all the men deny that they are conspirators; which is exactly what conspirators would do. His explanation covers the facts as much as yours."

"...his mind moves in a perfect but narrow circle. A small circle is quite as infinite as a large circle; but, though it is quite as infinite, it is not so large. The lunatic's theory explains a large number of things, but it does not explain them in a large way..."

(- G.K. Chesterton, Orthodoxy)

The problem is, that the only possible way of refuting these circuitous arguments, is from outside of their boundaries. Since they insist on categorizing any shade of grey as either black or white - and hence allowing their system to continue flowing smoothly - it is only after denying the logic that we can prove that it is flawed. It is not possible for those inside the loop to even perceive the possibility of an outside. This is why we see a specific kind of argument from delusion, such as the egoist who says that "everyone is an egoist, only they might delude themselves or others toward the idea that they aren't." Even the act of disagreeing with their system is really only seen as a specter.

This is why I see the concepts of 'axioms' and 'first-principles' as in themselves problematic; they immediately signal the tendency toward a closed-in style of thought which is inherently unhealthy, or at the least, somewhat cramped and claustrophobic.

So?

We might look forward to a day when, for once, people feel at last free, to allow their premises - the 'circumstances' of their arguments - to float in the vulnerable but free and open fresh air of unsureness; of specificity.


Why?

Those of us who end up engaging with these system-builders, are inevitably left being sucked further and further into their trap. On pushing one lever, we only trigger the other side of their argument, and we follow them along in their infinite loop, in a 'ping-pong' backward and forward, each movement triggering the other. Those who simply move on, when challenged by their arguments, might only admit that yes, their system is complete, and no, we cannot refute it. Regardless, it is indeed a very small circle.

You're now using the same argument as Chesterton. Lol. You prove his point.
"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."
zmikecuber
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4/8/2015 9:26:47 AM
Posted: 1 year ago
At 4/8/2015 7:01:45 AM, sdavio wrote:
Any philosophical system which claims some kind of totality, must for the most part consist of conditional claims such as derivations of the form 'If / Then', or arguments formed as premises and conclusions. However, in order to avoid these becoming mere castles in the sky, which onlookers might disregard simply by denying the predicates, one major tactic of injecting necessity has been the concept of axioms.

An axiom, we are told, is a statement which we may not deny without also affirming it. Thus, if I say that the statement, "Statements may have truth-value" is false, then I am implying that statements can have truth-values, and we are to conclude that the statement is an axiom. Observing simply the shape of this tactic, we might be reminded of a rat-trap; the opponent is caught within a catch-22: either engage and be caught, or sustain disengagement. The fact that everyone who engages is caught, supposedly proves the veracity of the statement itself.

We see, in conclusion, a kind of closed-circuit of thinking. The paradigm can account for every possibility, and therefore it is valid, true, universal and imperative. G.K. Chesterton discusses this mode of thinking, with reference to madmen:

"If a man says (for instance) that men have a conspiracy against him, you cannot dispute it except by saying that all the men deny that they are conspirators; which is exactly what conspirators would do. His explanation covers the facts as much as yours."

"...his mind moves in a perfect but narrow circle. A small circle is quite as infinite as a large circle; but, though it is quite as infinite, it is not so large. The lunatic's theory explains a large number of things, but it does not explain them in a large way..."

(- G.K. Chesterton, Orthodoxy)

The problem is, that the only possible way of refuting these circuitous arguments, is from outside of their boundaries.

According to your logic. But if your argument is true, and there are no first principles, then why should I believe you?

Since they insist on categorizing any shade of grey as either black or white - and hence allowing their system to continue flowing smoothly - it is only after denying the logic that we can prove that it is flawed. It is not possible for those inside the loop to even perceive the possibility of an outside. This is why we see a specific kind of argument from delusion, such as the egoist who says that "everyone is an egoist, only they might delude themselves or others toward the idea that they aren't." Even the act of disagreeing with their system is really only seen as a specter.

This is why I see the concepts of 'axioms' and 'first-principles' as in themselves problematic; they immediately signal the tendency toward a closed-in style of thought which is inherently unhealthy, or at the least, somewhat cramped and claustrophobic. We might look forward to a day when, for once, people feel at last free, to allow their premises - the 'circumstances' of their arguments - to float in the vulnerable but free and open fresh air of unsureness; of specificity.

Those of us who end up engaging with these system-builders, are inevitably left being sucked further and further into their trap. On pushing one lever, we only trigger the other side of their argument, and we follow them along in their infinite loop, in a 'ping-pong' backward and forward, each movement triggering the other. Those who simply move on, when challenged by their arguments, might only admit that yes, their system is complete, and no, we cannot refute it. Regardless, it is indeed a very small circle.

Your entire argument is based upon premises and conclusions drawn from these. You're implicitly assuming you can draw conclusions from premises. Why should anyone believe you can do that?

If you can deny truth, why can't I deny logic and thus not accept your argument?
"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."
UndeniableReality
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4/8/2015 9:30:28 AM
Posted: 1 year ago
At 4/8/2015 8:32:40 AM, sdavio wrote:
At 4/8/2015 8:10:34 AM, UndeniableReality wrote:
At 4/8/2015 7:35:02 AM, sdavio wrote:
At 4/8/2015 7:32:13 AM, UndeniableReality wrote:
It seems to me that "axiom" and "premise" are incorrectly being used interchangeably here. Please correct me if I'm wrong.

I would see a premise as simply the presumed first part of an argument, where it's like, if you don't agree with the premise then the argument doesn't apply. Whereas an axiom applies to everyone. I'd see my main argument as promoting the use of premises as opposed to axioms.

But reading your post, what I see is the suggestion that the use of axioms is problematic because they cannot be rejected from within the confines of the argument. Yet you define "axiom" as a statement which cannot be denied generally. In the second to last paragraph, the switch from "axiom" to "premise" takes place.

