This thread was inspired by a comment made on another thread which suggested that using logic to justify logic was circular. My first reaction to that comment was to appeal to empiricism, but the more I thought about it the less I thought that argument applies.

In one way the typical laws of logic are axiomatic. Appealing to their axiomatic nature seems sufficient for formal systems as we simply define what constitutes a valid line of reasoning in those systems. However, we often step outside the confines of our formal system and assume that the laws of logic apply to the universe as well. We can look at the universe and say, well, empirically the universe seems to obey some logical structure. However, I think this is insufficient as the laws of logic somehow seem more fundamental than even empiricism. I think a juxtaposition with the empirical sciences may help clarify what I mean.

Our scientific laws are subject to revision if we find empirical evidence contradicting those laws. While there is certainly some truth to quantum mechanics, it may turn out that it too needs revision. I don't feel like we can make similar claims to, for example, the law of identity or the law of noncontradiction. While a rabbit in the precambrian seems highly unlikely, the simulataneous existence of an immovable object and an unstoppable force is outright impossible, and I don't feel the need for any empirical evidence to make that claim. This is what I mean by the laws of logic seeming more fundamental than even empiricism.

I know that religious folks can appeal to God as the explanation for the logical structure of the universe. Is there a secular explanation for why logic is true as well that doesn't resort to some kind of circular reasoning? Or is there no secular explanation, and my belief in the logical structure of the universe is faith and intuition based? I'm having a hard time with this, so I'd be interested in your comments.

Not glib perhaps this has some food for thought?

https://plato.stanford.edu/entries/logic-ontology/

Particularly 4.6?

Yea, I saw that page earlier. That doesn't provide a satisfactory answer for me. It raises more questions, if anything.

I think logic is empiracle at it's core. It's seems peculiar to say but I don't see any reason the laws of logic would not potentially be subject to revision. In fact QM has made many think this should be done in certain circumstances. If our universe had been fundamentally different we'd have some different laws.

https://en.m.wikipedia.org/wiki/Is_Logic_Empirical%3F

In short I agree with Quine

I know that quantum logic changes the propositional algebra some, and I understand that the precise structure of the universe's propositional algebra must be empirical at some point, but would you not say that there are certain things that can be stated without the need for empiricism? What would happen if an unstoppable force and an immovable object met? Can God create a stone so heavy he can't lift it? To me, while I grant that the precise nature of the algebra is empirical, certain things like the law of identity seem to be incontrovertible.

dargscisyhp said:

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I know that quantum logic changes the propositional algebra some, and I understand that the precise structure of the universe's propositional algebra must be empirical at some point, but would you not say that there are certain things that can be stated without the need for empiricism? What would happen if an unstoppable force and an immovable object met? Can God create a stone so heavy he can't lift it? To me, while I grant that the precise nature of the algebra is empirical, certain things like the law of identity seem to be incontrovertible.

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Instant singularity, where both objects are sucked into another dimension, and one object keeps moving and the other remains stationary.

Only halfway joking.

Isn't logic just a structure for analysis? I don't see how the structure itself can be true or false. It is just a method to reason.

Now, when we talk about logic, we often incorporate a lot of logical devices that we assume to be true that might not be. Is it possible that two states are mutually exclusive and can still exist at the same time? Ask Schroedingers cat. But, while that logical device might not be true, that Schroedingers cat really can exist, that doesn't mean that logic itself can be falsified.

BusterAg said:

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dargscisyhp said:

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I know that quantum logic changes the propositional algebra some, and I understand that the precise structure of the universe's propositional algebra must be empirical at some point, but would you not say that there are certain things that can be stated without the need for empiricism? What would happen if an unstoppable force and an immovable object met? Can God create a stone so heavy he can't lift it? To me, while I grant that the precise nature of the algebra is empirical, certain things like the law of identity seem to be incontrovertible.

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Instant singularity, where both objects are sucked into another dimension, and one object keeps moving and the other remains stationary.

Only halfway joking.

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Thanks for the comment! I think this precisely demonstrates my point. The law of noncontradiction is so sacrosanct that we are willing to postulate an entirely new dynamics involving singularities and extra dimensions just to avoid altering it.

dargscisyhp said:

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BusterAg said:

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dargscisyhp said:

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I know that quantum logic changes the propositional algebra some, and I understand that the precise structure of the universe's propositional algebra must be empirical at some point, but would you not say that there are certain things that can be stated without the need for empiricism? What would happen if an unstoppable force and an immovable object met? Can God create a stone so heavy he can't lift it? To me, while I grant that the precise nature of the algebra is empirical, certain things like the law of identity seem to be incontrovertible.

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Instant singularity, where both objects are sucked into another dimension, and one object keeps moving and the other remains stationary.

Only halfway joking.

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Thanks for the comment! I think this precisely demonstrates my point. The law of noncontradiction is so sacrosanct that we are willing to postulate an entirely new dynamics involving singularities and extra dimensions just to avoid altering it.

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You saw my other post, about Schroedingers cat, right? Physics can be weird.

