Naturalism, Science and Reason

[dakoski]

This is a quote from Nagel on reasoning as the grounds for knowledge and scientific methods. He points out the challenges regarding the validity of our reasoning within a naturalistic worldview:

In ordinary perception, we are like mechanisms governed by a (roughly) truth-preserving algorithm. But when we reason, we are like a mechanism that can see that the algorithm it follows is truth-preserving. Something has happened that has gotten our minds into immediate contact with the rational order of the world, or at least with the basic elements of that order, which can in turn be used to reach a great deal more. That enables us to possess concepts that display the compatibility or incompatibility of particular beliefs with general hypotheses...

Certain things can be assumed, if there is such a thing as reason. First, there are objective, mind-independent truths of different kinds: factual truths about the natural world, including scientific laws; eternal and necessary truths of logic and mathematics….. Second, by starting from the way things initially appear to us, we can use reason collectively to achieve justified beliefs about some of those objective truths—though some of those beliefs will probably be mistaken. (Mind and Cosmos p85-86)

Points for discussion for those who hold a naturalistic worldview (but of course those who don't hold that worldview are also more than welcome to comment):
1) If Naturalism is true,

a) is logic a necessary truth? If so, why?
b) are there objective truths about the world? If so, why?

2) If Naturalism is true, can we achieve justified beliefs about some of these objective truths?

To preempt possible misunderstanding:
1)This isn't a question about the validity of logic per se (I'm assuming we agree that the laws of logic are valid) but the validity of logic conditional on the naturalist worldview being true.

2)This isn't a question about the validity of the scientific method (I'm assuming we agree that the scientific method is valid) but the validity of the scientific method conditional on the naturalist worldview being true

[Divine Insight]

I have objections to the philosophical ideas you've posted by Nagel

Certain things can be assumed, if there is such a thing as reason. First, there are objective, mind-independent truths of different kinds: factual truths about the natural world, including scientific laws; eternal and necessary truths of logic and mathematics…..

I understand that this is a very commonly accepted view, but I do not personally accept this view. I do not accept that there are mind-independent truths of "difference kinds". And especially not in the way described in the quote above.

This line of thinking already assumes a conclusion that has not been established to be true. I see no reason to create this imaginary dichotomy of "truths".

As far as I'm concerned the first recognition of truths is all that is required. In other words the laws and properties of the actual world is all that needs to exist.

The very notion that there then also exists some "other" independent truths of logic and mathematics is, IMHO, a totally unnecessary hypothesis.

In fact, I hold that we have created both of these formal was of reasoning. These are our creations. And I hold that these creations are actually based upon the observations that we have made from our observations of how the physical world behaves. Not only this, but I also hold that since our brains have evolved from the material of the universe that naturally obeys these scientific laws, it's a natural consequence that our brains would then also be naturally wired to think this way.

Finally, I hold that those who believe that it is necessary to invoke a totally "independent" set of truths for logic and mathematics have already assumed the existence of the "supernatural".

Why? Well where would these rules of logic and mathematics exist? Clearly the idea that these exist in some imagined "Platonic World" that is somehow above, beyond, or external to the natural world.

It seems to me that once we have assumed this to be the case, we have then automatically become "supernaturalists" in the very act of this unnecessary assumption.

And I hold that this assumption is indeed totally unnecessary. It's not even a useful, productive, or enlightening idea. It's simply not needed.

Having said all of the above I hope you'll understand why it's not necessary to answer the questions you've asked. There simply is no "external" logic or mathematics that needs to be accounted for. It all arises directly from the natural processes.

So nature gives rise to what we call "logic" (not the other way around).

Please note that what I have stated above is my own personal view on this topic. Clearly others will differ as the idea that logic and mathematics somehow transcend the natural world has been embraced by philosophers and mathematicians for centuries. But no longer see any value in that idea. It just don't see where that idea is justified, required, or even informative in any way.

That idea is basically already an assumption of supernaturalism.

