> "“I can just grasp its truth by thinking.” But if that’s true of any non-natural fact, then NR must be true!"
How does that follow? I think we can grasp truths just by thinking. But I don't think that our grasping truths involves non-natural causes shifting atoms around in our brains. Rather, I think that grasping truths is an epiphenomenal process: there are neural underpinnings that (together with the psychophysical bridging laws) give rise to our conscious understanding or "grasp" of various abstract or otherwise non-physical truths. To count as knowledge, the connection has to be non-chancy in the right kind of way. But (as I argue in Knowing What Matters) beliefs can be reliable/non-chancy in this way without needing to be literally caused by their truth-makers. A kind of structural isomorphism to mathematical facts can reliably yield mathematical knowledge, for example, without needing the numbers themselves to do the causal work. It's neither magical nor mysterious that computers can reliably do arithmetic, after all. We're different in that when our brains do arithmetic, it produces in us some *conscious understanding* of the mathematics that is (presumably) missing in computers. But I don't see any basis for thinking that introspection on this process reveals non-mechanistic causes operating on our brains.
Surely it's not the merely possible world itself that changes atoms, but rather the psychological projection of that possible world (which is itself a movement of physical particles) that changes atoms. In the same way that my thinking about Gandalf can influence my behavior, although the non-existent Gandalf himself can't influence my behavior.
Re: 1, anyone inclined to accept a more physicalistic view of the mind probably wouldn’t be too impressed by this sort of introspective evidence. You wouldn’t necessarily expect a physical system to have the kind of complete, infallible introspective access the argument seems to assume.
Re: 4, I’ve never understood why we’re supposed to assume that human mathematical cognition is complete in the way Gödel showed no consistent formal system can be.
I've come across a paper called 'Grasping the third realm's written by John Bengson that I think you'll find interesting. I'm still trying to wrap my head around it, but he offers an account of how we can come to know things like non-natural facts just by thinking. He puts forward a constitution model.
> "Many suppose, for example, that to generate knowledge, a belief-forming process has to be safe, such that the one who affirms it would believe the truth in nearby possible worlds, or sensitive, in that it has to be dependent on the truth of the proposition. But both of these are undermined by denial of NR."
This isn't right. Any belief in a necessary truth is maximally "safe", no matter its cause. There is no possible world at all (let alone nearby one) in which one holds *that* belief falsely.
Perhaps you're thinking of assessing a coarse-grained process like "believing what seems intuitive" rather than specific beliefs (or any more fine-grained characterization of the process that builds in something about its substantive starting points). But then I think it's that coarse-grained approach, not the rejection of NR, that is really responsible for the skeptical results. At any rate, one certainly should not combine epiphenomenalism with such a coarse-grained epistemology.
> "“I can just grasp its truth by thinking.” But if that’s true of any non-natural fact, then NR must be true!"
How does that follow? I think we can grasp truths just by thinking. But I don't think that our grasping truths involves non-natural causes shifting atoms around in our brains. Rather, I think that grasping truths is an epiphenomenal process: there are neural underpinnings that (together with the psychophysical bridging laws) give rise to our conscious understanding or "grasp" of various abstract or otherwise non-physical truths. To count as knowledge, the connection has to be non-chancy in the right kind of way. But (as I argue in Knowing What Matters) beliefs can be reliable/non-chancy in this way without needing to be literally caused by their truth-makers. A kind of structural isomorphism to mathematical facts can reliably yield mathematical knowledge, for example, without needing the numbers themselves to do the causal work. It's neither magical nor mysterious that computers can reliably do arithmetic, after all. We're different in that when our brains do arithmetic, it produces in us some *conscious understanding* of the mathematics that is (presumably) missing in computers. But I don't see any basis for thinking that introspection on this process reveals non-mechanistic causes operating on our brains.
Surely it's not the merely possible world itself that changes atoms, but rather the psychological projection of that possible world (which is itself a movement of physical particles) that changes atoms. In the same way that my thinking about Gandalf can influence my behavior, although the non-existent Gandalf himself can't influence my behavior.
Re: 1, anyone inclined to accept a more physicalistic view of the mind probably wouldn’t be too impressed by this sort of introspective evidence. You wouldn’t necessarily expect a physical system to have the kind of complete, infallible introspective access the argument seems to assume.
Re: 4, I’ve never understood why we’re supposed to assume that human mathematical cognition is complete in the way Gödel showed no consistent formal system can be.
I've come across a paper called 'Grasping the third realm's written by John Bengson that I think you'll find interesting. I'm still trying to wrap my head around it, but he offers an account of how we can come to know things like non-natural facts just by thinking. He puts forward a constitution model.
> "Many suppose, for example, that to generate knowledge, a belief-forming process has to be safe, such that the one who affirms it would believe the truth in nearby possible worlds, or sensitive, in that it has to be dependent on the truth of the proposition. But both of these are undermined by denial of NR."
This isn't right. Any belief in a necessary truth is maximally "safe", no matter its cause. There is no possible world at all (let alone nearby one) in which one holds *that* belief falsely.
Perhaps you're thinking of assessing a coarse-grained process like "believing what seems intuitive" rather than specific beliefs (or any more fine-grained characterization of the process that builds in something about its substantive starting points). But then I think it's that coarse-grained approach, not the rejection of NR, that is really responsible for the skeptical results. At any rate, one certainly should not combine epiphenomenalism with such a coarse-grained epistemology.