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“God created logic”
Posted: 15 January 2009 05:26 AM   [ Ignore ]   [ # 31 ]
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wandering - 15 January 2009 04:17 AM

I think the chaos would be an interesting one.

How? If you allow contradiction, you are able to assert truthfully everything and its contrary. You end up saying absolutely everything, or (in a different way of looking at it) absolutely nothing.

It’s about the least interesting alternative.

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Posted: 15 January 2009 07:25 AM   [ Ignore ]   [ # 32 ]
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dougsmith - 15 January 2009 05:26 AM
wandering - 15 January 2009 04:17 AM

I think the chaos would be an interesting one.

How? If you allow contradiction, you are able to assert truthfully everything and its contrary. You end up saying absolutely everything, or (in a different way of looking at it) absolutely nothing.

It’s about the least interesting alternative.

I imagine that something like Alic in Illogicland could be written.

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Posted: 16 January 2009 12:10 PM   [ Ignore ]   [ # 33 ]
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wandering - 14 January 2009 07:17 AM

What do you think of the argument

“God created logic, so he can do illogical things. (Like preparing a breakfast too big for him to eat, and still be omniscient) “

?

What about the obvious response that logic isn’t the type of thing one can “create”? Just like one can’t “create” prime numbers.

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Posted: 12 March 2009 02:15 PM   [ Ignore ]   [ # 34 ]
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The big problem here is that people are regarding logic to, for some reason, be a set of physical, binding laws that govern the universe; instead of what it actually is, a man-made abstract concept based upon specific axioms that describe natural observations and build upon them through a system of inductive/deductive reasoning.  To say that some god created logic is a disservice to the philosophers and thinkers of earlier times that developed the basis of the formal system.


The whole ‘god created logic’ bit is one of the poorer attempts at rationalizing a creator-god whose existence goes against anything that makes sense.

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Posted: 12 March 2009 03:07 PM   [ Ignore ]   [ # 35 ]
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Mathenaut - 12 March 2009 02:15 PM

... what it actually is, a man-made abstract concept based upon specific axioms that describe natural observations and build upon them through a system of inductive/deductive reasoning.

Well, although our own logical concepts are in a sense “man made”, it’s a limited sense. It’s not as though we could have decided on some other logic, some other mathematics, and made sense of the world ... except in the vacuous sense that we could have made up some other logical or numbering system that was isomorphic to the one we actually use, but with different symbols, or the like.

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Posted: 12 March 2009 03:12 PM   [ Ignore ]   [ # 36 ]
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If observations of our world were different, then the axioms upon which the formal system was based would be different.

As for mathematics….the whole principle behind the SI system speaks against any form of mathematics being ‘universal laws’.  The natural world, the universe - it is what it is.  That we create concepts and systems to describe them does not assert that the universe is bounded by said created systems.

If your logic says one thing, and reality demonstrates another, then there is something wrong with your logic.  If the math says one thing, and reality demonstrates something else; then there is something wrong with your math.

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Posted: 12 March 2009 03:18 PM   [ Ignore ]   [ # 37 ]
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There is no possible world in which the law of noncontradiction is violated. There is no possible world in which 1 + 1 = 3.

These claims cannot be invalidated by experience.  They do not come from experiment. They are a priori.

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Posted: 12 March 2009 08:41 PM   [ Ignore ]   [ # 38 ]
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Non-contradiction is not a ‘law’ which can be ‘violated’.  You can’t even describe how you would even make a valid attempt.  That ‘law’ is simply a rationalization of an observation.  An object can’t be itself (red) and not-itself (something else: i.e. blue) at the same time - not because of some ‘universal law’ that prevents it, but because of how we would identify it.  Even if an object managed to accomplish that feat, we would identify it as something else entirely (purple).

1 + 1 =/= 3?

Where 1 + 1 = 11 and 4 + 2 = 12; that kind of statement simply demonstrates that you are not familiar with abstract algebra.

Additionally, they wouldn’t be invalidated by experience because they aren’t ‘real’.  They do not come from experience because they are made up.  They are concepts, not established boundaries to our universe.

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Posted: 13 March 2009 04:32 AM   [ Ignore ]   [ # 39 ]
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Mathenaut - 12 March 2009 08:41 PM

Non-contradiction is not a ‘law’ which can be ‘violated’.  You can’t even describe how you would even make a valid attempt.  That ‘law’ is simply a rationalization of an observation.  An object can’t be itself (red) and not-itself (something else: i.e. blue) at the same time - not because of some ‘universal law’ that prevents it, but because of how we would identify it.  Even if an object managed to accomplish that feat, we would identify it as something else entirely (purple).