The point being made makes sense when talking about premises. But by the very definition of "axiom" being used here, it does not apply to axioms. Premises are already open to debate, making the point somewhat moot anyway. In contrast, axioms are by definition effectively not subject to debate.

It's the fact that they're not open to debate that is what I'm addressing. It seems like you've assumed that, since I'm making a point that you regard as impossible, you conclude that I must be making a mistake or not communicating my position clearly. However, it is just that impossibility which is the subject; what does it consist in? In my view, it is nothing but a disposition on the part of the 'holder' of the axiom.

I do think that you're not communicating your position clearly, but it is not for the reasons you are asserting. Here is my main reason:

Your definition of "axiom" is not correct. Here is a more common definition from dictionary.com: "a statement or proposition that is regarded as being established, accepted, or self-evidently true." What you are talking about seems to be "non-falsifiable premises", not axioms. If you correct this terminology, I think I agree with your basic point. You may find value in reading some of the works by Karl Popper.

I might put it in simple terms like this: If what we hold as an 'axiom' is really so convincing, then one could just use it as a premise and nobody would find occasion to take issue with it. If we need to call it an axiom, this indicates that someone might find reason to take issue with it; and it is in these cases that we get stuck in the kind of mental circuitry, going around in circles because you will always interpret any criticism within the confines of your own paradigm, which has a kind of rat-trap system going on.

This follows from the equivocation of "axiom" and "non-falsifiable premise". You are free to challenge axioms, by the way.

The rejection of axioms would result in a kind of 'intellectual anarchy', if I can use my terms loosely.

That is actually quite a good description. As an anarchist, I'd regard what I'm getting at as a translation of anarchist principles into philosophy.

Explain how you are injecting "anarchist principles" into philosophy. If you are using the term "anarchy" in the loose sense of "chaos", then sure, I agree.

We could say that all of math is wrong because I reject the notion that X + 0 = X, or that (A) + (B) = (A+B). Is this being philosophically open and brave, or is this just being silly? It really depends on the basis for such a rejection, I think.

I wouldn't find the above example as silly whatsoever. It would be an interesting argument, certainly. Of course, it would require additional argumentation beyond that rejection - the rejection itself is not sufficient reason for math being invalid - but neither does it automatically invalidate the argument.

As I said, if you had a basis for this rejection, then it wouldn't be silly. These are basic axioms of number theory. Most of mathematics is built upon these axioms, which were arrived at empirically and are considered self-evident for countable objects. Rejecting these axioms is necessarily rejecting most of mathematics, unless you can prove that a different set of axioms retains all or most of the results derived from the previous axioms.

However, we should also see the much more common example where it's not that I want to necessarily say that something is 'wrong', but that I reject the terms of the statement itself. This somewhat even applies to your math example, actually, because people sometimes use the fact that maths 'has axioms' to therefore justify seeing everything in mathematical terms. See for instance, the egoist example I gave in the OP. The egoist sees everything as binary, either egoist / altruist; and says "all preferences are my own preferences, therefore they are egoic." Now, I don't want to want to say that all action is altruistic; but simply I want to reject the terms themselves. However, whenever I try to do so, the egoist will interpret my arguments as arguments for altruism and now I'm trapped in their little game.

The same for your math thing; it is very different from claiming that math is "wrong", to claiming that "math equally applies for all people at all times." However, the two are conflated under the 'axiomatic' mode of thinking.

I have never heard someone use the fact that math has axioms to justify that everything can or should be viewed mathematically. I'm not sure how someone who understand what axioms are and has studied pure mathematics could come to that conclusion based on that premise. Can you explain?

Axioms also do not imply that they, or the results derived from them, apply universally. Axioms can be defined to apply under a local set of conditions.

Your examples in the OP, by the way, are examples of non-falsifiable premises, not axioms.
UndeniableReality
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4/8/2015 9:43:38 AM
Posted: 1 year ago
At 4/8/2015 8:32:40 AM, sdavio wrote:
At 4/8/2015 8:10:34 AM, UndeniableReality wrote:
At 4/8/2015 7:35:02 AM, sdavio wrote:
At 4/8/2015 7:32:13 AM, UndeniableReality wrote:
It seems to me that "axiom" and "premise" are incorrectly being used interchangeably here. Please correct me if I'm wrong.

I would see a premise as simply the presumed first part of an argument, where it's like, if you don't agree with the premise then the argument doesn't apply. Whereas an axiom applies to everyone. I'd see my main argument as promoting the use of premises as opposed to axioms.

But reading your post, what I see is the suggestion that the use of axioms is problematic because they cannot be rejected from within the confines of the argument. Yet you define "axiom" as a statement which cannot be denied generally. In the second to last paragraph, the switch from "axiom" to "premise" takes place.

The point being made makes sense when talking about premises. But by the very definition of "axiom" being used here, it does not apply to axioms. Premises are already open to debate, making the point somewhat moot anyway. In contrast, axioms are by definition effectively not subject to debate.

It's the fact that they're not open to debate that is what I'm addressing. It seems like you've assumed that, since I'm making a point that you regard as impossible, you conclude that I must be making a mistake or not communicating my position clearly. However, it is just that impossibility which is the subject; what does it consist in? In my view, it is nothing but a disposition on the part of the 'holder' of the axiom.

I might put it in simple terms like this: If what we hold as an 'axiom' is really so convincing, then one could just use it as a premise and nobody would find occasion to take issue with it. If we need to call it an axiom, this indicates that someone might find reason to take issue with it; and it is in these cases that we get stuck in the kind of mental circuitry, going around in circles because you will always interpret any criticism within the confines of your own paradigm, which has a kind of rat-trap system going on.

The rejection of axioms would result in a kind of 'intellectual anarchy', if I can use my terms loosely.

That is actually quite a good description. As an anarchist, I'd regard what I'm getting at as a translation of anarchist principles into philosophy.

We could say that all of math is wrong because I reject the notion that X + 0 = X, or that (A) + (B) = (A+B). Is this being philosophically open and brave, or is this just being silly? It really depends on the basis for such a rejection, I think.

