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Does it follow that one should use logic?

toolpot462
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3/12/2013 1:56:04 PM
Posted: 3 years ago
How can one logically conclude that the use of logic is a viable means of drawing conclusions?

Here is a potential first impression attempt:

1. It is logical to use a system that has reproduceable practical applications to draw conclusions.
2. Logic has such practical applications.
C. Therefore, it is logical that one should use logic to draw conclusions.

This kind of reasoning seems flawed. The first premise assumes that one should use logic - in fact, the very use of logic assumes the conclusion.

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bladerunner060
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3/12/2013 2:03:35 PM
Posted: 3 years ago
How about:

1. It is best (most useful in the search for what is true) to use the system that has the most reproduceable practical applications to draw conclusions.
2. Logic has the most reproduceable practical applications to draw conclusions.

C. Therefore, it is best (most useful in the search for what is true) that one should use logic to draw conclusions.
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Noumena
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3/12/2013 2:10:37 PM
Posted: 3 years ago
P1: You should use what makes the most sense.
P2: Logic makes the most sense.
C: Use logic already (oh wait we already did because we're conceptually forced into it)
: At 5/13/2014 7:05:20 PM, Crescendo wrote:
: The difference is that the gay movement is currently pushing their will on Churches, as shown in the link to gay marriage in Denmark. Meanwhile, the Inquisition ended several centuries ago.
RyuuKyuzo
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3/12/2013 2:11:03 PM
Posted: 3 years ago
There are also flaws to logic that further call into question its validity. We use logic not because it's perfect, but because it's practical, and that's good enough.
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Noumena
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3/12/2013 2:14:38 PM
Posted: 3 years ago
At 3/12/2013 2:11:03 PM, RyuuKyuzo wrote:
There are also flaws to logic that further call into question its validity.

Presupposing logico-normative thought process in saying this.

What I'm saying is there's no way to get around and question logic from the "outside". We're conceptually trapped in the paradigm dude.
: At 5/13/2014 7:05:20 PM, Crescendo wrote:
: The difference is that the gay movement is currently pushing their will on Churches, as shown in the link to gay marriage in Denmark. Meanwhile, the Inquisition ended several centuries ago.
RyuuKyuzo
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3/12/2013 3:06:45 PM
Posted: 3 years ago
At 3/12/2013 2:14:38 PM, Noumena wrote:
At 3/12/2013 2:11:03 PM, RyuuKyuzo wrote:
There are also flaws to logic that further call into question its validity.

Presupposing logico-normative thought process in saying this.

What I'm saying is there's no way to get around and question logic from the "outside". We're conceptually trapped in the paradigm dude.

I'll give you an example of what I mean. Consider the law of non-contradiction (something cannot be both X and NOT X at the same time). If I can find something that is two contradictory things simultaneously, then we have logically concluded that logic if flawed. Therefore, if logic is valid, then we must accept that logic is flawed, and if logic is not valid, then it is flawed anyway.

Let's look at mathematics. I'll start of with a simple statement, 0=/=1=/=infinity. I think we can all agree that these numbers cannot be equal (although infinity is technically not a number).

In mathematics, 1^0=0 and 0^1=1, but 0^0 is undefined. When it needs to be defined, it is commonly defined as being equal to 1 for practical purposes. But, let us give this a real-world suit to wear. Apples. If I have 0 groups of 0 apples, do I have 1 apple? Intuitively, you would think you have 0 apples, but let's go a little bit deeper. If I have zero groups of zero apples, then it means nothing is not apple, so I have an infinite amount of apples.

Okay, but there can't be gaps between the apples, otherwise otherwise there would be some places that are not apple, so we need an infinitely large apple, but that doesn't quite fit either, because if we ever get to the point where the apple has a skin, we would have limited the scope of the apple and therefore it would not be infinite, so we can never actually have one whole apple.

So, if we have 0 groups of 0 apples then we have 1 apple, infinite apple, and no apple simultaneously. This is why 0^0 is commonly held as "undefined", because it leads to contradictory answers which, of course, violate the law of non-contradiction. Since we have logically violated a logical law, logic cannot be perfectly valid and so it is flawed.

I'll give a more "purely" mathematical argument for those who don't like applying mathematical arguments to IRL objects.

0.1/0.1=1, 0.01/0.01=1, 0.001/0.001=1 -- Therefore, it is reasonable to assume that 0/0 will also equal 1

However

0/0.1=0, 0/0.01=0, 0/0.001=0 -- Therefore, it is equally reasonable to assume that 0/0=0

Furthermore, you can also conclude that 0/0 = infinity as approaching 0 from both the positive and the negative sides of a number line approach infinity and -infinity, respectively. (x/y = x/0 = +-infinity)

Since 1=/=0=/=infinity, yet must given this mathematical argument, we have violated the law of non-contradiction.

In this way, we can conclude that there are flaws within logic.

This video gives you a visual demonstration of what I'm saying, just skip to 6:45.
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Skepsikyma
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3/12/2013 3:24:20 PM
Posted: 3 years ago
The problem with attempting to disprove logic is that once you succeed you've also invalidated the argument disproving logic because said argument is based on logic, which means that logic is no longer disproved. Basically, if you arrive at a contradiction, then you've done something wrong. You can't say that logic is wrong and your results are right without yanking the rug out from underneath your own feet.
"The Collectivist experiment is thoroughly suited (in appearance at least) to the Capitalist society which it proposes to replace. It works with the existing machinery of Capitalism, talks and thinks in the existing terms of Capitalism, appeals to just those appetites which Capitalism has aroused, and ridicules as fantastic and unheard-of just those things in society the memory of which Capitalism has killed among men wherever the blight of it has spread."
- Hilaire Belloc -
RyuuKyuzo
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3/12/2013 3:30:00 PM
Posted: 3 years ago
At 3/12/2013 3:24:20 PM, Skepsikyma wrote:
The problem with attempting to disprove logic is that once you succeed you've also invalidated the argument disproving logic because said argument is based on logic, which means that logic is no longer disproved. Basically, if you arrive at a contradiction, then you've done something wrong. You can't say that logic is wrong and your results are right without yanking the rug out from underneath your own feet.