Hmmm ... it sounds to me like you’re just saying the same thing I did, only you’re using different words for it. A law is, at the very least, a universal regularity, and your not being able to describe how you could even construct a valid experiment to distinguish contradiction from noncontradiction confirms my point that there is a law of noncontradiction. Noncontradiction is a universal regularity.

Mathenaut - 12 March 2009 08:41 PM

1 + 1 =/= 3?

Where 1 + 1 = 11 and 4 + 2 = 12; that kind of statement simply demonstrates that you are not familiar with abstract algebra.

Additionally, they wouldn’t be invalidated by experience because they aren’t ‘real’.  They do not come from experience because they are made up.  They are concepts, not established boundaries to our universe.

You’re changing the meanings of the terms when you make these claims. They aren’t cases where 1 + 1 doesn’t equal 3. They’re cases where either “+”, “=” or the numerals are interpreted differently.

In that sense I can say that a bachelor is a married man, or a red frog.

And they don’t come from experience. Or to put it another way, outline for me the experience that confirms that 1 + 1 = 2, and tell me how that experience could have been otherwise; tell me how the claim could be falsified. Give me the experiment you run to find that 1 + 1 = 2.

Although the numbers we use are “made up” in the sense that “3” could have looked like “4”, or the function symbolized by “+” could have been some different function, they are not “made up” in the sense that we get to decide what’s contradictory and what isn’t; or as though 1 + 1 wouldn’t still have equalled 2 had there been no humans around to notice it.

[ Edited: 13 March 2009 04:36 AM by dougsmith ]
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Posted: 13 March 2009 04:55 AM   [ Ignore ]   [ # 40 ]
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Again, what you have described with non-contradiction is not a binding, physical law (like the gas laws, for instance).  It is not a phenomena, it is not about contrasting physical properties, it is about semantics.  So no, we’re not saying the same thing with different words in that.  The world isn’t defined by logic.  Logic is defined by what we have observed in our world.  These ‘laws’ and rules of inference have little meaning outside of our concepts and our ability to communicate them.

With mathematics, I am not talking about the symbols we use to describe quantity.  I am talking about the formal system itself.  Again, it is a developed system, not a binding law.  You can’t imagine 1 + 1 not equaling 2 because you are not familiar with mathematics outside of conventional base 10, much less another system entirely.  Now, if you are saying that, regardless of any system to identify them, a number of objects would remain as they are….well, sure, that’s nice, but it is not exactly saying much, and it is a far cry from asserting mathematics as a binding law of the universe.

The only thing the formal system depends upon is consistency within itself, such is how it was and how it continues to develop.

[ Edited: 13 March 2009 04:59 AM by Mathenaut ]
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Posted: 13 March 2009 06:41 AM   [ Ignore ]   [ # 41 ]
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Mathenaut - 13 March 2009 04:55 AM

Again, what you have described with non-contradiction is not a binding, physical law (like the gas laws, for instance).  It is not a phenomena, it is not about contrasting physical properties, it is about semantics.  So no, we’re not saying the same thing with different words in that.  The world isn’t defined by logic.  Logic is defined by what we have observed in our world.  These ‘laws’ and rules of inference have little meaning outside of our concepts and our ability to communicate them.

These certainly aren’t physical laws; they are laws of logic. (Mathematical laws reducing to laws of logic and set theory). Logic is not defined by what we observe in our world. There is no observation we could possibly make, in our world or any other conceivable one, which could call them into question.

Mathenaut - 13 March 2009 04:55 AM

With mathematics, I am not talking about the symbols we use to describe quantity.  I am talking about the formal system itself.  Again, it is a developed system, not a binding law.  You can’t imagine 1 + 1 not equaling 2 because you are not familiar with mathematics outside of conventional base 10, much less another system entirely.  Now, if you are saying that, regardless of any system to identify them, a number of objects would remain as they are….well, sure, that’s nice, but it is not exactly saying much, and it is a far cry from asserting mathematics as a binding law of the universe.

The only thing the formal system depends upon is consistency within itself, such is how it was and how it continues to develop.