I wouldn't find the above example as silly whatsoever. It would be an interesting argument, certainly. Of course, it would require additional argumentation beyond that rejection - the rejection itself is not sufficient reason for math being invalid - but neither does it automatically invalidate the argument.

However, we should also see the much more common example where it's not that I want to necessarily say that something is 'wrong', but that I reject the terms of the statement itself. This somewhat even applies to your math example, actually, because people sometimes use the fact that maths 'has axioms' to therefore justify seeing everything in mathematical terms. See for instance, the egoist example I gave in the OP. The egoist sees everything as binary, either egoist / altruist; and says "all preferences are my own preferences, therefore they are egoic." Now, I don't want to want to say that all action is altruistic; but simply I want to reject the terms themselves. However, whenever I try to do so, the egoist will interpret my arguments as arguments for altruism and now I'm trapped in their little game.

The same for your math thing; it is very different from claiming that math is "wrong", to claiming that "math equally applies for all people at all times." However, the two are conflated under the 'axiomatic' mode of thinking.

I forgot to mention that you also haven't addressed my comment about your switch from "axiom" to "premise" in your second to last paragraph.
Mhykiel
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4/8/2015 11:27:05 AM
Posted: 1 year ago
At 4/8/2015 7:01:45 AM, sdavio wrote:
Any philosophical system which claims some kind of totality, must for the most part consist of conditional claims such as derivations of the form 'If / Then', or arguments formed as premises and conclusions. However, in order to avoid these becoming mere castles in the sky, which onlookers might disregard simply by denying the predicates, one major tactic of injecting necessity has been the concept of axioms.

An axiom, we are told, is a statement which we may not deny without also affirming it. Thus, if I say that the statement, "Statements may have truth-value" is false, then I am implying that statements can have truth-values, and we are to conclude that the statement is an axiom. Observing simply the shape of this tactic, we might be reminded of a rat-trap; the opponent is caught within a catch-22: either engage and be caught, or sustain disengagement. The fact that everyone who engages is caught, supposedly proves the veracity of the statement itself.

We see, in conclusion, a kind of closed-circuit of thinking. The paradigm can account for every possibility, and therefore it is valid, true, universal and imperative. G.K. Chesterton discusses this mode of thinking, with reference to madmen:

"If a man says (for instance) that men have a conspiracy against him, you cannot dispute it except by saying that all the men deny that they are conspirators; which is exactly what conspirators would do. His explanation covers the facts as much as yours."

"...his mind moves in a perfect but narrow circle. A small circle is quite as infinite as a large circle; but, though it is quite as infinite, it is not so large. The lunatic's theory explains a large number of things, but it does not explain them in a large way..."

(- G.K. Chesterton, Orthodoxy)

The problem is, that the only possible way of refuting these circuitous arguments, is from outside of their boundaries. Since they insist on categorizing any shade of grey as either black or white - and hence allowing their system to continue flowing smoothly - it is only after denying the logic that we can prove that it is flawed. It is not possible for those inside the loop to even perceive the possibility of an outside. This is why we see a specific kind of argument from delusion, such as the egoist who says that "everyone is an egoist, only they might delude themselves or others toward the idea that they aren't." Even the act of disagreeing with their system is really only seen as a specter.

This is why I see the concepts of 'axioms' and 'first-principles' as in themselves problematic; they immediately signal the tendency toward a closed-in style of thought which is inherently unhealthy, or at the least, somewhat cramped and claustrophobic. We might look forward to a day when, for once, people feel at last free, to allow their premises - the 'circumstances' of their arguments - to float in the vulnerable but free and open fresh air of unsureness; of specificity.

Those of us who end up engaging with these system-builders, are inevitably left being sucked further and further into their trap. On pushing one lever, we only trigger the other side of their argument, and we follow them along in their infinite loop, in a 'ping-pong' backward and forward, each movement triggering the other. Those who simply move on, when challenged by their arguments, might only admit that yes, their system is complete, and no, we cannot refute it. Regardless, it is indeed a very small circle.

Thats why an axiom is a statement that to prove wrong you have to accept it being true. This a lot easier to see with first order statements. Like the axiom of identity in logic. A =A. To prove that wrong during the coarse of the argument there will be an underlining assumption that the entities being stated are the same as the ones being staed earlier in the argument.

As you can see denying axioms leads to nonsensical reasoning.

Many people are suggesting that if it is not possible to falsify a statement than it is illogical to accept as true. And they back this view with analogies to science and philosophers like Karl Popper. This criteria relate to the inductive methodology of science and would be self refuting to apply as an ideology.

Becuase the axioms of science can not themselves be falsified.

Doubt does not confirm claim. Take a deductive argument, the conclusion is said to 100 percent certain. But it's not, thats a imperfect summary. The conclusion of deductive arguments is the conclusion has to follow from the premises. The thing is 'truth' is a weak property of logically valid and sound arguments. Validity can be discerned and the actual nature of the premises investigated but whether or not the conclusion is actually really what is in fact is weakly bond to the argument.

And we have goedel's incomplete theorem.

So if you want to say all of knowledge stems from some presupposed statements, I agree. If you think this means there are no true axioms I disagree.
sdavio
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4/8/2015 11:31:17 AM
Posted: 1 year ago
At 4/8/2015 9:26:47 AM, zmikecuber wrote:
At 4/8/2015 7:01:45 AM, sdavio wrote:
The problem is, that the only possible way of refuting these circuitous arguments, is from outside of their boundaries.

According to your logic. But if your argument is true, and there are no first principles, then why should I believe you?

If you are adamant on not being swayed by any argument which does not include first principles, then obviously you will not believe me. I'm not going to provide you any reason that you 'should', morally believe me. All I have is an analysis of the concepts of 'axioms' and 'first principles' which in my view, when understood, reveals their bankruptcy as ways of structuring belief-systems.

