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Logical Absolutes
#11
RE: Logical Absolutes
(March 21, 2021 at 7:40 pm)Angrboda Wrote:
(March 21, 2021 at 7:21 pm)polymath257 Wrote: First, there are several different 'logics'. Aristotle produced the first list of 'laws of logic', but he was rather vague about specifics and it took later thinkers to straighten out some of his mess.

Boole gave a formal that, essentially, encompassed propositional logic, but his system didn't include phrases like 'there exists' and 'for every', which are usually seen as logical connectives.

That leads to quantifier logic. But that doesn't include aspects of equality or mathematics.

Because of the attempts to provide a logical foundation to mathematics that spanned the turn of the last century, a number of different approaches to logic were investigated. For example, intuitionist logic denies the classical 'law of excluded middle', especially as it applies to infinite systems. Other systems explicitly allow certain types of contradiction, but still manage to avoid triviality.

I would claim that the statement 2+2=4 seems obvious cause the number of definitions and assumptions required to prove it are minimal. I would bet that it is far less obvious that 29*31=899 or that a number is divisible by three if and only if the sum of its decimal digits is divisible by three.

In fact, the assumptions required to prove 2+2=4 are few enough that they would NOT be enough to show that 3 and 4 are different numbers. In essence, simply having a notion of 'next' and definitions of 2,4, and + are enough.

It wasn't the triviality of proving 2 + 2 = 4, but rather that as abstracts, the numbers seem to reflect metaphysical truths, that there's something underlying them that's ontic in a way that linguistic conventions aren't.

And do the other statements I made also 'reflect metaphysical truths'?

Does it 'reflect a metaphysical truth' to say that a certain chess position allows mate in 3 moves? Because, when it comes down to it, mathematical 'truths' are in the same category as that statement.
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#12
RE: Logical Absolutes
(March 21, 2021 at 2:45 pm)Angrboda Wrote: With regard to Dillahunty and Slick, theism does provide an explanation for the origin or source of these things that naturalism currently lacks.

In what way does naturalism lack an explanation for logical absolutes? Could you expand on that?

Quote:As to things like the laws of logic being reflections of empirical facts or merely descriptive, I'd have to disagree.  The idea that 2 + 2 = 4 seems true in a way that is more than just a convention of language.

But when we say 2 + 2 = 4, we’re referencing something tangible. “1” meaning “a thing.” “2” meaning “a thing and another of that thing.” I’d argue that logical absolutes (here I mean the law of identity, non-contradiction, and excluded middle) are contingent upon the existence of some world or reality; of some thing. I think where it gets dicey is when we try to conceive of a world that operates so differently from ours that it has a different set of fundamental logical truths, and if something like that is even possible. But, asking myself if that’s possible seems  akin to asking what came “before” the big bang.
Nay_Sayer: “Nothing is impossible if you dream big enough, or in this case, nothing is impossible if you use a barrel of KY Jelly and a miniature horse.”

Wiser words were never spoken. 
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#13
RE: Logical Absolutes
(March 21, 2021 at 1:33 pm)LadyForCamus Wrote: ...regarding the logical absolutes. They’re just descriptions of what appear to be immutable facts of reality.

I think the issue is: why are the immutable facts of reality as they are? 

Obviously lots of people don't care about this question. And most likely it has no practical value in our lives, since it isn't going to change anything about how the world works or how we live our lives. You can't make money off it.

So most people ignore it with no problem. But others continue to wonder "why these immutable facts and not others." And as Polymath points out, they may not be so immutable -- different logics may be possible.

Quote: Theists go on and on about how they have “no grounding,” and therefore must be “transcendent.” 

The word "transcendent" has a few different meanings. For Kant, it means "being beyond the limits of all possible experience and knowledge." That is, we can know the laws of logic and of math, but we can't experience or know what makes them that way. Or it means something that is "above" and independent of materiality. This is not so scary -- it just means that it is a law which applies overall, non-contingently.

I think in the discussion you're referring to, it means that there's no way we can derive the laws from material conditions -- they aren't caused by matter, in the way that heat is caused by vibrating atoms. 

Quote:They’re grounded by reality itself.

They make themselves visible to us in the way material reality behaves. But does that mean they are "grounded" there? Does matter CAUSE the rules of logic? 

And of course you're using "reality" in a particular way. You'd have to show that immaterial laws, not grounded in matter, are not somehow also "reality." 

Quote:They’re merely labels we use to talk about the world in its current state, just like numbers are symbols that represent quantities of things that exist. 

Here you're going to get a lot of people who disagree with you. 