Logic is empirical. That is its proof.

I'm aware that QM changes the algebra of logic some, but the point is that there are certain logical principles that are treated as incontrovertible when it comes to the universe. For the purpose of this discussion, let's say those are the law of identity, the law of the excluded middle and the law of noncontradiction. I don't think the Schrodinger's cat example violates any of those.

Doc Daneeka said:

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Logic is empirical. That is its proof.

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What observation disproves the law of identity?

dargscisyhp said:

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I know that quantum logic changes the propositional algebra some, and I understand that the precise structure of the universe's propositional algebra must be empirical at some point, but would you not say that there are certain things that can be stated without the need for empiricism? What would happen if an unstoppable force and an immovable object met? Can God create a stone so heavy he can't lift it? To me, while I grant that the precise nature of the algebra is empirical, certain things like the law of identity seem to be incontrovertible.

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I would say even that is based on us living in a universe where unstoppable force or immovable object are coherent definitions. The law of non-contradiction doesn't apply across time, but only at a single moment otherwise it can be freely violated.

The law of identity could seemingly be violated in a universe where every object or atom or what have you share two identities that coexist kind of like particle wave duality but simultaneous. The law of the excluded middle is tougher, and I think any universe where it wasn't true would be fundamentally chaotic.

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I would say even that is based on us living in a universe where unstoppable force or immovable object are coherent definitions.

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They're certainly conceivable ideas. I'm not sure they are coherent ideas in the universe. Physically, I imagine these two objects being infinite energy objects. Obviously this cannot be physically realizable. However, even if I had no conception of physics and energy, I would be able to say that these two objects at the very least could not exist simultaneously.

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The law of non-contradiction doesn't apply across time, but only at a single moment otherwise it can be freely violated.

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This does not really seem to solve the issue, though. Even if the law of noncontradiction only applies at a single moment this is still a logical principle that seems incontrovertible. That said, I don't see why a proposition couldn't be constructed about something that was temporal in nature, in which case the law of noncontradiction should hold across time as well.

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The law of identity could seemingly be violated in a universe where every object or atom or what have you share two identities that coexist kind of like particle wave duality but simultaneous.

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Not sure I understand. Isn't this already the case when a particle exists as a superposition of eigenstates, before any observation is made? If so, |psi> = |psi> is certainly a requisite law.

Careful. You're gonna end up on my side of this thinking that there's something to the whole paradox and metaphysical truth business.

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I would be able to say that these two objects at the very least could not exist simultaneously.

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And this seems intuitive in a universe where they could crash into one another (or is intuitive period as all of these are). But in a universe where such things are on trajectories such that they will never collide? I'm not sure. It's a very compelling idea. So much so that god is often considered at the mercy of the law of non-contradiction and hence cannot actually be omnipotent. And if god is at the mercy of the law of non-contradiction, can he be said to have created it? If not, who did? Interesting question for a Platonist.

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This does not really seem to solve the issue, though. Even if the law of noncontradiction only applies at a single moment this is still a logical principle that seems incontrovertible.

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And I think that's true for any of the three laws as they are so fundamental to our universe. What I'm not sure is if that seems fundamental because a universe where they aren't true is too unstable to produce life or is a universe that isn't understandable in any fashion. Without these three laws nothing is knowable. There is no knowledge, there is no truth, no falsehood. I'm not sure what a universe without knowledge and truth would look like, but I don't have a problem saying I understand empirically that knowledge is possible, that the universe doesn't appear chaotic at a fundamental level.

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Not sure I understand. Isn't this already the case when a particle exists as a superposition of eigenstates, before any observation is made? If so, |psi> = |psi> is certainly a requisite law.

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I was thinking more along the lines of a particle being actively observed in multiple states.

Thanks for your comments. I'm going to have to spend some time contemplating your argument about logic and empiricism before I have much more to add to this discussion.

I think a Platonist would merely say that God is the law of non-contradiction. Or perhaps more clearly that the law of non-contradiction is an eternal feature or working (energeia) of God.

I often ponder on what is the basis for logic in a perspective that an atheist would agree with.

The best I would be able to come up with is that, whatever line of reasoning brings about a desired result, or advances, or makes the most progress seams reasonable to me. Whatever actions brings about a win or completes a goal or furthers an agenda is most worthy of time and resources.

Take our math for example. I've read that math exists to explain natural phenomena and the outside world. To map certain patterns and trends.

During what little engineering courses I partook of during my undergrad, I starkly remember our prof mentioning the use of multivariate calculus (3 dimensional calculus) to predict the future. (ie. Given certain conditions, what is the path of a rocket launch into the outer space)


I guess one could judge the usefulness of logic, and math to judge how well it allows us to answer questions and make discoveries of the unknown.

dds08 said:

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During what little engineering courses I partook of during my undergrad, I starkly remember our prof mentioning the use of multivariate calculus (3 dimensional calculus) to predict the future. (ie. Given certain conditions, what is the path of a rocket launch into the outer space)

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Even predicting the future assumes axiomatic rules: the future will resemble the past.