[Kenisaw]

This is a quote from Nagel on reasoning as the grounds for knowledge and scientific methods. He points out the challenges regarding the validity of our reasoning within a naturalistic worldview:

In ordinary perception, we are like mechanisms governed by a (roughly) truth-preserving algorithm. But when we reason, we are like a mechanism that can see that the algorithm it follows is truth-preserving. Something has happened that has gotten our minds into immediate contact with the rational order of the world, or at least with the basic elements of that order, which can in turn be used to reach a great deal more. That enables us to possess concepts that display the compatibility or incompatibility of particular beliefs with general hypotheses...

Certain things can be assumed, if there is such a thing as reason. First, there are objective, mind-independent truths of different kinds: factual truths about the natural world, including scientific laws; eternal and necessary truths of logic and mathematics….. Second, by starting from the way things initially appear to us, we can use reason collectively to achieve justified beliefs about some of those objective truths—though some of those beliefs will probably be mistaken. (Mind and Cosmos p85-86)

Points for discussion for those who hold a naturalistic worldview (but of course those who don't hold that worldview are also more than welcome to comment):
1) If Naturalism is true,

a) is logic a necessary truth? If so, why?
b) are there objective truths about the world? If so, why?

2) If Naturalism is true, can we achieve justified beliefs about some of these objective truths?

To preempt possible misunderstanding:
1)This isn't a question about the validity of logic per se (I'm assuming we agree that the laws of logic are valid) but the validity of logic conditional on the naturalist worldview being true.

2)This isn't a question about the validity of the scientific method (I'm assuming we agree that the scientific method is valid) but the validity of the scientific method conditional on the naturalist worldview being true

This discussion I fear is going to get sloppy pretty quickly, given that there isn't even a consistent formal definition of logic. I myself in fact am struggling with what to say and how to say it, because we are trying to compare two things (naturalism and logic) that aren't necessarily directly related.

Logic works because animals, human or otherwise, have the ability to connect actions and sequences together that are related. To put it more crudely they recognize cause and effect, and sometimes adjust their behavior according to that new understanding. Logic doesn't just exist out in the universe as a separate thing however. It's a process of learning that living things do.

In that process specifically among humans, we have been able to identify consistencies in the universe we live in. We call these consistencies laws, or rules, and through countless attempts at experimentation we have been unable to find anything that defies these laws (like gravity). We frequently assign mathematical values to represent these rules, so that we can do computational tests and derivatives for useful purposes.

We also use the same process to determine things that are not so consistent, like the weather, and who loves us, and who is going to win a sporting event that we bet on. Logic is not a fail safe thing. It can be used inappropriately and lead to what we call bad decisions.

So I think I would state that logic is required for everything we do and think. To say logic is required for naturalism is no different than saying logic is required to drive a car, or play soccer, or function as a living vertebrate. We "logic" all the time.

I don't know that logic is a "necessary truth", because I have no idea if there is another way to go about recognizing cause and effect and learning from that. There very well may be a different way, but since we don't do it another way we can't discuss it intelligently.

Part b) is, in my opinion, unrelated to the whole logic discussion. Of course there are objective truths. There is an objective truth to whether or not the god of the Bible exist for example. Do I know what it is? No, me knowing is not required for objective truth to exist. Even if you lived in a universe with variable laws (rules that changed), there still would be objective truths. They would only be objective until a rule change however, at which point they could stay the same or a new objective truth would hold true. Same for the scientific method.

[Divine Insight]

Part b) is, in my opinion, unrelated to the whole logic discussion. Of course there are objective truths. There is an objective truth to whether or not the god of the Bible exist for example. Do I know what it is? No, me knowing is not required for objective truth to exist. Even if you lived in a universe with variable laws (rules that changed), there still would be objective truths. They would only be objective until a rule change however, at which point they could stay the same or a new objective truth would hold true. Same for the scientific method.

I take a slightly different stance on the above questions.

For one thing I think it's misguided to even talk about an "objective truth" concerning whether or not the "God of the Bible" exists. And the key to understanding this is in the very descriptive phrase "of the Bible". This already makes this question a relative question, and not an objective question. In other words, we are asking whether a God Character that is described in a specific collection of stories could actually exist.

For me, the answer to this question is very simple. No, the God described in the Bible cannot exist. And why is that? Well because the description of this God within the Bible includes self-contradictory descriptions that cannot be simultaneously true.