Your entire argument is based upon premises and conclusions drawn from these. You're implicitly assuming you can draw conclusions from premises. Why should anyone believe you can do that?

The fact that both 'UndeniableReality' and yourself have conflated my use of the concepts of 'principles' and 'first principles' makes me think I didn't make the distinction clear enough. I am totally fine with structuring arguments as premises and conclusions. This is different from an axiom in that an axiom is considered impossible to deny. I don't see any possible justification nor benefit in claiming that something is impossible to deny; it might only serve to entrench people in belief systems.

If you can deny truth, why can't I deny logic and thus not accept your argument?

You can if you'd like. However, I wouldn't view logic as a set of propositions which are true or false; I'd view it as a structure which one uses to present such propositions, and one which is particularly useful in that it maximizes clarity.
"Logic is the money of the mind." - Karl Marx
sdavio
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4/8/2015 12:06:06 PM
Posted: 1 year ago
At 4/8/2015 9:30:28 AM, UndeniableReality wrote:
At 4/8/2015 8:32:40 AM, sdavio wrote:
It's the fact that they're not open to debate that is what I'm addressing. It seems like you've assumed that, since I'm making a point that you regard as impossible, you conclude that I must be making a mistake or not communicating my position clearly. However, it is just that impossibility which is the subject; what does it consist in? In my view, it is nothing but a disposition on the part of the 'holder' of the axiom.

I do think that you're not communicating your position clearly, but it is not for the reasons you are asserting. Here is my main reason:

Your definition of "axiom" is not correct. Here is a more common definition from dictionary.com: "a statement or proposition that is regarded as being established, accepted, or self-evidently true." What you are talking about seems to be "non-falsifiable premises", not axioms. If you correct this terminology, I think I agree with your basic point. You may find value in reading some of the works by Karl Popper.

It was my understanding that most definitions of 'axiom' would reduce to meaning the same thing as "impossible to deny without affirming". As for your alternative definitions; I do not see 'established' or 'accepted' as differentiating axioms from premises. As for 'self-evidently true', I don't understand what it means, and / or see no reason to think that anything is self-evidently true. I saw myself as actually being kind of generous in defining axioms the way I did, in that justifying anything as 'self-evident' or likewise has proven very difficult, unless you want to go the whole Cartesian / Phenomenological route.

My understanding of falsifiability in Popper is that an unfalsifiable premise would be one in which no course of events would not apply to the premise positively. This is different from my definition of axioms as propositions which one cannot deny without simultaneously affirming.

This follows from the equivocation of "axiom" and "non-falsifiable premise". You are free to challenge axioms, by the way.

By your definition, it doesn't seem that I'm free to challenge axioms: if they're 'accepted' or 'self-evident', I could not sensibly reject them.

Explain how you are injecting "anarchist principles" into philosophy. If you are using the term "anarchy" in the loose sense of "chaos", then sure, I agree.

I don't think I could explain this at the moment.

I wouldn't find the above example as silly whatsoever. It would be an interesting argument, certainly. Of course, it would require additional argumentation beyond that rejection - the rejection itself is not sufficient reason for math being invalid - but neither does it automatically invalidate the argument.

As I said, if you had a basis for this rejection, then it wouldn't be silly. These are basic axioms of number theory. Most of mathematics is built upon these axioms, which were arrived at empirically and are considered self-evident for countable objects. Rejecting these axioms is necessarily rejecting most of mathematics, unless you can prove that a different set of axioms retains all or most of the results derived from the previous axioms.

Are you conflating axioms with premises? Do you perceive a difference between the two?

The same for your math thing; it is very different from claiming that math is "wrong", to claiming that "math equally applies for all people at all times." However, the two are conflated under the 'axiomatic' mode of thinking.

I have never heard someone use the fact that math has axioms to justify that everything can or should be viewed mathematically.

Perhaps 'everything' was an exaggeration. Although, Pythagoras did do precisely that:

"The so-called Pythagoreans, who were the first to take up mathematics, not only advanced this subject, but saturated with it, they fancied that the principles of mathematics were the principles of all things."

- Aristotle

However, more modern / prevalent examples would be Objectivism, phenomenology, moral realism, and other philosophies which claim total and unquestionable authority (objective truth).

I'm not sure how someone who understand what axioms are and has studied pure mathematics could come to that conclusion based on that premise. Can you explain?

I don't think pure mathematics would require axioms or first principles, as distinct from premises. I was talking primarily about philosophy.

Axioms also do not imply that they, or the results derived from them, apply universally. Axioms can be defined to apply under a local set of conditions.

They universalize onto those who might be tempted to deny them. That is their function, by definition.

Your examples in the OP, by the way, are examples of non-falsifiable premises, not axioms.
"Logic is the money of the mind." - Karl Marx
sdavio
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4/8/2015 12:20:29 PM
Posted: 1 year ago
At 4/8/2015 9:22:41 AM, zmikecuber wrote:
You're now using the same argument as Chesterton. Lol. You prove his point.

....? This bit I don't get at all. I quoted him because his argument fit with what I was saying.. so why wouldn't it be the same argument? Why wouldn't it prove his point?
"Logic is the money of the mind." - Karl Marx
zmikecuber
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4/8/2015 12:40:51 PM
Posted: 1 year ago
At 4/8/2015 11:31:17 AM, sdavio wrote:
At 4/8/2015 9:26:47 AM, zmikecuber wrote:
At 4/8/2015 7:01:45 AM, sdavio wrote:
The problem is, that the only possible way of refuting these circuitous arguments, is from outside of their boundaries.

According to your logic. But if your argument is true, and there are no first principles, then why should I believe you?

If you are adamant on not being swayed by any argument which does not include first principles, then obviously you will not believe me. I'm not going to provide you any reason that you 'should', morally believe me. All I have is an analysis of the concepts of 'axioms' and 'first principles' which in my view, when understood, reveals their bankruptcy as ways of structuring belief-systems.