The problem I presented accounts for that. If you can logically conclude that logic is flawed, then logic must be long if we assume that logic is valid. If logic is not valid, then logic is flawed.

The point is that if we can make the system defeat itself, then we must conclude that it is flawed. Since both options = logic is flawed and there are no other options, logic must be flawed. You can say "you're just using logic to prove that logic is flawed", well, I am. That's the point. If logic says that logic is flawed, then either logic is too flawed to use (therefore flawed) or logic is valid, but onyl enough to invalidate itself (therefore flawed).
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Skepsikyma
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3/12/2013 4:16:28 PM
Posted: 3 years ago
At 3/12/2013 3:30:00 PM, RyuuKyuzo wrote:
At 3/12/2013 3:24:20 PM, Skepsikyma wrote:
The problem with attempting to disprove logic is that once you succeed you've also invalidated the argument disproving logic because said argument is based on logic, which means that logic is no longer disproved. Basically, if you arrive at a contradiction, then you've done something wrong. You can't say that logic is wrong and your results are right without yanking the rug out from underneath your own feet.

The problem I presented accounts for that. If you can logically conclude that logic is flawed, then logic must be long if we assume that logic is valid. If logic is not valid, then logic is flawed.

The point is that if we can make the system defeat itself, then we must conclude that it is flawed. Since both options = logic is flawed and there are no other options, logic must be flawed. You can say "you're just using logic to prove that logic is flawed", well, I am. That's the point. If logic says that logic is flawed, then either logic is too flawed to use (therefore flawed) or logic is valid, but onyl enough to invalidate itself (therefore flawed).

So you no longer use logic in your day to day life?

Besides, your post points out flaws in mathematics, not logic. They are not the same thing. If anything it points out flaws in the concept zero, which is to be expected. After all, zero is strictly a concept, one that doesn't exist is the real world (I cannot, in fact, have zero apples, in logical terms I believe that would be expressed as not having apples, which is a negation of having apples, a state which can be described numerically.) We describe it numerically anyway to make various calculations, like the limits which you described. And though those sort of assumptions are used in calculus all of the time the value is still undefined because we realize the limitations of the zero.
"The Collectivist experiment is thoroughly suited (in appearance at least) to the Capitalist society which it proposes to replace. It works with the existing machinery of Capitalism, talks and thinks in the existing terms of Capitalism, appeals to just those appetites which Capitalism has aroused, and ridicules as fantastic and unheard-of just those things in society the memory of which Capitalism has killed among men wherever the blight of it has spread."
- Hilaire Belloc -
Sidewalker
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3/12/2013 4:39:50 PM
Posted: 3 years ago
At 3/12/2013 2:14:38 PM, Noumena wrote:
At 3/12/2013 2:11:03 PM, RyuuKyuzo wrote:
There are also flaws to logic that further call into question its validity.

Presupposing logico-normative thought process in saying this.

What I'm saying is there's no way to get around and question logic from the "outside". We're conceptually trapped in the paradigm dude.

Well, not everybody is trapped in the logic paradigm, haven't you read the posts on DDO? Some are trapped in the completely illogical whack job paradigm.
"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
RyuuKyuzo
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3/12/2013 4:44:29 PM
Posted: 3 years ago
At 3/12/2013 4:16:28 PM, Skepsikyma wrote:
At 3/12/2013 3:30:00 PM, RyuuKyuzo wrote:
At 3/12/2013 3:24:20 PM, Skepsikyma wrote:
The problem with attempting to disprove logic is that once you succeed you've also invalidated the argument disproving logic because said argument is based on logic, which means that logic is no longer disproved. Basically, if you arrive at a contradiction, then you've done something wrong. You can't say that logic is wrong and your results are right without yanking the rug out from underneath your own feet.

The problem I presented accounts for that. If you can logically conclude that logic is flawed, then logic must be long if we assume that logic is valid. If logic is not valid, then logic is flawed.

The point is that if we can make the system defeat itself, then we must conclude that it is flawed. Since both options = logic is flawed and there are no other options, logic must be flawed. You can say "you're just using logic to prove that logic is flawed", well, I am. That's the point. If logic says that logic is flawed, then either logic is too flawed to use (therefore flawed) or logic is valid, but onyl enough to invalidate itself (therefore flawed).

So you no longer use logic in your day to day life?

Besides, your post points out flaws in mathematics, not logic. They are not the same thing. If anything it points out flaws in the concept zero, which is to be expected. After all, zero is strictly a concept, one that doesn't exist is the real world (I cannot, in fact, have zero apples, in logical terms I believe that would be expressed as not having apples, which is a negation of having apples, a state which can be described numerically.) We describe it numerically anyway to make various calculations, like the limits which you described. And though those sort of assumptions are used in calculus all of the time the value is still undefined because we realize the limitations of the zero.

In my original post, you'll see that I say we use logic because it is practical, but that doesn't mean it's the right tool for every job.

Mathematics is logic.

The solution you bring up is practical, this is where logic is valid -- but it doesn't matter if logic is valid over there so long as it's invalid over here, we still have a logical contradiction.
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RyuuKyuzo
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3/12/2013 4:45:34 PM
Posted: 3 years ago
At 3/12/2013 4:39:50 PM, Sidewalker wrote:
At 3/12/2013 2:14:38 PM, Noumena wrote:
At 3/12/2013 2:11:03 PM, RyuuKyuzo wrote:
There are also flaws to logic that further call into question its validity.

Presupposing logico-normative thought process in saying this.

What I'm saying is there's no way to get around and question logic from the "outside". We're conceptually trapped in the paradigm dude.

Well, not everybody is trapped in the logic paradigm, haven't you read the posts on DDO? Some are trapped in the completely illogical whack job paradigm.