In fact, we might even say that this is our "Definition of Logic". Our very ideas of logic are based upon the concept of contradiction. We even say that if a contradiction can be shown to exist then we have proven that something is "logically false" via a "proof by contradiction".

So the crux of logic amounts to "p and not-p cannot be true". Everything else follows from that.

We might further observe that there is an important temporal element here as well that is implied but not always explicitly stated and this is that the actual condition is: "p and not-p cannot be simultaneously true". Obviously there is no logical contradiction if p exists at certain times (or under certain conditions) but not others.

So our logic is actually founded on the notion that contradictory objects or events cannot simultaneously be true.

This is the crux of logic, and we also believe that this is a fundamental natural property of our reality, although with the discovery of quantum mechanics this fundamental assumption has been brought into question. But then again, as a resolution to the problems of quantum mechanics multi-dimensional spaces have been hypothesized to exist. This introduction of multi-dimensional spaces allows for the existence of "p and not-p" to be simultaneously true in difference dimensions. As long as they aren't both true within a single dimension our logic is preserved.

I'm probably getting too involved with this discussing problems in physics. But the bottom line is that our concept of logic basically reduces to the observation and acceptance that "p and not-p" cannot be simultaneously true. At least not within our observable universe.

Also if "p and not-p" could be simultaneously true in our world, then our brains could not exist here and we would not have been able to formulate what we are calling "logic".

So the fact that "p and not-p" cannot be simultaneously true appears to be a property of nature, rather than an underlying rule that drives nature from some imaginary supernatural Platonic World.

Or to put this another way. There is no reason to imagine that this property of nature would need to be placed upon it by some external supernatural world. Allowing that this property is simply a property of nature is sufficient in and of itself. No need to invoke an imaginary Platonic World that basically adds nothing to the problem especially in the way of having any explanatory power.

[dakoski]

[Replying to Kenisaw]

This discussion I fear is going to get sloppy pretty quickly, given that there isn't even a consistent formal definition of logic. I myself in fact am struggling with what to say and how to say it, because we are trying to compare two things (naturalism and logic) that aren't necessarily directly related.

Fair point, I'll try and clarify. Naturalism is a worldview - i.e. its a set of assumptions about how to interpret and understand the world.

Part of examining the validity of a worldview is to look at the coherence of its assumptions. One of the potential challenges to the internal coherence of naturalism are mind independent truths. For example, if an argument contains a contradiction within it, then whether the person or a society agrees or disagrees with the principle of non-contradiction, their argument is invalid.

Either advocates of naturalism can seek to show the internal coherence of holding to mind independent truths and naturalism or to deny that mind independent truths are possible. As you see above Divine Insight has decided to deny that there are mind independent truths. From your response it appears you do think that objective truths are possible.

Logic works because animals, human or otherwise, have the ability to connect actions and sequences together that are related. To put it more crudely they recognize cause and effect, and sometimes adjust their behavior according to that new understanding. Logic doesn't just exist out in the universe as a separate thing however. It's a process of learning that living things do.

In that process specifically among humans, we have been able to identify consistencies in the universe we live in. We call these consistencies laws, or rules, and through countless attempts at experimentation we have been unable to find anything that defies these laws (like gravity). We frequently assign mathematical values to represent these rules, so that we can do computational tests and derivatives for useful purposes.

We also use the same process to determine things that are not so consistent, like the weather, and who loves us, and who is going to win a sporting event that we bet on. Logic is not a fail safe thing. It can be used inappropriately and lead to what we call bad decisions.

Are you arguing that logical principles, such as the law of non-contradiction, are social conventions that we have learnt over time through induction and testing their validity empirically?

There's a few things problematic about that view:
a) generally its agreed the laws of logic are categorised as a priori knowledge - they're not something that we learn inductively. Inductive reasoning requires the assumption of the validity of logic - i.e. such reasoning relies on these logical principles in order to be viable. So we can't affirm these 'laws' of logic inductively without circularity.

b) we can't empirically test the laws of logic either as the process of experimentation is grounded in assumptions of the objective validity of the laws of logic.