Right—the formal system depends on the law of noncontradiction, i.e., that it is self-consistent. When using different notation, the symbol system is given a different interpretation—that is, a different meaning. So it is a semantic trick to say that:

1 + 1 = 10

Because in base 2 that is correct. Whenever we make public claims, they come in a background context. And like it or not, the background context in public fora is typically that we are talking about base 10 notation. And we aren’t talking about strange interpretations of the addition or equivalence symbols, either.

I would not say simply that the laws of logic (and thereby the laws of mathematics, if we include set theory among the laws of logic) are “binding laws of the universe”. This could imply that there are other possible universes in which they are not binding. Instead it is that these laws bind all possible universes. Indeed, they define the limits of possibility itself.  As such, they are independent of us. Or to put it another way, we can be wrong about them, even in our most considered moments. Our considerations don’t make them so.

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Posted: 13 March 2009 11:33 AM   [ Ignore ]   [ # 42 ]
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Logic is not defined by observations?  The non-contradiction concept is exactly that.  These aren’t magical boundaries that were secretly revealed to a select few people and were spontaneously drawn in their entirety.  It started as a vague concept that took literally generations to fully develop into the formal system most commonly used and the variety of other logical systems that exist.

Why you would single out non-contradiction is puzzling.  ANY logical system is dependent upon it’s axioms, regardless of what they are.  Consistency is required for any model we have made to reliably develop upon itself.  However, you imply consistency to be more than what it is.  Again, not binding universal laws, ala physics, but ‘laws’ in the sense of the framework of the concept of logic.

Lastly, to say that a man-made concept is the defining point of all possibility across all universes (much less just our own) is….a bit much, to say the least.  I’ll just leave it at that.

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Posted: 13 March 2009 12:10 PM   [ Ignore ]   [ # 43 ]
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Mathenaut - 13 March 2009 11:33 AM

Logic is not defined by observations?  The non-contradiction concept is exactly that.  These aren’t magical boundaries that were secretly revealed to a select few people and were spontaneously drawn in their entirety.  It started as a vague concept that took literally generations to fully develop into the formal system most commonly used and the variety of other logical systems that exist.

And? So did physics, but Newton was responsible for discovering regularities, not inventing them.

The law of non-contradiction is not defined by observations, it is prior to observation. Without assuming it, no meaningful observation would be possible.

Mathenaut - 13 March 2009 11:33 AM

Lastly, to say that a man-made concept is the defining point of all possibility across all universes (much less just our own) is….a bit much, to say the least.  I’ll just leave it at that.

Exactly my point. We aren’t any more responsible for those laws than we are for the laws of physics. To say otherwise is just hubris.

NB: when I talk about the laws of physics and logic, I am assuming we are talking about the perfected ones—that is, the ones we’d assent to if given all the data. We have to keep metaphysics and epistemology distinct here—clearly any given law will be formulated given imperfect information, and hence prone to error.

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Posted: 13 March 2009 01:05 PM   [ Ignore ]   [ # 44 ]
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“The law of non-contradiction is not defined by observations, it is prior to observation. Without assuming it, no meaningful observation would be possible.”

Not only is this not necessarily true, but there were observations and explorations done long before the concept of logic arose.  I don’t see people assuming concepts that they are unaware of, nor is it necessary for meaningful observation and induction.


Additionally, again, the ‘laws’ of physics describe patterns in observed phenomena by how consistent they are, they do not define them.  Regardless of any data, our models of what we perceive(i.e. ‘laws’) may or may not hold consistent for areas and worlds unknown.  There are axioms and normative statements behind every single model and diagram, the likes of which would not hold outside of those axioms and statements.  It is ludicrous to insist that the whole of our world and worlds beyond are held by the laws we have defined, or must otherwise be held by a magical set of unknown laws that exist when ours fail to measure up.

This is a particular reason why I don’t like using misnomers like ‘laws’ and ‘absolute’.  Many interpret those to mean more than they do outside of their specific context.

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Posted: 13 March 2009 01:18 PM   [ Ignore ]   [ # 45 ]
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Mathenaut - 13 March 2009 01:05 PM

Not only is this not necessarily true, but there were observations and explorations done long before the concept of logic arose.  I don’t see people assuming concepts that they are unaware of, nor is it necessary for meaningful observation and induction.

And there were people flinging rocks at each other before anyone understood the laws of gravity. One can implicitly or tacitly make use of a concept, or an objective structure, of which one is entirely unaware.

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