Lol
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Skepsikyma
Posts: 8,280
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3/12/2013 5:10:04 PM
Posted: 3 years ago
At 3/12/2013 4:44:29 PM, RyuuKyuzo wrote:
At 3/12/2013 4:16:28 PM, Skepsikyma wrote:
At 3/12/2013 3:30:00 PM, RyuuKyuzo wrote:
At 3/12/2013 3:24:20 PM, Skepsikyma wrote:
The problem with attempting to disprove logic is that once you succeed you've also invalidated the argument disproving logic because said argument is based on logic, which means that logic is no longer disproved. Basically, if you arrive at a contradiction, then you've done something wrong. You can't say that logic is wrong and your results are right without yanking the rug out from underneath your own feet.

The problem I presented accounts for that. If you can logically conclude that logic is flawed, then logic must be long if we assume that logic is valid. If logic is not valid, then logic is flawed.

The point is that if we can make the system defeat itself, then we must conclude that it is flawed. Since both options = logic is flawed and there are no other options, logic must be flawed. You can say "you're just using logic to prove that logic is flawed", well, I am. That's the point. If logic says that logic is flawed, then either logic is too flawed to use (therefore flawed) or logic is valid, but onyl enough to invalidate itself (therefore flawed).

So you no longer use logic in your day to day life?

Besides, your post points out flaws in mathematics, not logic. They are not the same thing. If anything it points out flaws in the concept zero, which is to be expected. After all, zero is strictly a concept, one that doesn't exist is the real world (I cannot, in fact, have zero apples, in logical terms I believe that would be expressed as not having apples, which is a negation of having apples, a state which can be described numerically.) We describe it numerically anyway to make various calculations, like the limits which you described. And though those sort of assumptions are used in calculus all of the time the value is still undefined because we realize the limitations of the zero.

In my original post, you'll see that I say we use logic because it is practical, but that doesn't mean it's the right tool for every job.

Mathematics is logic.

The solution you bring up is practical, this is where logic is valid -- but it doesn't matter if logic is valid over there so long as it's invalid over here, we still have a logical contradiction.

Logic isn't invalid, you are using a flawed premise, the zero, and getting the flawed results, which logic would predict. This is the whole point behind Zeno's paradox: the use of the concept of zero can lead to absurd and false conclusions. But, if manipulated correctly, we can also get true conclusions that we might not otherwise have gotten. So you are right about practicality and the selective application, but you need to apply it to the premise which you are using and not the system to which you are plugging it into. Mathematics is, essentially, a symbolic tool which simplifies complex tautologies into workable forms.

If 'I' represents an object:

I I = 2
I I I = 3
...
I I I I I = 5
etc.

2+2=4
I I + I I = I I I I

2x4=8
2+2+2+2=8
I I + I I + I I + I I = I I I I I I I I

0=?

Zero is not the same as other numbers because it doesn't represent anything, so you have to apply it carefully and in ways which do not validate the laws of mathematics derived from working with other values. This has all been codified and is taught, including the dire and oft-mocked warning to 'never divide by zero', so many take it as just a quirky number. But zero is fundamentally different from other numbers, even though it is often treated like them because, in most cases, it doesn't lead to false conclusions.
"The Collectivist experiment is thoroughly suited (in appearance at least) to the Capitalist society which it proposes to replace. It works with the existing machinery of Capitalism, talks and thinks in the existing terms of Capitalism, appeals to just those appetites which Capitalism has aroused, and ridicules as fantastic and unheard-of just those things in society the memory of which Capitalism has killed among men wherever the blight of it has spread."
- Hilaire Belloc -
RyuuKyuzo
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3/12/2013 5:27:24 PM
Posted: 3 years ago
At 3/12/2013 5:10:04 PM, Skepsikyma wrote:
At 3/12/2013 4:44:29 PM, RyuuKyuzo wrote:
At 3/12/2013 4:16:28 PM, Skepsikyma wrote:
At 3/12/2013 3:30:00 PM, RyuuKyuzo wrote:
At 3/12/2013 3:24:20 PM, Skepsikyma wrote:
The problem with attempting to disprove logic is that once you succeed you've also invalidated the argument disproving logic because said argument is based on logic, which means that logic is no longer disproved. Basically, if you arrive at a contradiction, then you've done something wrong. You can't say that logic is wrong and your results are right without yanking the rug out from underneath your own feet.

The problem I presented accounts for that. If you can logically conclude that logic is flawed, then logic must be long if we assume that logic is valid. If logic is not valid, then logic is flawed.

The point is that if we can make the system defeat itself, then we must conclude that it is flawed. Since both options = logic is flawed and there are no other options, logic must be flawed. You can say "you're just using logic to prove that logic is flawed", well, I am. That's the point. If logic says that logic is flawed, then either logic is too flawed to use (therefore flawed) or logic is valid, but onyl enough to invalidate itself (therefore flawed).

So you no longer use logic in your day to day life?

Besides, your post points out flaws in mathematics, not logic. They are not the same thing. If anything it points out flaws in the concept zero, which is to be expected. After all, zero is strictly a concept, one that doesn't exist is the real world (I cannot, in fact, have zero apples, in logical terms I believe that would be expressed as not having apples, which is a negation of having apples, a state which can be described numerically.) We describe it numerically anyway to make various calculations, like the limits which you described. And though those sort of assumptions are used in calculus all of the time the value is still undefined because we realize the limitations of the zero.

In my original post, you'll see that I say we use logic because it is practical, but that doesn't mean it's the right tool for every job.

Mathematics is logic.

The solution you bring up is practical, this is where logic is valid -- but it doesn't matter if logic is valid over there so long as it's invalid over here, we still have a logical contradiction.

Logic isn't invalid, you are using a flawed premise, the zero, and getting the flawed results, which logic would predict. This is the whole point behind Zeno's paradox: the use of the concept of zero can lead to absurd and false conclusions. But, if manipulated correctly, we can also get true conclusions that we might not otherwise have gotten. So you are right about practicality and the selective application, but you need to apply it to the premise which you are using and not the system to which you are plugging it into. Mathematics is, essentially, a symbolic tool which simplifies complex tautologies into workable forms.

If 'I' represents an object:

I I = 2
I I I = 3
...
I I I I I = 5
etc.