The question then becomes, if naturalism is true do we have any reason to think that such a priori logical principles that we cannot test empirically should be accepted as valid? I.e. if naturalism is true, would that lead us to doubt the validity of the scientific method (which is grounded in the assumption of the objective validity of logic)?

So I think I would state that logic is required for everything we do and think. To say logic is required for naturalism is no different than saying logic is required to drive a car, or play soccer, or function as a living vertebrate. We "logic" all the time.

I don't know that logic is a "necessary truth", because I have no idea if there is another way to go about recognizing cause and effect and learning from that. There very well may be a different way, but since we don't do it another way we can't discuss it intelligently.

Yeah I guess the use of the term 'necessary truth' isn't needed here. The main question is whether the laws of logic should be seen as mind-independent truths or social conventions. If they are social conventions then we might say the principle of non-contradiction might be true for some societies that hold these conventions and not true for others. Some have tried to argue this although in my view unconvincingly.

Part b) is, in my opinion, unrelated to the whole logic discussion. Of course there are objective truths. There is an objective truth to whether or not the god of the Bible exist for example. Do I know what it is? No, me knowing is not required for objective truth to exist. Even if you lived in a universe with variable laws (rules that changed), there still would be objective truths. They would only be objective until a rule change however, at which point they could stay the same or a new objective truth would hold true. Same for the scientific method.

I think the point of part b) is given naturalism is true can we trust our cognitive faculties to produce valid inferences about the world? Since:
i) these inferences are based on a priori principles of logic which we cannot empirically investigate or test
ii) even if the laws of logic are valid - how could we know they are valid? This assumes our cognitive faculties are capable of valid inferences - why would we assume that's the case?

So it seems to me naturalism leads to agnosticism about logic and the scientific method. And also agnosticism about all knowledge. Which I think are in contradiction with foundational principles of the scientific method: i.e. 1) the objectivity of logic as a framework for producing valid inferences about the world 2) the application of our cognitive faculties in a transparent and systematic manner - and according to the laws of logic - to understand the world

[dakoski]

I have objections to the philosophical ideas you've posted by Nagel

Certain things can be assumed, if there is such a thing as reason. First, there are objective, mind-independent truths of different kinds: factual truths about the natural world, including scientific laws; eternal and necessary truths of logic and mathematics…..

I understand that this is a very commonly accepted view, but I do not personally accept this view. I do not accept that there are mind-independent truths of "difference kinds". And especially not in the way described in the quote above.

This line of thinking already assumes a conclusion that has not been established to be true. I see no reason to create this imaginary dichotomy of "truths".

As far as I'm concerned the first recognition of truths is all that is required. In other words the laws and properties of the actual world is all that needs to exist.

The very notion that there then also exists some "other" independent truths of logic and mathematics is, IMHO, a totally unnecessary hypothesis.

I think the question then simply becomes how do you know about the laws and properties of the actual world?

The answer I think is the correct application of the laws of logic - if you are agnostic about the laws of logic you'll also be agnostic about the laws and properties of the actual world. I.e. you will be agnostic about all knowledge.

In fact, I hold that we have created both of these formal was of reasoning. These are our creations. And I hold that these creations are actually based upon the observations that we have made from our observations of how the physical world behaves. Not only this, but I also hold that since our brains have evolved from the material of the universe that naturally obeys these scientific laws, it's a natural consequence that our brains would then also be naturally wired to think this way.

I think you make two arguments here:

1) The laws of logic and reasoning are a result of our scientific observations about the world. The problem with this is that the scientific method is grounded in the assumptions of the validity of logic to draw valid inferences about the world. Observation alone does not result in valid inferences - that's why there's such an emphasis on transparency in science so that we can evaluate the logical coherency between methods and data collected and between data collected and conclusions drawn.

2) Our brains are evolved to understand the universe - therefore our inferences are valid.

Yes, of course I partly agree with you. I can see why natural selection would result in valid perceptual systems and how this would be associated with a greater chance of survival.

However, as natural selection is primarily concerned with survival rather than truth I'm at least agnostic whether we could necessarily conclude that our logical inferences are therefore true and valid - since survival and truth are not necessarily synonymous.