Your entire argument is based upon premises and conclusions drawn from these. You're implicitly assuming you can draw conclusions from premises. Why should anyone believe you can do that?

The fact that both 'UndeniableReality' and yourself have conflated my use of the concepts of 'principles' and 'first principles' makes me think I didn't make the distinction clear enough. I am totally fine with structuring arguments as premises and conclusions. This is different from an axiom in that an axiom is considered impossible to deny. I don't see any possible justification nor benefit in claiming that something is impossible to deny; it might only serve to entrench people in belief systems.


So you deny self-evident principles, but not principles in general? Like you do accept certain principles or basic premises, in a general sense, but you don't accept statements as prima facie true such as "A is A"?

If you can deny truth, why can't I deny logic and thus not accept your argument?

You can if you'd like. However, I wouldn't view logic as a set of propositions which are true or false; I'd view it as a structure which one uses to present such propositions, and one which is particularly useful in that it maximizes clarity.

Alright. I deny logic. Now convince me that you have defeated first principles.

Also, logic can be expressed as statements. For example, if I make the proposition "Modus ponens is valid reasoning" this is a statement that a certain sort of reasoning accurately leads from one statement to the other.
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"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."
zmikecuber
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4/8/2015 12:41:42 PM
Posted: 1 year ago
At 4/8/2015 12:20:29 PM, sdavio wrote:
At 4/8/2015 9:22:41 AM, zmikecuber wrote:
You're now using the same argument as Chesterton. Lol. You prove his point.

....? This bit I don't get at all. I quoted him because his argument fit with what I was saying.. so why wouldn't it be the same argument? Why wouldn't it prove his point?

It is the same argument. My point is that you're saying his argument is nonsense and then going on to use his argument yourself.
"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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4/8/2015 1:30:36 PM
Posted: 1 year ago
Logical axioms are those premises which are necessarily taken for granted by any intelligible proposition. Basically, logic consists of the rules to which an intelligible (coherently defined) predicate must conform (the rules are simply extensions of the identity principle). Obviously, those worlds which are anything less than coherently defined are not defined at all, and therefore do not constitute a sensible counterexample to the absolute generality of logic.
dylancatlow
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4/8/2015 1:51:14 PM
Posted: 1 year ago
Information may only be purchased at the price of coherency, and coherency may only be purchased at the price of conformance with the rules of logic. That which lacks informational distinctions is no different from what it is supposedly "not", and therefore has not been defined at all. You have no rational basis on which to claim this practice "confines itself" to a box that is anything but infinite in size and scope.
sdavio
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4/8/2015 11:22:27 PM
Posted: 1 year ago
At 4/8/2015 12:41:42 PM, zmikecuber wrote:
At 4/8/2015 12:20:29 PM, sdavio wrote:
At 4/8/2015 9:22:41 AM, zmikecuber wrote:
You're now using the same argument as Chesterton. Lol. You prove his point.

....? This bit I don't get at all. I quoted him because his argument fit with what I was saying.. so why wouldn't it be the same argument? Why wouldn't it prove his point?

It is the same argument. My point is that you're saying his argument is nonsense and then going on to use his argument yourself.

The opposite: my point of using it was to say that I agree with it, that it's a good articulation of my idea.
"Logic is the money of the mind." - Karl Marx
sdavio
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4/9/2015 7:40:49 AM
Posted: 1 year ago
At 4/8/2015 1:51:14 PM, dylancatlow wrote:
Information may only be purchased at the price of coherency, and coherency may only be purchased at the price of conformance with the rules of logic.

Insofar as you want to preclude whatever kind of discourse doesn't fit your criteria; for 'truth', for 'science', for 'coherence', or whatever else, your unwillingness to allow that discourse into some given category, is justified simply through definitions of terms. This is clearly an 'If/Then' type statement, and trying to bolt it into the foundations of the universe using axioms betrays nothing else than an unwillingness to allow others to use a different vocabulary.

In essence: All a non-compliance with your terms involves, is a different language, different definitions; a different vocabulary. By upholding your own criteria, therefore, as, not only valid in a conditional sense (in an 'If/Then' form), but valid in a 'transcendental' sense, you are simply claiming the spiritual superiority of your own vocabulary over all others. This is the difference between an axiom and a premise; a principle and a 'first' principle.

That which lacks informational distinctions is no different from what it is supposedly "not", and therefore has not been defined at all.

This category of 'informational distinctions' is, as far as I'm concerned, a non-entity, being with the fact that it is unilateral (there is nothing in the realm of philosophy to which it doesn't apply) and therefore does not distinguish anything. Thus you have locked the universe into a box labeled 'informational distinctions' (or, more accurately, you've written 'everything that isn't informational distinctions' on an empty box), but the term and the theory themselves really only serve to unnecessarily limit vocabulary insofar as they disallow something, when really in not distinguishing anything, they have no right to disallow anything. If someone claims to be talking about something that isn't an informational distinction, all we can derive from that is that they don't mean the same thing by that term as you do. (And this is a trivial fact, since all you mean by the phrase is, "that which nothing isn't.")

A philosophy consisting of nothing but empty tautologies is at best unnecessary. There is no need to precede any discourse by reminding everyone that you mean by the words you use, the same thing that you mean by the words you use.

You have no rational basis on which to claim this practice "confines itself" to a box that is anything but infinite in size and scope.

As the Chesterton quote said, yes it's infinite in a certain sense, but a very small infinity. It can account for the facts, but it does so using a very small set of tools. Of course, I could conceivably split the world in two with a vocabulary consisting of only two concepts; however, in doing so I've not achieved very much.

As for the position that your practice is infinite in 'all senses', this is impossible, especially for the fact that what you're describing involves informational distinctions. If you are distinguishing something, you are limiting it. The fact that the justification for this limitation is present nowhere else but in the terms of the limitation itself should give you cause for hesitation.
"Logic is the money of the mind." - Karl Marx
Welfare-Worker
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4/9/2015 9:23:55 AM
Posted: 1 year ago
sdavidio
If you are adamant on not being swayed by any argument which does not include first principles, then obviously you will not believe me. I'm not going to provide you any reason that you 'should', morally believe me. All I have is an analysis of the concepts of 'axioms' and 'first principles' which in my view, when understood, reveals their bankruptcy as ways of structuring belief-systems.

