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The solution to induction
 Posted: 27 June 2011 06:19 PM [ Ignore ]   [ # 31 ]
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You mean “I think, therefore I am”? How is it inductive?

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 Posted: 27 June 2011 06:55 PM [ Ignore ]   [ # 32 ]
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Stormy Fairweather - 27 June 2011 01:23 AM

That is what my suppostition is; human reason is the proper use of both induction and deduction in harmony.

Each validates the other.

Your example is deductive, but is built from induction.

Watch how you are using the word “validate.”  A deductive argument can be valid even though the premises are false.  It does not need induction to be valid.

Example:
If the moon is made of cheese, then pigs have wings.
The moon is made of cheese.
Therefore pigs have wings.

This deductive argument is valid but not “sound.”  In order for a deductive argument to be “SOUND” it must be valid AND have all true premises.  If all the premises in a valid deductive argument are true then the conclusion must be true.  In an inductive argument true premises don’t guarantee a true conclusion all the time.  It’s possible to have exceptions.

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 Posted: 27 June 2011 07:59 PM [ Ignore ]   [ # 33 ]
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brightfut - 27 June 2011 06:55 PM
Stormy Fairweather - 27 June 2011 01:23 AM

That is what my suppostition is; human reason is the proper use of both induction and deduction in harmony.

Each validates the other.

Your example is deductive, but is built from induction.

Watch how you are using the word “validate.”  A deductive argument can be valid even though the premises are false.  It does not need induction to be valid.

Example:
If the moon is made of cheese, then pigs have wings.
The moon is made of cheese.
Therefore pigs have wings.

This deductive argument is valid but not “sound.”  In order for a deductive argument to be “SOUND” it must be valid AND have all true premises.  If all the premises in a valid deductive argument are true then the conclusion must be true.  In an inductive argument true premises don’t guarantee a true conclusion all the time.  It’s possible to have exceptions.

Questions:
Is an original premise always inductive?
If so how can you prove it is true?
If you cannot prove it true, can a deduction from the premise be relied on to be true?

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 Posted: 28 June 2011 03:59 AM [ Ignore ]   [ # 34 ]
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Write4U - 27 June 2011 07:59 PM

Is an original premise always inductive?

No.

(1) All even numbers are divisible by two
(2) 43,876,120 is an even number

——————
(3) 43,876,120 is divisible by two

None of these premises are “inductive” in the sense of being known true by induction.

Write4U - 27 June 2011 07:59 PM

If so how can you prove it is true?

By another non-inductive argument, presumably. Or it may be true on its face. (It may not need arguing, like the claim “all bachelors are unmarried”).

Write4U - 27 June 2011 07:59 PM

If you cannot prove it true, can a deduction from the premise be relied on to be true?

Depends what you mean by “prove” and “rely”. Any argument is only as good as its weakest premise. But virtually all arguments we accept are less than perfect. We could always be dreaming, as Descartes said. E.g., take the argument:

(1) If it’s raining I should take my umbrella
(2) It’s raining

—————————-
(3) I should take my umbrella

How do I know (2)? By looking out the window. That’s about as good an evidence as I could ever have! But what if I’ve been dreaming, or hallucinating? Visual corroboration may be very good evidence but it is not perfect.

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 Posted: 28 June 2011 05:03 AM [ Ignore ]   [ # 35 ]
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I suppose, domo, I should have used ‘verify’ instead of ‘valdate’ considering the specific usage of the term in philsophical discussions.

As for doug’s example (apparantly I no longer worth speaking to, so I will simply reference the man), any abstract concept, such as numbers, depends on one’s understanding of that concept. It depends on one’s peception. So if you start tracing the premise backwards, how does one know what even is? How do you identify 43,876,120? You realize it is just as ‘sound’ as looking out the window to verify it is raining. A very strong indication it is true, but no guarantee.

Human knowledge is dependant on human perception.
Human perception may be false.
Therefore;
Any human conclusion may be false.

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 Posted: 28 June 2011 09:56 AM [ Ignore ]   [ # 36 ]
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Stormy Fairweather - 28 June 2011 05:03 AM

So if you start tracing the premise backwards, how does one know what even is? How do you identify 43,876,120?

Axiomatically, i.e. by definition. Not by induction.

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 Posted: 28 June 2011 01:00 PM [ Ignore ]   [ # 37 ]
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Write4U - 27 June 2011 07:59 PM

If you cannot prove it true, can a deduction from the premise be relied on to be true?