Finally, I hold that those who believe that it is necessary to invoke a totally "independent" set of truths for logic and mathematics have already assumed the existence of the "supernatural".

Why? Well where would these rules of logic and mathematics exist? Clearly the idea that these exist in some imagined "Platonic World" that is somehow above, beyond, or external to the natural world.

It seems to me that once we have assumed this to be the case, we have then automatically become "supernaturalists" in the very act of this unnecessary assumption.

And I hold that this assumption is indeed totally unnecessary. It's not even a useful, productive, or enlightening idea. It's simply not needed.

I agree there's debate about realist vs anti-realist views of mathematics. But I don't think its as neatly divided in the way you describe. There are plenty of atheists who take a realist view - Nagel himself is an atheist for example and many others do too. There's also no reason why a theist wouldn't take an anti-realist view.

Having said all of the above I hope you'll understand why it's not necessary to answer the questions you've asked. There simply is no "external" logic or mathematics that needs to be accounted for. It all arises directly from the natural processes.

So nature gives rise to what we call "logic" (not the other way around).

Please note that what I have stated above is my own personal view on this topic. Clearly others will differ as the idea that logic and mathematics somehow transcend the natural world has been embraced by philosophers and mathematicians for centuries. But no longer see any value in that idea. It just don't see where that idea is justified, required, or even informative in any way.

That idea is basically already an assumption of supernaturalism.

Thanks, I enjoyed your reply and thought it was a good thoughtful response.

[Divine Insight]

I think the question then simply becomes how do you know about the laws and properties of the actual world?

My answer to that is simple. Observation is how we know. We observe the actual world and take note of what we have observed. However, you need to also recognize and acknowledge that science does not just consider any "observation". Science demands that we are very careful about how we make observations and that only observations that can be dependably repeated by non-biased peers are considered valid. In fact, science has even determined that some humans imagine to see things that they obviously are not seeing, at least not physically.

The answer I think is the correct application of the laws of logic - if you are agnostic about the laws of logic you'll also be agnostic about the laws and properties of the actual world. I.e. you will be agnostic about all knowledge.

I don't claim to be "agnostic" of the laws of logic. To the contrary, I suggest that our laws of logic are created by us because of the the observations we make. So our laws of logic ultimately stem from observing the real world as well, even though it may not always be obvious that this is the case.

After all, think about it. The discovery of time dilation and the fact that time and space are actually malleable, at first seemed to be extremely "illogical" to us. Almost everyone who encounters Relativity for the first time is convinced that there is a logical flaw in the theory. But then after much observation of the situations in which time dilation must take place we eventually come to realize that Relativity is not only "logical" but it's also the way the world works.

So often times we even need to change our very concept of "logic" to fit the real world.

I think you make two arguments here:

1) The laws of logic and reasoning are a result of our scientific observations about the world. The problem with this is that the scientific method is grounded in the assumptions of the validity of logic to draw valid inferences about the world. Observation alone does not result in valid inferences - that's why there's such an emphasis on transparency in science so that we can evaluate the logical coherency between methods and data collected and between data collected and conclusions drawn.

I disagree. I think what you are doing here is mistaking "logic" with thoroughness. In fact, we even talk about "chains" of logic. If A is true, and B is true, and C is true, then it becomes clear that D is true.

Obviously this appears to be a change of "logical reasoning". But what it really amount to is a list of checking that each "observation" we are making along the way truly is a valid observation.

We can even then go further and recognize that If observation A is true, and observation B is true, and observation C is true, then it must also be true that if we set up experiment D we will indeed observe that D is also true.

This appears to be pure "logic", but all it truly amounts to is the recognition that if all our previous observations are known to be true, then we can actually predict something about what must happen when we combine these events.

This actually demonstrates that logic is nothing more than an understanding of how things already work.

2) Our brains are evolved to understand the universe - therefore our inferences are valid.

I would disagree with this idea actually and suggest that it is slightly misguided. Our brains did not evolve to understand the universe. Our brains evolved from the universe and therefore are necessarily equipped to make sense of it. It's not that they evolved to understand something that is alien to them.