No doubt when people started using numbers, we used them for quantities of material objects. Or perhaps units of time. But the ancient Greeks and Indians made that problematic pretty early on. There are numbers which don't refer to quantities of objects. 

I'm no mathematician, but some very smart people -- e.g. Roland Penrose -- claim that numbers have an independent existence, not related to physical quantities. So maybe be careful here.

Quote:But they don’t come from anywhere. They just are.

This is what they call "brute facts" in philosophy. "Why are things this way? They just are." 

Isaac Newton changed the way science works by changing his metaphysical approach to looking at the world. Before Newton, people weren't satisfied with the "it's just that way" explanation. But Newton announced that he couldn't say what gravity is or why it acted that way, only that he could describe how it acts. And that's been how science works ever since. With lots and lots of "it just does" included. 

Galileo was less willing to do this. So for example he rejected the idea that the moon causes the tides, despite abundant evidence, because he couldn't explain how distant objects could act on each other, and he wasn't satisfied with "they just do." 

But "they just do" is not an explanation. "They do because they do." It's basically giving up, and saying that no answer can be given. But not everyone is willing to do that. Obviously a lot of people will reject any attempt to go beyond "they just do", because it can't be done through science. It's metaphysics. But if they want to work on it I don't see why that's bad.

(March 21, 2021 at 7:47 pm)polymath257 Wrote: Does it 'reflect a metaphysical truth' to say that a certain chess position allows mate in 3 moves? Because, when it comes down to it, mathematical 'truths' are in the same category as that statement.

Since the rules of chess are made by people, here you're making a case for Intelligent Design.
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#14
RE: Logical Absolutes
(March 21, 2021 at 8:13 pm)Belacqua Wrote:
(March 21, 2021 at 1:33 pm)LadyForCamus Wrote: ...regarding the logical absolutes. They’re just descriptions of what appear to be immutable facts of reality.

I think the issue is: why are the immutable facts of reality as they are? 

Obviously lots of people don't care about this question. And most likely it has no practical value in our lives, since it isn't going to change anything about how the world works or how we live our lives. You can't make money off it.

So most people ignore it with no problem.

Sure. So, if the contention is: why are these seemingly immutable facts about reality the way that they are or, “why is reality the way that it is?” then yes. I agree, the answer to that as far as we can tell is “we don’t know, and we may never know.” But, appealing to a god simply kicks the can further down the road. Why is god’s immutable nature the way that it is? The theist’s response is, “because that’s what god is.”

Quote:Theists go on and on about how they have “no grounding,” and therefore must be “transcendent.” 

Quote:I think in the discussion you're referring to, it means that there's no way we can derive the laws from material conditions -- they aren't caused by matter, in the way that heat is caused by vibrating atoms.

I could be wrong, but I disagree here. When we describe, for example, a rock as a rock and not not a rock, there needs to be something thing we’re referring to in order for that concept to be coherent, no?

Quote:They make themselves visible to us in the way material reality behaves. But does that mean they are "grounded" there? Does matter CAUSE the rules of logic?

Without a thing or things existing, there isn’t a fact of any thing to be able to know and then describe.

Quote:And of course you're using "reality" in a particular way. You'd have to show that immaterial laws, not grounded in matter, are not somehow also "reality."

Hmm. I’d say it’s the burden of someone asserting the possibility and/or existence of immaterial laws to demonstrate that.

Quote:They’re merely labels we use to talk about the world in its current state, just like numbers are symbols that represent quantities of things that exist. 

Quote:Here you're going to get a lot of people who disagree with you. 

No doubt when people started using numbers, we used them for quantities of material objects. Or perhaps units of time. But the ancient Greeks and Indians made that problematic pretty early on. There are numbers which don't refer to quantities of objects. 

I'm no mathematician, but some very smart people -- e.g. Roland Penrose -- claim that numbers have an independent existence, not related to physical quantities. So maybe be careful here.

That’s a fair objection. I’m probably oversimplifying here. I’m certainly no mathematician myself.
Quote:But they don’t come from anywhere. They just are.

Quote:This is what they call "brute facts" in philosophy. "Why are things this way? They just are."

Or, “they are, but we don’t yet know why,” which again, is not a problem that is solved by theism.
Nay_Sayer: “Nothing is impossible if you dream big enough, or in this case, nothing is impossible if you use a barrel of KY Jelly and a miniature horse.”

Wiser words were never spoken. 
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#15
RE: Logical Absolutes
(March 21, 2021 at 8:55 pm)LadyForCamus Wrote: So, if the contention is: why are these seemingly immutable facts about reality the way that they are or, “why is reality the way that it is?” then yes. I agree, the answer to that as far as we can tell is “we don’t know, and we may never know.” 