If a deductive argument is valid then at least the deductive part of the reasoning can be relied on to be truth preserving.  What comes out of the deduction will be at least as true as the premises put into the deduction.  The deductive part of a claim can be tested for validity without even knowing what the premises are.  The form of the argument has to be closely examined.  This is a triumph of abstracting by the human mind.

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 Posted: 28 June 2011 02:05 PM [ Ignore ]   [ # 38 ]
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It is one of the strangest side effects of logic. The logic can be flawless and perfectly valid. But if based on a false premise, it is absolutely useless, except as a mental excercise.
I guess this where reason becomes important, aside from verifiable (falsifiable) premises.

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 Posted: 28 June 2011 03:31 PM [ Ignore ]   [ # 39 ]
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dougsmith - 28 June 2011 03:59 AM

(1) All even numbers are divisible by two

I know that all even numbers are divisible by two, but how do we know that all even numbers are divisible by two?  I mean, what is this mathematical reasoning called?

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 Posted: 28 June 2011 03:56 PM [ Ignore ]   [ # 40 ]
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This is way over my head, but…

As I understand infinity, it is always the largest number + 1.

Thus infinity must be alternately odd and even. Does that mean it is only alternatively divisible by two ?

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 Posted: 28 June 2011 04:51 PM [ Ignore ]   [ # 41 ]
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Write4U - 28 June 2011 02:05 PM

It is one of the strangest side effects of logic. The logic can be flawless and perfectly valid. But if based on a false premise, it is absolutely useless, except as a mental exercise.

Another way to look at it is that a person could be totally convinced that the premises are true due to undeniably good observations and yet if the person used faulty deduction or faulty reasoning then that conclusion is also absolutely useless.

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 Posted: 28 June 2011 07:28 PM [ Ignore ]   [ # 42 ]
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brightfut - 28 June 2011 03:31 PM
dougsmith - 28 June 2011 03:59 AM

(1) All even numbers are divisible by two

I know that all even numbers are divisible by two, but how do we know that all even numbers are divisible by two?  I mean, what is this mathematical reasoning called?

I’m not sure what you mean. The reasoning is called a proof. You could also give a similar proof by reductio by assuming the contrary and proving a contradiction.

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 Posted: 28 June 2011 07:30 PM [ Ignore ]   [ # 43 ]
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Write4U - 28 June 2011 03:56 PM

As I understand infinity, it is always the largest number + 1.

False, and indeed completely mathematically senseless. (There is no such thing as “the largest number”, and if there were, you couldn’t add one to it). “Infinity” is not a number at all, and indeed there are an infinite range of orders of infinity, of provably different sizes.

[ Edited: 28 June 2011 07:35 PM by dougsmith ]
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 Posted: 28 June 2011 08:29 PM [ Ignore ]   [ # 44 ]
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dougsmith - 28 June 2011 07:30 PM
Write4U - 28 June 2011 03:56 PM

As I understand infinity, it is always the largest number + 1.

False, and indeed completely mathematically senseless. (There is no such thing as “the largest number”, and if there were, you couldn’t add one to it). “Infinity” is not a number at all, and indeed there are an infinite range of orders of infinity, of provably different sizes.

I was thinking of Hilbert’s Hotel with infinite number of rooms and an infinite number of guests, yet he is always able to accommodate one more guest, merely by moving each guest into the next room. Thus the hotel can always accommodate an infinite +1 number of guests

Thus my musing if that would not translate into an alternating infinite number of even numbered and odd numbered rooms, by accommodating 1 more arriving guest.

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 Posted: 29 June 2011 03:57 AM [ Ignore ]   [ # 45 ]
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Write4U - 28 June 2011 08:29 PM

I was thinking of Hilbert’s Hotel with infinite number of rooms and an infinite number of guests, yet he is always able to accommodate one more guest, merely by moving each guest into the next room. Thus the hotel can always accommodate an infinite +1 number of guests

Thus my musing if that would not translate into an alternating infinite number of even numbered and odd numbered rooms, by accommodating 1 more arriving guest.

“Infinite +1” is provably equal to infinity. That is, it’s of provably the same size. “Infinite +1” is not a meaningful number. Indeed, that was precisely the point of Hilbert’s proof: an infinitely large hotel can accommodate any finite number of additional guests (or even a countably infinite number of guests) without expanding the hotel. That is to say, a countable infinity plus a finite number equals a countable infinity. And a countable infinity plus another countable infinity equals a countable infinity.

For more on this see the Wiki on Hilbert’s ‘paradox’ (which isn’t a real paradox in the logical sense).

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