The fact that both 'UndeniableReality' and yourself have conflated my use of the concepts of 'principles' and 'first principles' makes me think I didn't make the distinction clear enough. I am totally fine with structuring arguments as premises and conclusions. This is different from an axiom in that an axiom is considered impossible to deny. I don't see any possible justification nor benefit in claiming that something is impossible to deny; it might only serve to entrench people in belief systems.
ttp://www.debate.org...

I get the distinct impression that you believe you have a belief system without axioms.
If so, that would be a interesting and unique thing.
Am I misreading?
dylancatlow
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4/9/2015 3:00:15 PM
Posted: 1 year ago
At 4/9/2015 7:40:49 AM, sdavio wrote:
At 4/8/2015 1:51:14 PM, dylancatlow wrote:
Information may only be purchased at the price of coherency, and coherency may only be purchased at the price of conformance with the rules of logic.

Insofar as you want to preclude whatever kind of discourse doesn't fit your criteria; for 'truth', for 'science', for 'coherence', or whatever else, your unwillingness to allow that discourse into some given category, is justified simply through definitions of terms. This is clearly an 'If/Then' type statement, and trying to bolt it into the foundations of the universe using axioms betrays nothing else than an unwillingness to allow others to use a different vocabulary.

In essence: All a non-compliance with your terms involves, is a different language, different definitions; a different vocabulary. By upholding your own criteria, therefore, as, not only valid in a conditional sense (in an 'If/Then' form), but valid in a 'transcendental' sense, you are simply claiming the spiritual superiority of your own vocabulary over all others. This is the difference between an axiom and a premise; a principle and a 'first' principle.


It doesn't matter what vocabulary you use. Insofar as the language in question is used to convey meaning, it conforms to the tautological structure of logic. Definition and meaning require closed informational boundaries to distinguish what something is from what something isn't. If something doesn't conform to logic then it can be implicated in the contradiction X=/= X which is literally false by definition (things are, by definition, what they are, not what they aren't).

That which lacks informational distinctions is no different from what it is supposedly "not", and therefore has not been defined at all.

This category of 'informational distinctions' is, as far as I'm concerned, a non-entity, being with the fact that it is unilateral (there is nothing in the realm of philosophy to which it doesn't apply) and therefore does not distinguish anything.

Your argument is that "according to its meaning, the concept of 'informational distinctions' applies everywhere, and therefore has no meaning and applies nowhere." Am I supposed to find this convincing?

Informational distinctions are defined in juxtaposition to paradox, which of course don't "exist", which is kind of the whole point.

Thus you have locked the universe into a box labeled 'informational distinctions' (or, more accurately, you've written 'everything that isn't informational distinctions' on an empty box), but the term and the theory themselves really only serve to unnecessarily limit vocabulary insofar as they disallow something, when really in not distinguishing anything, they have no right to disallow anything.

As I pointed out before, information requires coherence. That which is incoherent is simply a self-annihilating linguist construct which attempts to define a single concept by linguistically combining a bunch of mutually exclusive concepts. In other words, I'm not artificially disallowing contradictory concepts - they disallow themselves, since in order to exist, they must not exist as per their definition.

If someone claims to be talking about something that isn't an informational distinction, all we can derive from that is that they don't mean the same thing by that term as you do. (And this is a trivial fact, since all you mean by the phrase is, "that which nothing isn't.")

Why couldn't we conclude that they are mistaken? And if they are talking about something different, then why shouldn't we conclude that what they have in mind corresponds to our notion of "informational distinctions"?


A philosophy consisting of nothing but empty tautologies is at best unnecessary. There is no need to precede any discourse by reminding everyone that you mean by the words you use, the same thing that you mean by the words you use.


It's only "unnecessary" in the sense that it is self-evident. There's nothing which says that self-evident principles cannot yield useful information.

You have no rational basis on which to claim this practice "confines itself" to a box that is anything but infinite in size and scope.

As the Chesterton quote said, yes it's infinite in a certain sense, but a very small infinity. It can account for the facts, but it does so using a very small set of tools. Of course, I could conceivably split the world in two with a vocabulary consisting of only two concepts; however, in doing so I've not achieved very much.

How do you know it's a small infinity when there's nothing coherent beyond it to compare it to? You have no rational basis on which to make that assertion. In order to claim that it's a "small infinity", you must provide an alternative to informational distinctions stable enough to be real.


As for the position that your practice is infinite in 'all senses', this is impossible, especially for the fact that what you're describing involves informational distinctions. If you are distinguishing something, you are limiting it. The fact that the justification for this limitation is present nowhere else but in the terms of the limitation itself should give you cause for hesitation.

I don't know what you're trying to say.
dylancatlow
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4/9/2015 9:38:26 PM
Posted: 1 year ago
At 4/9/2015 7:40:49 AM, sdavio wrote:
At 4/8/2015 1:51:14 PM, dylancatlow wrote:
As the Chesterton quote said, yes it's infinite in a certain sense, but a very small infinity. It can account for the facts, but it does so using a very small set of tools. Of course, I could conceivably split the world in two with a vocabulary consisting of only two concepts; however, in doing so I've not achieved very much.


If something were real enough to invalidate the assumption that "reality" is a perfectly general context, it would by definition be included in reality. Thus, everything which is real must conform to the rules of reality. Since reality is by definition all and only that which is real - since it is meaningful - it conforms to logical structure. Therefore, illogical things are irrelevant to our notion of "reality". You can't claim that our notion of reality is incorrect or incomplete, since it is both consistent and totally comprehensive by definition.
sdavio
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4/9/2015 10:25:17 PM
Posted: 1 year ago
At 4/9/2015 9:23:55 AM, Welfare-Worker wrote:
I get the distinct impression that you believe you have a belief system without axioms.
If so, that would be a interesting and unique thing.
Am I misreading?