2+2=4
I I + I I = I I I I

2x4=8
2+2+2+2=8
I I + I I + I I + I I = I I I I I I I I

0=?

Zero is not the same as other numbers because it doesn't represent anything, so you have to apply it carefully and in ways which do not validate the laws of mathematics derived from working with other values. This has all been codified and is taught, including the dire and oft-mocked warning to 'never divide by zero', so many take it as just a quirky number. But zero is fundamentally different from other numbers, even though it is often treated like them because, in most cases, it doesn't lead to false conclusions.

In other words, so long as we limit the scope of logic to practical purposes, we don't run in to logical problems.

I don't think we disagree with one another. I'm saying logic is flawed when it comes to abstract things, but it's a useful tool when applied to problems it is apt to solve.

This doesn't mean logic is not free of flaws, but it also doesn't mean it's useless.
If you're reading this, you're awesome and you should feel awesome.
Skepsikyma
Posts: 8,280
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3/12/2013 5:32:31 PM
Posted: 3 years ago
At 3/12/2013 5:27:24 PM, RyuuKyuzo wrote:
At 3/12/2013 5:10:04 PM, Skepsikyma wrote:
At 3/12/2013 4:44:29 PM, RyuuKyuzo wrote:
At 3/12/2013 4:16:28 PM, Skepsikyma wrote:
At 3/12/2013 3:30:00 PM, RyuuKyuzo wrote:
At 3/12/2013 3:24:20 PM, Skepsikyma wrote:
The problem with attempting to disprove logic is that once you succeed you've also invalidated the argument disproving logic because said argument is based on logic, which means that logic is no longer disproved. Basically, if you arrive at a contradiction, then you've done something wrong. You can't say that logic is wrong and your results are right without yanking the rug out from underneath your own feet.

The problem I presented accounts for that. If you can logically conclude that logic is flawed, then logic must be long if we assume that logic is valid. If logic is not valid, then logic is flawed.

The point is that if we can make the system defeat itself, then we must conclude that it is flawed. Since both options = logic is flawed and there are no other options, logic must be flawed. You can say "you're just using logic to prove that logic is flawed", well, I am. That's the point. If logic says that logic is flawed, then either logic is too flawed to use (therefore flawed) or logic is valid, but onyl enough to invalidate itself (therefore flawed).

So you no longer use logic in your day to day life?

Besides, your post points out flaws in mathematics, not logic. They are not the same thing. If anything it points out flaws in the concept zero, which is to be expected. After all, zero is strictly a concept, one that doesn't exist is the real world (I cannot, in fact, have zero apples, in logical terms I believe that would be expressed as not having apples, which is a negation of having apples, a state which can be described numerically.) We describe it numerically anyway to make various calculations, like the limits which you described. And though those sort of assumptions are used in calculus all of the time the value is still undefined because we realize the limitations of the zero.

In my original post, you'll see that I say we use logic because it is practical, but that doesn't mean it's the right tool for every job.

Mathematics is logic.

The solution you bring up is practical, this is where logic is valid -- but it doesn't matter if logic is valid over there so long as it's invalid over here, we still have a logical contradiction.

Logic isn't invalid, you are using a flawed premise, the zero, and getting the flawed results, which logic would predict. This is the whole point behind Zeno's paradox: the use of the concept of zero can lead to absurd and false conclusions. But, if manipulated correctly, we can also get true conclusions that we might not otherwise have gotten. So you are right about practicality and the selective application, but you need to apply it to the premise which you are using and not the system to which you are plugging it into. Mathematics is, essentially, a symbolic tool which simplifies complex tautologies into workable forms.

If 'I' represents an object:

I I = 2
I I I = 3
...
I I I I I = 5
etc.

2+2=4
I I + I I = I I I I

2x4=8
2+2+2+2=8
I I + I I + I I + I I = I I I I I I I I

0=?

Zero is not the same as other numbers because it doesn't represent anything, so you have to apply it carefully and in ways which do not validate the laws of mathematics derived from working with other values. This has all been codified and is taught, including the dire and oft-mocked warning to 'never divide by zero', so many take it as just a quirky number. But zero is fundamentally different from other numbers, even though it is often treated like them because, in most cases, it doesn't lead to false conclusions.

In other words, so long as we limit the scope of logic to practical purposes, we don't run in to logical problems.

I don't think we disagree with one another. I'm saying logic is flawed when it comes to abstract things, but it's a useful tool when applied to problems it is apt to solve.

This doesn't mean logic is not free of flaws, but it also doesn't mean it's useless.

I wouldn't say that this holds true for all abstract things, but yes, to certain abstract things it cannot be applied effectively due to aspects of the nature of said abstract thing.
"The Collectivist experiment is thoroughly suited (in appearance at least) to the Capitalist society which it proposes to replace. It works with the existing machinery of Capitalism, talks and thinks in the existing terms of Capitalism, appeals to just those appetites which Capitalism has aroused, and ridicules as fantastic and unheard-of just those things in society the memory of which Capitalism has killed among men wherever the blight of it has spread."
- Hilaire Belloc -
dylancatlow
Posts: 12,242
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3/12/2013 5:38:43 PM
Posted: 3 years ago
At 3/12/2013 5:27:24 PM, RyuuKyuzo wrote:
At 3/12/2013 5:10:04 PM, Skepsikyma wrote:
At 3/12/2013 4:44:29 PM, RyuuKyuzo wrote:
At 3/12/2013 4:16:28 PM, Skepsikyma wrote:
At 3/12/2013 3:30:00 PM, RyuuKyuzo wrote:
At 3/12/2013 3:24:20 PM, Skepsikyma wrote:
The problem with attempting to disprove logic is that once you succeed you've also invalidated the argument disproving logic because said argument is based on logic, which means that logic is no longer disproved. Basically, if you arrive at a contradiction, then you've done something wrong. You can't say that logic is wrong and your results are right without yanking the rug out from underneath your own feet.

The problem I presented accounts for that. If you can logically conclude that logic is flawed, then logic must be long if we assume that logic is valid. If logic is not valid, then logic is flawed.