Sure, that seems reasonable. That doesn't necessarily mean that it's not an interesting question.

Quote:But, appealing to a god simply kicks the can further down the road. Why is god’s immutable nature the way that it is? The theist’s response is, “because that’s what god is.”

Well, you make it sound as if they just arbitrarily posit the existence of a god in order to answer an unanswerable question. I don't know, maybe the people in that podcast are guilty of that. But there are elaborate arguments and logical chains which lead some people to conclusions about the need for a Ground of Being, an actualization of all potentialities, which accounts for the existence of unchanging immaterial laws. 

So there's a lot to deal with before we reject their conclusions. 

Quote:[...] there needs to be something thing we’re referring to in order for that concept to be coherent, no? [...] 
Without a thing or things existing, there isn’t a fact of any thing to be able to know and then describe.

Yes, I think we're talking about how things behave in the existing world. It's hard to imagine any rules existing in a world where nothing existed, because rules are something, and therefore if there are rules there are something. 

Quote:
Quote:And of course you're using "reality" in a particular way. You'd have to show that immaterial laws, not grounded in matter, are not somehow also "reality."

Hmm. I’d say it’s the burden of someone asserting the possibility and/or existence of immaterial laws to demonstrate that.

Are the laws of logic, math, and nature not somehow part of reality? I'm pretty sure they're real. 
 
Quote:
Quote:But they don’t come from anywhere. They just are.

Quote:This is what they call "brute facts" in philosophy. "Why are things this way? They just are."

Or, “they are, but we don’t yet know why,” which again, is not a problem that is solved by theism.

That's fine -- I'm comfortable with "we don't know." 

I think you've shifted the thread topic from the existence of logical absolutes to the assertion that logical absolutes can't be solved by theism. So it's gone from a metaphysical argument about the relation of logical and mathematical rules to matter, to a more typical (for this forum) assertion that there certainly won't be an explanation that includes God. 

So that will require a whole lot more discussion about how people conceive of God, and the arguments for God as metaphysical grounding, if we want to avoid just begging the question.
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#16
RE: Logical Absolutes
(March 21, 2021 at 8:13 pm)Belacqua Wrote:
(March 21, 2021 at 1:33 pm)LadyForCamus Wrote: But they don’t come from anywhere. They just are.


This is what they call "brute facts" in philosophy. "Why are things this way? They just are." 

Isaac Newton changed the way science works by changing his metaphysical approach to looking at the world. Before Newton, people weren't satisfied with the "it's just that way" explanation. But Newton announced that he couldn't say what gravity is or why it acted that way, only that he could describe how it acts. And that's been how science works ever since. With lots and lots of "it just does" included. 

Galileo was less willing to do this. So for example he rejected the idea that the moon causes the tides, despite abundant evidence, because he couldn't explain how distant objects could act on each other, and he wasn't satisfied with "they just do." 

But "they just do" is not an explanation. "They do because they do." It's basically giving up, and saying that no answer can be given. But not everyone is willing to do that. Obviously a lot of people will reject any attempt to go beyond "they just do", because it can't be done through science. It's metaphysics. But if they want to work on it I don't see why that's bad.

I think it goes farther than that. When you answer why something happens, you are resorting to some type of *more* fundamental rules for your explanation. But that means that the *most* fundamental rules 'just are'. There can be no explanation because any explanation would have to be in terms of more fundamental rules.

And that is the role many people (rightly or wrongly) assign to logic: they see it as having some of the most fundamental rules. So to ask where the rules of logic 'come from', in that system, is to ask for something that is impossible.

Now, it may well be that logic is NOT at the 'most fundamental' level. In which case, there *would* be an explanation for logic, but maybe NOT for that more fundamental set of rules and truths.

(March 21, 2021 at 7:47 pm)polymath257 Wrote:
Quote:Does it 'reflect a metaphysical truth' to say that a certain chess position allows mate in 3 moves? Because, when it comes down to it, mathematical 'truths' are in the same category as that statement.

Since the rules of chess are made by people, here you're making a case for Intelligent Design.

And I am saying that the rules of math, just like the rules of language, are made by people to help us make sense of the world around us. So, no, I am NOT making a case for ID. i am saying that a language we made up to help us understand the world and its regularities can be used, sometimes surprisingly, to understand the world and its regularities.

Of course, this ignores the large parts of mathematics that (at least currently) don't seem to correspond to anything in the real world whatsoever.

But, even in the case of 2+2=4, the only reason we can reasonably use it is that we live in a certain temperature range and deal with objects that are often fairly solid.