If, by a hidden assumption on my part, I were to assume something as privileged or 'in-itself' justified, I would consider this a mistake, and would hopefully change it when it's pointed out. Of course, as has been said, my reasoning includes, well, reasoning, and moves from premises to conclusions; but insofar as people have considered this as a contradiction in my position, they have misunderstood me and probably willfully ignored my repeatedly distinguishing between an axiom and a premise.
"Logic is the money of the mind." - Karl Marx
bossyburrito
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4/10/2015 2:22:20 AM
Posted: 1 year ago
At 4/8/2015 1:51:14 PM, dylancatlow wrote:
Information may only be purchased at the price of coherency, and coherency may only be purchased at the price of conformance with the rules of logic. That which lacks informational distinctions is no different from what it is supposedly "not", and therefore has not been defined at all. You have no rational basis on which to claim this practice "confines itself" to a box that is anything but infinite in size and scope.

This is a wonderful post.

Sdavio, if you reject the axioms of logic, your entire position is, by definition, illogical. If you don't care, that doesn't make it any less illogical. Adopting your POV, I can literally say "But that's just what you say!" and have just as much impact behind my argument. You have no solid ground to stand on because you reject solid ground. It's pure sophistry.

I cannot argue with you, since you don't accept the premisses required for argumentation. I can only stop the conversation.
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wrichcirw
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4/10/2015 4:55:27 AM
Posted: 1 year ago
At 4/8/2015 7:01:45 AM, sdavio wrote:
Any philosophical system which claims some kind of totality, must for the most part consist of conditional claims such as derivations of the form 'If / Then', or arguments formed as premises and conclusions. However, in order to avoid these becoming mere castles in the sky, which onlookers might disregard simply by denying the predicates, one major tactic of injecting necessity has been the concept of axioms.

An axiom, we are told, is a statement which we may not deny without also affirming it. Thus, if I say that the statement, "Statements may have truth-value" is false, then I am implying that statements can have truth-values, and we are to conclude that the statement is an axiom. Observing simply the shape of this tactic, we might be reminded of a rat-trap; the opponent is caught within a catch-22: either engage and be caught, or sustain disengagement. The fact that everyone who engages is caught, supposedly proves the veracity of the statement itself.

We see, in conclusion, a kind of closed-circuit of thinking. The paradigm can account for every possibility, and therefore it is valid, true, universal and imperative. G.K. Chesterton discusses this mode of thinking, with reference to madmen:

"If a man says (for instance) that men have a conspiracy against him, you cannot dispute it except by saying that all the men deny that they are conspirators; which is exactly what conspirators would do. His explanation covers the facts as much as yours."

"...his mind moves in a perfect but narrow circle. A small circle is quite as infinite as a large circle; but, though it is quite as infinite, it is not so large. The lunatic's theory explains a large number of things, but it does not explain them in a large way..."

(- G.K. Chesterton, Orthodoxy)

The problem is, that the only possible way of refuting these circuitous arguments, is from outside of their boundaries. Since they insist on categorizing any shade of grey as either black or white - and hence allowing their system to continue flowing smoothly - it is only after denying the logic that we can prove that it is flawed. It is not possible for those inside the loop to even perceive the possibility of an outside. This is why we see a specific kind of argument from delusion, such as the egoist who says that "everyone is an egoist, only they might delude themselves or others toward the idea that they aren't." Even the act of disagreeing with their system is really only seen as a specter.

This is why I see the concepts of 'axioms' and 'first-principles' as in themselves problematic; they immediately signal the tendency toward a closed-in style of thought which is inherently unhealthy, or at the least, somewhat cramped and claustrophobic. We might look forward to a day when, for once, people feel at last free, to allow their premises - the 'circumstances' of their arguments - to float in the vulnerable but free and open fresh air of unsureness; of specificity.

Those of us who end up engaging with these system-builders, are inevitably left being sucked further and further into their trap. On pushing one lever, we only trigger the other side of their argument, and we follow them along in their infinite loop, in a 'ping-pong' backward and forward, each movement triggering the other. Those who simply move on, when challenged by their arguments, might only admit that yes, their system is complete, and no, we cannot refute it. Regardless, it is indeed a very small circle.

This is a very interesting post and I would recall a conversation we had recently about attaching labels upon people (I think the context was racism). By following this philosophy, one would question the entire business of labeling people, yes?
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?
Sidewalker
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4/10/2015 10:53:58 AM
Posted: 1 year ago
At 4/9/2015 9:38:26 PM, dylancatlow wrote:
At 4/9/2015 7:40:49 AM, sdavio wrote:
At 4/8/2015 1:51:14 PM, dylancatlow wrote:
As the Chesterton quote said, yes it's infinite in a certain sense, but a very small infinity. It can account for the facts, but it does so using a very small set of tools. Of course, I could conceivably split the world in two with a vocabulary consisting of only two concepts; however, in doing so I've not achieved very much.


If something were real enough to invalidate the assumption that "reality" is a perfectly general context, it would by definition be included in reality. Thus, everything which is real must conform to the rules of reality. Since reality is by definition all and only that which is real - since it is meaningful - it conforms to logical structure. Therefore, illogical things are irrelevant to our notion of "reality". You can't claim that our notion of reality is incorrect or incomplete, since it is both consistent and totally comprehensive by definition.

Godel proved that it can't logically be both consistent and totally comprehensive.
"It is one of the commonest of mistakes to consider that the limit of our power of perception is also the limit of all there is to perceive." " C. W. Leadbeater
dylancatlow
Posts: 12,252
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4/10/2015 11:14:41 AM
Posted: 1 year ago
At 4/10/2015 10:53:58 AM, Sidewalker wrote:
At 4/9/2015 9:38:26 PM, dylancatlow wrote:
At 4/9/2015 7:40:49 AM, sdavio wrote:
At 4/8/2015 1:51:14 PM, dylancatlow wrote:
As the Chesterton quote said, yes it's infinite in a certain sense, but a very small infinity. It can account for the facts, but it does so using a very small set of tools. Of course, I could conceivably split the world in two with a vocabulary consisting of only two concepts; however, in doing so I've not achieved very much.