The point is that if we can make the system defeat itself, then we must conclude that it is flawed. Since both options = logic is flawed and there are no other options, logic must be flawed. You can say "you're just using logic to prove that logic is flawed", well, I am. That's the point. If logic says that logic is flawed, then either logic is too flawed to use (therefore flawed) or logic is valid, but onyl enough to invalidate itself (therefore flawed).

So you no longer use logic in your day to day life?

Besides, your post points out flaws in mathematics, not logic. They are not the same thing. If anything it points out flaws in the concept zero, which is to be expected. After all, zero is strictly a concept, one that doesn't exist is the real world (I cannot, in fact, have zero apples, in logical terms I believe that would be expressed as not having apples, which is a negation of having apples, a state which can be described numerically.) We describe it numerically anyway to make various calculations, like the limits which you described. And though those sort of assumptions are used in calculus all of the time the value is still undefined because we realize the limitations of the zero.

In my original post, you'll see that I say we use logic because it is practical, but that doesn't mean it's the right tool for every job.

Mathematics is logic.

The solution you bring up is practical, this is where logic is valid -- but it doesn't matter if logic is valid over there so long as it's invalid over here, we still have a logical contradiction.

Logic isn't invalid, you are using a flawed premise, the zero, and getting the flawed results, which logic would predict. This is the whole point behind Zeno's paradox: the use of the concept of zero can lead to absurd and false conclusions. But, if manipulated correctly, we can also get true conclusions that we might not otherwise have gotten. So you are right about practicality and the selective application, but you need to apply it to the premise which you are using and not the system to which you are plugging it into. Mathematics is, essentially, a symbolic tool which simplifies complex tautologies into workable forms.

If 'I' represents an object:

I I = 2
I I I = 3
...
I I I I I = 5
etc.

2+2=4
I I + I I = I I I I

2x4=8
2+2+2+2=8
I I + I I + I I + I I = I I I I I I I I

0=?

Zero is not the same as other numbers because it doesn't represent anything, so you have to apply it carefully and in ways which do not validate the laws of mathematics derived from working with other values. This has all been codified and is taught, including the dire and oft-mocked warning to 'never divide by zero', so many take it as just a quirky number. But zero is fundamentally different from other numbers, even though it is often treated like them because, in most cases, it doesn't lead to false conclusions.

In other words, so long as we limit the scope of logic to practical purposes, we don't run in to logical problems.

I don't think we disagree with one another. I'm saying logic is flawed when it comes to abstract things, but it's a useful tool when applied to problems it is apt to solve.

This doesn't mean logic is not free of flaws, but it also doesn't mean it's useless.

The idea of logic isn't flawed, maybe the application... but logic is, by definition, correlated to reality and thus valid. Misuse of logic resulting in invalid conclusions would necessarily mean said logic was invalid, or inappropriately applied.
The_Fool_on_the_hill
Posts: 6,071
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3/12/2013 5:41:34 PM
Posted: 3 years ago
At 3/12/2013 1:56:04 PM, toolpot462 wrote:
How can one logically conclude that the use of logic is a viable means of drawing conclusions?

Here is a potential first impression attempt:

1. It is logical to use a system that has reproduceable practical applications to draw conclusions.
2. Logic has such practical applications.
C. Therefore, it is logical that one should use logic to draw conclusions.

This kind of reasoning seems flawed. The first premise assumes that one should use logic - in fact, the very use of logic assumes the conclusion.

What do you think?

The Fool: By which means are you able to tell if its flawed or not.

Foot in the mouth
"The bud disappears when the blossom breaks through, and we might say that the former is refuted by the latter; in the same way when the fruit comes, the blossom may be explained to be a false form of the plant's existence, for the fruit appears as its true nature in place of the blossom. These stages are not merely differentiated; they supplant one another as being incompatible with one another." G. W. F. HEGEL
RyuuKyuzo
Posts: 3,074
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3/12/2013 5:43:08 PM
Posted: 3 years ago
At 3/12/2013 5:38:43 PM, dylancatlow wrote:
At 3/12/2013 5:27:24 PM, RyuuKyuzo wrote:
At 3/12/2013 5:10:04 PM, Skepsikyma wrote:
At 3/12/2013 4:44:29 PM, RyuuKyuzo wrote:
At 3/12/2013 4:16:28 PM, Skepsikyma wrote:
At 3/12/2013 3:30:00 PM, RyuuKyuzo wrote:
At 3/12/2013 3:24:20 PM, Skepsikyma wrote:
The problem with attempting to disprove logic is that once you succeed you've also invalidated the argument disproving logic because said argument is based on logic, which means that logic is no longer disproved. Basically, if you arrive at a contradiction, then you've done something wrong. You can't say that logic is wrong and your results are right without yanking the rug out from underneath your own feet.

The problem I presented accounts for that. If you can logically conclude that logic is flawed, then logic must be long if we assume that logic is valid. If logic is not valid, then logic is flawed.

The point is that if we can make the system defeat itself, then we must conclude that it is flawed. Since both options = logic is flawed and there are no other options, logic must be flawed. You can say "you're just using logic to prove that logic is flawed", well, I am. That's the point. If logic says that logic is flawed, then either logic is too flawed to use (therefore flawed) or logic is valid, but onyl enough to invalidate itself (therefore flawed).

So you no longer use logic in your day to day life?

Besides, your post points out flaws in mathematics, not logic. They are not the same thing. If anything it points out flaws in the concept zero, which is to be expected. After all, zero is strictly a concept, one that doesn't exist is the real world (I cannot, in fact, have zero apples, in logical terms I believe that would be expressed as not having apples, which is a negation of having apples, a state which can be described numerically.) We describe it numerically anyway to make various calculations, like the limits which you described. And though those sort of assumptions are used in calculus all of the time the value is still undefined because we realize the limitations of the zero.

In my original post, you'll see that I say we use logic because it is practical, but that doesn't mean it's the right tool for every job.

Mathematics is logic.

The solution you bring up is practical, this is where logic is valid -- but it doesn't matter if logic is valid over there so long as it's invalid over here, we still have a logical contradiction.