Yes, of course I partly agree with you. I can see why natural selection would result in valid perceptual systems and how this would be associated with a greater chance of survival.

However, as natural selection is primarily concerned with survival rather than truth I'm at least agnostic whether we could necessarily conclude that our logical inferences are therefore true and valid - since survival and truth are not necessarily synonymous.

I would disagree with your proposal above. Survival is dependent on getting things right. So if natural selection is based on survival (which is necessarily must be), then this automatically makes natural selection favor truth. So I would argue that truth and survival are necessarily synonymous.

I agree there's debate about realist vs anti-realist views of mathematics. But I don't think its as neatly divided in the way you describe. There are plenty of atheists who take a realist view - Nagel himself is an atheist for example and many others do too. There's also no reason why a theist wouldn't take an anti-realist view.

I don't recall making any attempt to defend the beliefs of atheists in general.

I simply point out what I believe to be obvious.

1. There simply is no need to invoke the idea of a mystical magical Platonic World of supernatural laws of logic or mathematics. I hold that this idea is simply unnecessary.

2. Even if we do invoke such an idea, where does it lead? What can we conclude from this imaginary supernatural world of pure thought? Obviously we cannot conclude anything. It adds nothing. It's really no different from imagining the existence of a God. It's simply a superfluous idea that adds nothing. It can neither be proven to be true or false. And it adds nothing. There is nothing we can point to in this imagined Platonic World that explains something that we could not otherwise explain.

So of what value is it?

I also suggest that the very moment we take that "Leap of Faith" into the existence of a supernatural realm that we cannot prove, disprove, or even find useful we have already become supporters of super-naturalism, and for no good reason.

So I don't even see the point in going down that road.

If you could prove the existence of a Platonic World of pure logic and mathematics, then we could have a meaningful conversation.

I hold that such an imaginary world cannot be proven to exist, and I go even further than this and suggest that we can't even show any reason why it would be necessary.

In fact, before we continue further on this specific subject I would ask you to illustrate to me even one example where this idea could be used to provide us some truth or information that we couldn't otherwise know?

If we can't do that, then why are we even proposing it?

And if we can do that, then we would have very strong evidence that a Platonic World of logic and mathematics must then exist.

So I look forward to your evidence for it.

[Kenisaw]

[Replying to Kenisaw]

This discussion I fear is going to get sloppy pretty quickly, given that there isn't even a consistent formal definition of logic. I myself in fact am struggling with what to say and how to say it, because we are trying to compare two things (naturalism and logic) that aren't necessarily directly related.

Fair point, I'll try and clarify. Naturalism is a worldview - i.e. its a set of assumptions about how to interpret and understand the world.

Actually I'd disagree right there. Naturalism is not a set of assumptions. Naturalism is based on empirical data and evidence. I know, technically we have axioms that are a part of the foundation of knowledge, and those are "assumptions" in that they cannot be independently verified although there is no reason to doubt them. But outside of axioms I don't see where naturalism assumes anything. The reason there is no supernatural component to a naturalism is because there is zero evidence and data for such a thing. It's not assumed it doesn't exist, it's not considered because of the lack of proof for it.

Part of examining the validity of a worldview is to look at the coherence of its assumptions. One of the potential challenges to the internal coherence of naturalism are mind independent truths. For example, if an argument contains a contradiction within it, then whether the person or a society agrees or disagrees with the principle of non-contradiction, their argument is invalid.

Makes general sense. I've no comment to this at the moment.

Either advocates of naturalism can seek to show the internal coherence of holding to mind independent truths and naturalism or to deny that mind independent truths are possible. As you see above Divine Insight has decided to deny that there are mind independent truths. From your response it appears you do think that objective truths are possible.

I think something can true whether or not it can be proven to be true. I don't want to get in to the uncertainty principle here, or Schrödinger's Cat (quantum superposition). Some people have hypothesized that the universe doesn't exist unless something is around to observe it, but that topic is more a thought experiment and I don't get into it much.