But, for example, if you take 2 quarts of water and 2 quarts of alcohol, you will NOT get 4 quarts of mixture. The formal, mathematical system does not yield valid predictions in that case.

Alternatively, if you want to deal with subatomic particles and their interactions, it is quite common for, say, two protons to collide and produce many protons, many pions, and many other particles. Again, a simple 1+1=2 simply does not describe the actualities of what happens physically.

The way I see it is that mathematics is a language we have made. Some aspects of that language are useful for modeling some aspects of the world around us. Some are not. And even those aspects that are useful are not universally useful. Whether any particular piece of mathematics applies to the 'real world' is a matter of observation and testing.

Oh, and I *am* a mathematician. I have been a research mathematician for the last 35 years.

(March 21, 2021 at 9:32 pm)Belacqua Wrote: Are the laws of logic, math, and nature not somehow part of reality? I'm pretty sure they're real. 

Are the rules of English real or not? i see the rules of logic and math being similar.

The laws of nature are a bit harder. I see them more as 'our best description so far'.
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#17
RE: Logical Absolutes
(March 21, 2021 at 7:47 pm)polymath257 Wrote:
(March 21, 2021 at 7:40 pm)Angrboda Wrote: It wasn't the triviality of proving 2 + 2 = 4, but rather that as abstracts, the numbers seem to reflect metaphysical truths, that there's something underlying them that's ontic in a way that linguistic conventions aren't.

And do the other statements I made also 'reflect metaphysical truths'?

Does it 'reflect a metaphysical truth' to say that a certain chess position allows mate in 3 moves? Because, when it comes down to it, mathematical 'truths' are in the same category as that statement.

We can make a rook move like a bishop, or a queen like a pawn. Mathematical objects are not thusly mutable. 2 + 2 = 4 can only be changed by changing the entire system, but then you've just created an isomorphism.

ETA: The rules of chess which describe mating in three moves constitute a system which is entangled with the laws of logic and mathematics, so your question isn't very informative.
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#18
RE: Logical Absolutes
That we can make a rook move like a bishop probably shows a meaningful difference between whatever that is and what we're looking for with logical absolutes. We can't seem to make those things move any way that we like.
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#19
RE: Logical Absolutes
(March 21, 2021 at 9:32 pm)Belacqua Wrote:
(March 21, 2021 at 8:55 pm)LadyForCamus Wrote: So, if the contention is: why are these seemingly immutable facts about reality the way that they are or, “why is reality the way that it is?” then yes. I agree, the answer to that as far as we can tell is “we don’t know, and we may never know.” 

Sure, that seems reasonable. That doesn't necessarily mean that it's not an interesting question.

Where did I say it wasn’t?

Quote:[...] there needs to be something thing we’re referring to in order for that concept to be coherent, no? [...] 
Without a thing or things existing, there isn’t a fact of any thing to be able to know and then describe.

Quote:Yes, I think we're talking about how things behave in the existing world. It's hard to imagine any rules existing in a world where nothing existed, because rules are something, and therefore if there are rules there are something.

”Nothing existed” is logically contradictory, but that’s beside the point. I don’t know if I’m comfortable with the word “rules” here. I’d say descriptions of a world requires, first, a world; something to describe.

Quote:Are the laws of logic, math, and nature not somehow part of reality? I'm pretty sure they're real.

Yes. They refer to a material world that exists.
 
Quote:think you've shifted the thread topic from the existence of logical absolutes to the assertion that logical absolutes can't be solved by theism. So it's gone from a metaphysical argument about the relation of logical and mathematical rules to matter, to a more typical (for this forum) assertion that there certainly won't be an explanation that includes God.

I’m not shifting the thread topic at all. I’m following along with the flow of our specific dialogue. You clarified that when theists argue there is no grounding for the logical absolutes, what they mean is that we currently have no explanation for why our reality exists as it does. I conceded that fact. We don’t know. The second half of the theist claim is that their world view solves this problem, and I don’t think it does.
Nay_Sayer: “Nothing is impossible if you dream big enough, or in this case, nothing is impossible if you use a barrel of KY Jelly and a miniature horse.”

Wiser words were never spoken. 
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#20
RE: Logical Absolutes
(March 21, 2021 at 10:25 pm)LadyForCamus Wrote:
(March 21, 2021 at 9:32 pm)Belacqua Wrote: Yes, I think we're talking about how things behave in the existing world. It's hard to imagine any rules existing in a world where nothing existed, because rules are something, and therefore if there are rules there are something.

”Nothing existed” is logically contradictory, but that’s beside the point. I don’t know if I’m comfortable with the word “rules” here. I’d say descriptions of a world requires, first,  a world; to describe.

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