Logic isn't invalid, you are using a flawed premise, the zero, and getting the flawed results, which logic would predict. This is the whole point behind Zeno's paradox: the use of the concept of zero can lead to absurd and false conclusions. But, if manipulated correctly, we can also get true conclusions that we might not otherwise have gotten. So you are right about practicality and the selective application, but you need to apply it to the premise which you are using and not the system to which you are plugging it into. Mathematics is, essentially, a symbolic tool which simplifies complex tautologies into workable forms.

If 'I' represents an object:

I I = 2
I I I = 3
...
I I I I I = 5
etc.

2+2=4
I I + I I = I I I I

2x4=8
2+2+2+2=8
I I + I I + I I + I I = I I I I I I I I

0=?

Zero is not the same as other numbers because it doesn't represent anything, so you have to apply it carefully and in ways which do not validate the laws of mathematics derived from working with other values. This has all been codified and is taught, including the dire and oft-mocked warning to 'never divide by zero', so many take it as just a quirky number. But zero is fundamentally different from other numbers, even though it is often treated like them because, in most cases, it doesn't lead to false conclusions.

In other words, so long as we limit the scope of logic to practical purposes, we don't run in to logical problems.

I don't think we disagree with one another. I'm saying logic is flawed when it comes to abstract things, but it's a useful tool when applied to problems it is apt to solve.

This doesn't mean logic is not free of flaws, but it also doesn't mean it's useless.

The idea of logic isn't flawed, maybe the application... but logic is, by definition, correlated to reality and thus valid. Misuse of logic resulting in invalid conclusions would necessarily mean said logic was invalid, or inappropriately applied.

I've provided a logical argument for why 1=0=infinity. If we apply this to reality with apples, we see that logic is invalid. If we constrain the scope of logic to practical purposes, there's no problem. The problem only exists when we travel outwards to the fringes of logic. That's all I'm saying.

When it comes to the question of "does it follow that one should use logic?", I think we can all agree the answer is "depends on what you want to use it for".
If you're reading this, you're awesome and you should feel awesome.
dylancatlow
Posts: 12,242
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3/12/2013 5:44:50 PM
Posted: 3 years ago
At 3/12/2013 5:43:08 PM, RyuuKyuzo wrote:
At 3/12/2013 5:38:43 PM, dylancatlow wrote:
At 3/12/2013 5:27:24 PM, RyuuKyuzo wrote:
At 3/12/2013 5:10:04 PM, Skepsikyma wrote:
At 3/12/2013 4:44:29 PM, RyuuKyuzo wrote:
At 3/12/2013 4:16:28 PM, Skepsikyma wrote:
At 3/12/2013 3:30:00 PM, RyuuKyuzo wrote:
At 3/12/2013 3:24:20 PM, Skepsikyma wrote:
The problem with attempting to disprove logic is that once you succeed you've also invalidated the argument disproving logic because said argument is based on logic, which means that logic is no longer disproved. Basically, if you arrive at a contradiction, then you've done something wrong. You can't say that logic is wrong and your results are right without yanking the rug out from underneath your own feet.

The problem I presented accounts for that. If you can logically conclude that logic is flawed, then logic must be long if we assume that logic is valid. If logic is not valid, then logic is flawed.

The point is that if we can make the system defeat itself, then we must conclude that it is flawed. Since both options = logic is flawed and there are no other options, logic must be flawed. You can say "you're just using logic to prove that logic is flawed", well, I am. That's the point. If logic says that logic is flawed, then either logic is too flawed to use (therefore flawed) or logic is valid, but onyl enough to invalidate itself (therefore flawed).

So you no longer use logic in your day to day life?

Besides, your post points out flaws in mathematics, not logic. They are not the same thing. If anything it points out flaws in the concept zero, which is to be expected. After all, zero is strictly a concept, one that doesn't exist is the real world (I cannot, in fact, have zero apples, in logical terms I believe that would be expressed as not having apples, which is a negation of having apples, a state which can be described numerically.) We describe it numerically anyway to make various calculations, like the limits which you described. And though those sort of assumptions are used in calculus all of the time the value is still undefined because we realize the limitations of the zero.

In my original post, you'll see that I say we use logic because it is practical, but that doesn't mean it's the right tool for every job.

Mathematics is logic.

The solution you bring up is practical, this is where logic is valid -- but it doesn't matter if logic is valid over there so long as it's invalid over here, we still have a logical contradiction.

Logic isn't invalid, you are using a flawed premise, the zero, and getting the flawed results, which logic would predict. This is the whole point behind Zeno's paradox: the use of the concept of zero can lead to absurd and false conclusions. But, if manipulated correctly, we can also get true conclusions that we might not otherwise have gotten. So you are right about practicality and the selective application, but you need to apply it to the premise which you are using and not the system to which you are plugging it into. Mathematics is, essentially, a symbolic tool which simplifies complex tautologies into workable forms.

If 'I' represents an object:

I I = 2
I I I = 3
...
I I I I I = 5
etc.

2+2=4
I I + I I = I I I I

2x4=8
2+2+2+2=8
I I + I I + I I + I I = I I I I I I I I

0=?

Zero is not the same as other numbers because it doesn't represent anything, so you have to apply it carefully and in ways which do not validate the laws of mathematics derived from working with other values. This has all been codified and is taught, including the dire and oft-mocked warning to 'never divide by zero', so many take it as just a quirky number. But zero is fundamentally different from other numbers, even though it is often treated like them because, in most cases, it doesn't lead to false conclusions.

In other words, so long as we limit the scope of logic to practical purposes, we don't run in to logical problems.

I don't think we disagree with one another. I'm saying logic is flawed when it comes to abstract things, but it's a useful tool when applied to problems it is apt to solve.

This doesn't mean logic is not free of flaws, but it also doesn't mean it's useless.

The idea of logic isn't flawed, maybe the application... but logic is, by definition, correlated to reality and thus valid. Misuse of logic resulting in invalid conclusions would necessarily mean said logic was invalid, or inappropriately applied.