If something were real enough to invalidate the assumption that "reality" is a perfectly general context, it would by definition be included in reality. Thus, everything which is real must conform to the rules of reality. Since reality is by definition all and only that which is real - since it is meaningful - it conforms to logical structure. Therefore, illogical things are irrelevant to our notion of "reality". You can't claim that our notion of reality is incorrect or incomplete, since it is both consistent and totally comprehensive by definition.

Godel proved that it can't logically be both consistent and totally comprehensive.

When a language self-refers, it stratifies or separates into levels, with reference flowing directionally from metalanguage to language. E.g., each the following statements " "this statement is about itself", "the subject of this statement is this statement", and "this formula x is a description of x" " is actually a statement and the object of a statement, with statement and object occupying the metalanguage and object levels respectively. The operative rule in such cases is that reference never flows upward from object to statement, but only downward (from metalanguage to object) or laterally (from object to object, by virtue of the expression of these objects within a higher-level metalanguage mediating their mutual influence). This stratification is very important from a proof-theoretic standpoint, as the following example shows.

Theorem: "This statement is false" is false.

Proof: If the statement in quotes is indeed false, then it is true. On the other hand, if it is true, then it is false. This is a contradiction. Since the quoted statement generates a contradiction, it is logically inconsistent and therefore false. (Q.E.D.)

But wait! Unfortunately, if the quoted statement is false, then it is true (as stated in the proof). This would seem to contradict not only the overall statement including the quoted statement, i.e. the "theorem", but the proof as well"unless we have a rule saying that the statement in quotes can refer to neither the overall statement of which it is part, nor to the proof of the overall statement. In that case, it can invalidate only itself, which is exactly what it is taken to be doing, and can do so only within a metalanguage capable of expressing the reflexive self-invalidating relationship. It should be noted that technically, "this statement is false" is invalid on purely formal grounds; it is in fact a forbidden instance of self-reference. But since it is analogous to any statement that implies its own negation in an axiomatic context - and such statements are routinely dealt with in mathematics without immediate concern for their "bad syntax" - its clarity makes it valuable for illustrative purposes.

In the above example, self-reference is confined to a formula that pronounces itself false. Because this formula refers negatively to its own veracity, it is a self-contained paradox attempting to double as its own falsifying metalanguage and thus possessing a whole new level of "falsehood". But aside from true or false, what else could a formula say about itself? Could it pronounce itself, say, unprovable? Let"s try it: "This formula is unprovable". If the given formula is in fact unprovable, then it is true (and therefore a theorem). But sadly, we cannot recognize it as such without a proof. On the other hand, suppose it is provable. Then it is false (because its provability contradicts what it states of itself) and yet true (because provable)! It seems that we still have the makings of a paradox"a statement that is "provably unprovable" and therefore absurd.

But what if we now introduce a distinction between levels of proof, calling one level the basic or "language" level and the other (higher) level the "metalanguage" level? Then we would have either a statement that can be metalinguistically proven to be linguistically unprovable, and thus recognizable as a theorem conveying valuable information about the limitations of the basic language, or a statement that cannot be metalinguistically proven to be linguistically unprovable, which, though uninformative, is at least not a paradox. Presto: self-reference without the possibility of paradox! In the year 1931, an Austrian mathematical logician named Kurt Godel actually performed this magic trick for the entertainment and edification of the mathematical world.
Wocambs
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4/10/2015 12:41:32 PM
Posted: 1 year ago
At 4/8/2015 7:01:45 AM, sdavio wrote:
The fact that you can't tell me that I ought to believe something without affirming that there is something that ought to be believed is hardly something to complain about, unless you're trying to build a castle of philosophical bullsh*t upon the idea that there is no reason to believe anything.

I'd see my main argument as promoting the use of premises as opposed to axioms

Sorry, but the 'rat-trap' is real, and it is simply that if there are only premises, then there are only things which you may decide to accept, which leaves no reason to believe anything, something contradicted by your belief in anything. It is awfully cruel but there does actually have to be a reason for you to believe something.
sdavio
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4/10/2015 9:35:20 PM
Posted: 1 year ago
At 4/10/2015 12:41:32 PM, Wocambs wrote:
At 4/8/2015 7:01:45 AM, sdavio wrote:
The fact that you can't tell me that I ought to believe something without affirming that there is something that ought to be believed is hardly something to complain about, unless you're trying to build a castle of philosophical bullsh*t upon the idea that there is no reason to believe anything.

Premise: "If you tell me that I ought to believe something, then you are affirming that something ought to be believed."

Conclusion: "Something ought to be believed."

Would you agree that this conclusion does not follow (purely logically) from the premise?

I'd see my main argument as promoting the use of premises as opposed to axioms

Sorry, but the 'rat-trap' is real, and it is simply that if there are only premises, then there are only things which you may decide to accept, which leaves no reason to believe anything, something contradicted by your belief in anything. It is awfully cruel but there does actually have to be a reason for you to believe something.

I keep distinguishing between two things: one that I'm affirming and one that I'm denying; and then every time I'm arguing with 'realists' the same tactic keeps repeating, of conflating the two and claiming that it's a contradiction in my argument. For instance, axioms and premises (because I use premises, I must be contradicting my criticism of axioms,) or belief and 'objective' belief (because I believe something, I'm contradicting my criticism of objectivity).

I'd feel a great sense of progress at this point, if at least someone would - not even necessarily agree with - but at least acknowledge the distinction. In fact, if you could refute it you'd probably have me convinced.. but not just by ignoring it.
"Logic is the money of the mind." - Karl Marx