Logic works because animals, human or otherwise, have the ability to connect actions and sequences together that are related. To put it more crudely they recognize cause and effect, and sometimes adjust their behavior according to that new understanding. Logic doesn't just exist out in the universe as a separate thing however. It's a process of learning that living things do.

In that process specifically among humans, we have been able to identify consistencies in the universe we live in. We call these consistencies laws, or rules, and through countless attempts at experimentation we have been unable to find anything that defies these laws (like gravity). We frequently assign mathematical values to represent these rules, so that we can do computational tests and derivatives for useful purposes.

We also use the same process to determine things that are not so consistent, like the weather, and who loves us, and who is going to win a sporting event that we bet on. Logic is not a fail safe thing. It can be used inappropriately and lead to what we call bad decisions.

Are you arguing that logical principles, such as the law of non-contradiction, are social conventions that we have learnt over time through induction and testing their validity empirically?

No. I was attempting to explain that logic is how animals learn, and that logic does not guarantee success or accuracy in that learning.

There's a few things problematic about that view:
a) generally its agreed the laws of logic are categorised as a priori knowledge - they're not something that we learn inductively. Inductive reasoning requires the assumption of the validity of logic - i.e. such reasoning relies on these logical principles in order to be viable. So we can't affirm these 'laws' of logic inductively without circularity.

b) we can't empirically test the laws of logic either as the process of experimentation is grounded in assumptions of the objective validity of the laws of logic.

The question then becomes, if naturalism is true do we have any reason to think that such a priori logical principles that we cannot test empirically should be accepted as valid? I.e. if naturalism is true, would that lead us to doubt the validity of the scientific method (which is grounded in the assumption of the objective validity of logic)?

Since that wasn't the point I was making, I've left a) and b) alone for the time being. To answer the question in your last paragraph, I don't agree that axioms are not tested. Axioms are self-evidence truths, kind of the basic knowledge that acts as a starting point, right? If the work done via the scientific method, which seems to align itself with naturalism since no evidence can be found for the supernatural (that I am aware of anyway), is accurate and dependable, isn't that an indirect proof of the axiom? I realize it is not a direct proof, yet what reason would there be to "doubt the validity" of axioms if work built on them is verifiable and validated?

So I think I would state that logic is required for everything we do and think. To say logic is required for naturalism is no different than saying logic is required to drive a car, or play soccer, or function as a living vertebrate. We "logic" all the time.

I don't know that logic is a "necessary truth", because I have no idea if there is another way to go about recognizing cause and effect and learning from that. There very well may be a different way, but since we don't do it another way we can't discuss it intelligently.

Yeah I guess the use of the term 'necessary truth' isn't needed here. The main question is whether the laws of logic should be seen as mind-independent truths or social conventions. If they are social conventions then we might say the principle of non-contradiction might be true for some societies that hold these conventions and not true for others. Some have tried to argue this although in my view unconvincingly.

I don't think they are either. I think logic is the process of recognition that animals use to understand the world. They aren't mind independent since it takes a mind to use the logic, and I don't think it is a learned behavior but rather the behavior that is used in order to learn. (I hope I've explained that in an understandable way).

Part b) is, in my opinion, unrelated to the whole logic discussion. Of course there are objective truths. There is an objective truth to whether or not the god of the Bible exist for example. Do I know what it is? No, me knowing is not required for objective truth to exist. Even if you lived in a universe with variable laws (rules that changed), there still would be objective truths. They would only be objective until a rule change however, at which point they could stay the same or a new objective truth would hold true. Same for the scientific method.

I think the point of part b) is given naturalism is true can we trust our cognitive faculties to produce valid inferences about the world? Since:
i) these inferences are based on a priori principles of logic which we cannot empirically investigate or test
ii) even if the laws of logic are valid - how could we know they are valid? This assumes our cognitive faculties are capable of valid inferences - why would we assume that's the case?

So it seems to me naturalism leads to agnosticism about logic and the scientific method. And also agnosticism about all knowledge. Which I think are in contradiction with foundational principles of the scientific method: i.e. 1) the objectivity of logic as a framework for producing valid inferences about the world 2) the application of our cognitive faculties in a transparent and systematic manner - and according to the laws of logic - to understand the world

I think we can trust our cognitive abilities because we can (and have) verified the work of others time and again. I can't see how that is possible if the axioms used were fundamentally flawed.