I've provided a logical argument for why 1=0=infinity. If we apply this to reality with apples, we see that logic is invalid. If we constrain the scope of logic to practical purposes, there's no problem. The problem only exists when we travel outwards to the fringes of logic. That's all I'm saying.

When it comes to the question of "does it follow that one should use logic?", I think we can all agree the answer is "depends on what you want to use it for".

Truly valid logic isn't myopic. Thinking that leads to obviously false conclusion =/= valid logic.
KeytarHero
Posts: 612
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3/12/2013 7:59:40 PM
Posted: 3 years ago
At 3/12/2013 3:30:00 PM, RyuuKyuzo wrote:
At 3/12/2013 3:24:20 PM, Skepsikyma wrote:
The problem with attempting to disprove logic is that once you succeed you've also invalidated the argument disproving logic because said argument is based on logic, which means that logic is no longer disproved. Basically, if you arrive at a contradiction, then you've done something wrong. You can't say that logic is wrong and your results are right without yanking the rug out from underneath your own feet.

The problem I presented accounts for that. If you can logically conclude that logic is flawed, then logic must be long if we assume that logic is valid. If logic is not valid, then logic is flawed.

The point is that if we can make the system defeat itself, then we must conclude that it is flawed. Since both options = logic is flawed and there are no other options, logic must be flawed. You can say "you're just using logic to prove that logic is flawed", well, I am. That's the point. If logic says that logic is flawed, then either logic is too flawed to use (therefore flawed) or logic is valid, but onyl enough to invalidate itself (therefore flawed).

The argument you gave was just a bunch of nonsense. Skep is correct. We can't escape the use of logic. Claiming that we can draw reasonable conclusions without the use of logic is self-defeating, because you must use logic to draw that conclusion.

The Law of Non-Contradiction is secure. I cannot both be me and not-me at the same time, and in the same sense. When a human zygote twins, the original zygote is not now both twins, he either ceases to exist or exists as the original twin and not the other (depending on what you believe happens to a zygote once it twins).
RyuuKyuzo
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3/12/2013 8:17:05 PM
Posted: 3 years ago
At 3/12/2013 7:59:40 PM, KeytarHero wrote:
At 3/12/2013 3:30:00 PM, RyuuKyuzo wrote:
At 3/12/2013 3:24:20 PM, Skepsikyma wrote:
The problem with attempting to disprove logic is that once you succeed you've also invalidated the argument disproving logic because said argument is based on logic, which means that logic is no longer disproved. Basically, if you arrive at a contradiction, then you've done something wrong. You can't say that logic is wrong and your results are right without yanking the rug out from underneath your own feet.

The problem I presented accounts for that. If you can logically conclude that logic is flawed, then logic must be long if we assume that logic is valid. If logic is not valid, then logic is flawed.

The point is that if we can make the system defeat itself, then we must conclude that it is flawed. Since both options = logic is flawed and there are no other options, logic must be flawed. You can say "you're just using logic to prove that logic is flawed", well, I am. That's the point. If logic says that logic is flawed, then either logic is too flawed to use (therefore flawed) or logic is valid, but onyl enough to invalidate itself (therefore flawed).

The argument you gave was just a bunch of nonsense. Skep is correct. We can't escape the use of logic. Claiming that we can draw reasonable conclusions without the use of logic is self-defeating, because you must use logic to draw that conclusion.

The Law of Non-Contradiction is secure. I cannot both be me and not-me at the same time, and in the same sense. When a human zygote twins, the original zygote is not now both twins, he either ceases to exist or exists as the original twin and not the other (depending on what you believe happens to a zygote once it twins).

It's not a hard concept to understand if you approach it honestly. If you can logically show that logic has flaws, then, assuming logic is valid, it has flaws. If logic is not valid, it is not valid and therefore flawed.

Furthermore, I never said anything along the lines of "we can draw reasonable conclusions without the use of logic"... I don't think you understood my argument.
If you're reading this, you're awesome and you should feel awesome.
toolpot462
Posts: 289
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3/13/2013 1:29:21 PM
Posted: 3 years ago
At 3/12/2013 7:59:40 PM, KeytarHero wrote:
The argument you gave was just a bunch of nonsense. Skep is correct. We can't escape the use of logic. Claiming that we can draw reasonable conclusions without the use of logic is self-defeating, because you must use logic to draw that conclusion.

That you must use logic to come to a conclusion is the point. How do you know that the fundamental principles of logic are valid if you need to use logic to determine that they're valid?
I'll be the one to protect you from
Your enemies and all your demons.
I'll be the one to protect you from
A will to survive and a voice of reason.
I'll be the one to protect you from
Your enemies and your choices, son.
KeytarHero
Posts: 612
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3/15/2013 11:13:39 PM
Posted: 3 years ago
At 3/13/2013 1:29:21 PM, toolpot462 wrote:
At 3/12/2013 7:59:40 PM, KeytarHero wrote:
The argument you gave was just a bunch of nonsense. Skep is correct. We can't escape the use of logic. Claiming that we can draw reasonable conclusions without the use of logic is self-defeating, because you must use logic to draw that conclusion.

That you must use logic to come to a conclusion is the point. How do you know that the fundamental principles of logic are valid if you need to use logic to determine that they're valid?

You don't use logic to determine that they're valid, they just are valid, necessarily. You can't escape them. If you're going to try and argue against a law of logic, you must use logic to do so. Take the first principles of logic (e.g. the Law of Identity, Non-Contradiction, etc.). You must use a first principle to deny any of those first principles. You just can't escape logic; it exists necessarily.

The thing about logical arguments is that if your argument is sound, then the conclusion must be true. Take the following standard argument:

P1: All men are mortal.
P2: Socrates was a man.
C: Therefore, Socrates is mortal.

If the premises are true, then the conclusion must be true. There are flaws that can creep into your arguments, but that's not a fault of logic, it's a fault of the person making the argument. Logic has been used since the dawn of mankind. I think it's pretty safe to say that logic can be trusted.
Apeiron
Posts: 2,446
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3/16/2013 12:05:20 AM
Posted: 3 years ago
At 3/12/2013 1:56:04 PM, toolpot462 wrote:
How can one logically conclude that the use of logic is a viable means of drawing conclusions?