[Kenisaw]

Part b) is, in my opinion, unrelated to the whole logic discussion. Of course there are objective truths. There is an objective truth to whether or not the god of the Bible exist for example. Do I know what it is? No, me knowing is not required for objective truth to exist. Even if you lived in a universe with variable laws (rules that changed), there still would be objective truths. They would only be objective until a rule change however, at which point they could stay the same or a new objective truth would hold true. Same for the scientific method.

I take a slightly different stance on the above questions.

For one thing I think it's misguided to even talk about an "objective truth" concerning whether or not the "God of the Bible" exists. And the key to understanding this is in the very descriptive phrase "of the Bible". This already makes this question a relative question, and not an objective question. In other words, we are asking whether a God Character that is described in a specific collection of stories could actually exist.

For me, the answer to this question is very simple. No, the God described in the Bible cannot exist. And why is that? Well because the description of this God within the Bible includes self-contradictory descriptions that cannot be simultaneously true.

In fact, we might even say that this is our "Definition of Logic". Our very ideas of logic are based upon the concept of contradiction. We even say that if a contradiction can be shown to exist then we have proven that something is "logically false" via a "proof by contradiction".

So the crux of logic amounts to "p and not-p cannot be true". Everything else follows from that.

We might further observe that there is an important temporal element here as well that is implied but not always explicitly stated and this is that the actual condition is: "p and not-p cannot be simultaneously true". Obviously there is no logical contradiction if p exists at certain times (or under certain conditions) but not others.

So our logic is actually founded on the notion that contradictory objects or events cannot simultaneously be true.

This is the crux of logic, and we also believe that this is a fundamental natural property of our reality, although with the discovery of quantum mechanics this fundamental assumption has been brought into question. But then again, as a resolution to the problems of quantum mechanics multi-dimensional spaces have been hypothesized to exist. This introduction of multi-dimensional spaces allows for the existence of "p and not-p" to be simultaneously true in difference dimensions. As long as they aren't both true within a single dimension our logic is preserved.

I'm probably getting too involved with this discussing problems in physics. But the bottom line is that our concept of logic basically reduces to the observation and acceptance that "p and not-p" cannot be simultaneously true. At least not within our observable universe.

Also if "p and not-p" could be simultaneously true in our world, then our brains could not exist here and we would not have been able to formulate what we are calling "logic".

So the fact that "p and not-p" cannot be simultaneously true appears to be a property of nature, rather than an underlying rule that drives nature from some imaginary supernatural Platonic World.

Or to put this another way. There is no reason to imagine that this property of nature would need to be placed upon it by some external supernatural world. Allowing that this property is simply a property of nature is sufficient in and of itself. No need to invoke an imaginary Platonic World that basically adds nothing to the problem especially in the way of having any explanatory power.

I understood the physics just fine, and I think your explanation was well written. I don't disagree with you in any meaningful way. In fact the Bible example was a poor one, because I too don't think the Bible god as stated can possibly exist.

The uncertainty principle and fuzzy logic really do put into question the validity of non-contradiction, at least at that level. I'm gonna go pet and not pet Schrödinger's cat now...

[Divine Insight]

The uncertainty principle and fuzzy logic really do put into question the validity of non-contradiction, at least at that level. I'm gonna go pet and not pet Schrödinger's cat now...

I totally agree. In fact, our notion of "logic" is indeed based upon our observations of what we now call the "Macro World". And because of this our notion of logic (including P and not-p must always be false) may ultimately not even apply to the ultimate nature of reality.

There is also another element of "simultaneity and time" that we take for granted in our "Macro World" that may not apply to the ultimate nature of reality. After all, our very concept of time is based on entropy and on Relativity where time is actually property of spatial separation. Therefore our ideas of "logic" are based on a concept of "entropic time" (i.e. a unidirectional time that moves from past to future). But that too may be a property of the macro physical universe and not hold true in any underlying ultimate nature of reality.

So "logic", as we understand, it may not even apply to the ultimate nature of reality at all.