Here is a potential first impression attempt:

1. It is logical to use a system that has reproduceable practical applications to draw conclusions.
2. Logic has such practical applications.
C. Therefore, it is logical that one should use logic to draw conclusions.

This kind of reasoning seems flawed. The first premise assumes that one should use logic - in fact, the very use of logic assumes the conclusion.

What do you think?

Weak Foundationalism.
Apeiron
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3/16/2013 8:52:18 AM
Posted: 3 years ago
At 3/12/2013 1:56:04 PM, toolpot462 wrote:
How can one logically conclude that the use of logic is a viable means of drawing conclusions?

Here is a potential first impression attempt:

1. It is logical to use a system that has reproduceable practical applications to draw conclusions.
2. Logic has such practical applications.
C. Therefore, it is logical that one should use logic to draw conclusions.

This kind of reasoning seems flawed. The first premise assumes that one should use logic - in fact, the very use of logic assumes the conclusion.

What do you think?

You're perfectly correct, how can you support this premise 1 without using logic?

This is why I suggest weak foundationalism since ultimately we can't reason our way to reliably functioning cognitive faculties, but can only have trust in their a good functioning design for our environment.
Lizard
Posts: 53
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3/16/2013 12:26:20 PM
Posted: 3 years ago
If you use logic to prove logic, you're pretty much assuming what you're trying to prove.
toolpot462
Posts: 289
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3/16/2013 5:50:27 PM
Posted: 3 years ago
Although, it seems that in the same way one doesn't have to use language to prove that it's "valid", one shouldn't have to use logic to conclude that logic is "valid" - language works for communicating, and logic works for drawing conclusions.
I'll be the one to protect you from
Your enemies and all your demons.
I'll be the one to protect you from
A will to survive and a voice of reason.
I'll be the one to protect you from
Your enemies and your choices, son.
Apeiron
Posts: 2,446
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3/16/2013 7:15:17 PM
Posted: 3 years ago
At 3/16/2013 5:50:27 PM, toolpot462 wrote:
Although, it seems that in the same way one doesn't have to use language to prove that it's "valid", one shouldn't have to use logic to conclude that logic is "valid" - language works for communicating, and logic works for drawing conclusions.

What makes you think logic's unnecessary to conclude its validity just because it 'works' for drawing conclusions? Why take a pragmatist take on the reliability of logic?
toolpot462
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3/16/2013 9:18:08 PM
Posted: 3 years ago
At 3/16/2013 7:15:17 PM, Apeiron wrote:
At 3/16/2013 5:50:27 PM, toolpot462 wrote:
Although, it seems that in the same way one doesn't have to use language to prove that it's "valid", one shouldn't have to use logic to conclude that logic is "valid" - language works for communicating, and logic works for drawing conclusions.

What makes you think logic's unnecessary to conclude its validity just because it 'works' for drawing conclusions? Why take a pragmatist take on the reliability of logic?

The idea is that logic is concrete. The validity of logic rests on that which is self-evident (for example, A = A). That itself is not logic, it is the foundation of logic. It is hopeless to try to reinforce said foundation with the use of logic. We can see that it is true, we don't need to reason that it is any more than we need to reason that... well, honestly I can't think of anything more self-evident.

At any rate, trying to rationalize logic with the use of logic is like trying to pull yourself up by your own bootstraps.
I'll be the one to protect you from
Your enemies and all your demons.
I'll be the one to protect you from
A will to survive and a voice of reason.
I'll be the one to protect you from
Your enemies and your choices, son.
Apeiron
Posts: 2,446
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3/16/2013 10:12:56 PM
Posted: 3 years ago
At 3/16/2013 9:18:08 PM, toolpot462 wrote:
At 3/16/2013 7:15:17 PM, Apeiron wrote:
At 3/16/2013 5:50:27 PM, toolpot462 wrote:
Although, it seems that in the same way one doesn't have to use language to prove that it's "valid", one shouldn't have to use logic to conclude that logic is "valid" - language works for communicating, and logic works for drawing conclusions.

What makes you think logic's unnecessary to conclude its validity just because it 'works' for drawing conclusions? Why take a pragmatist take on the reliability of logic?

The idea is that logic is concrete. The validity of logic rests on that which is self-evident (for example, A = A). That itself is not logic, it is the foundation of logic. It is hopeless to try to reinforce said foundation with the use of logic. We can see that it is true, we don't need to reason that it is any more than we need to reason that... well, honestly I can't think of anything more self-evident.

At any rate, trying to rationalize logic with the use of logic is like trying to pull yourself up by your own bootstraps.

I agree that the laws of logic are concrete, self evident and that we can't use logic to infer its laws. But that's not my point.

Ultimately our apprehension of these laws presuppose that we have reliable cognitive faculties or properly functioning noetics. You saying that you can 'see' them as true is therefore an confessed trust of the most basic type, but it's an unidentified faith on your part with no reason whatever for thinking its unidentifiable.

I happen to think such a faith is identifiable through further experience. Nevertheless whenever a Christian is talking about faith and it's benefits in life, there are altogether three types of faith she's referring to. The first faith is that God created us with good, properly functioning cognitive faculties so that we can ultimately have knowledge of our creator. This then is a reasonable faith, since it grounds our reasoning and the laws of logic in a reliable way. At least more so than that of naturalism, where the naturalist would have to owe us an account of properly functioning noetics without a designer. This has yet to be done.

This is extra but the second faith stems from the first faith in that we have trust that our experience of God is true for the person who really experiences him. This faith also confirms scripture, morality, the external world, the ability to have knowledge of ourselves, etc.

Finally, the third faith simply trusts that God will fulfill his promises that he spoke of through his personal witness to us and in scripture. This is the common, "man on the street" usage of the term faith, but all three are a type of faith.

Ultimately everyone must have faith, it just boils down to how reliable their ground is.