No fair! I’m the one arguing . . .

I try to keep you nimble.

In truth, my objection isn’t to metaphysical claims per se, it is to those vast swathes of metaphysical claims that are vacuuous hand waving.

It seems to me even basic logic (nevermind something like modal logic) is predicated on metaphysical presumptions; after all, even the principle of noncontradiction implies something nontrivial about the nature of being: “nothing can be and not be at the same time in the same respect” is both the foundation of all rational thought and a statement about what it is to be.

Maybe I should petition to reclaim my Thomist card, perhaps on a probationary basis.

I’ve looked over this, and–while I realize you are being lighthearted–I take there to be some substance to your critique below the levity; yet I’m not sure what inconsistencies you have in mind.

Concerning my attitude to metaphysics: I am hostile in the sense that I view with profound skepticism the the vast majority of metaphysical arguments that are passed off (including a good number of the arguments Aquinas made). A lot of metaphysical arguments are facile, and even those that are not are still sufficiently obscure that I have little confidence they are sound. It isn’t a principled objection to all metaphysical truth; it is rather that the set of metaphysical assertions (and by consequence, also metaphysical arguments) I’m inclined to accept with any confidence is exceptionally modest.

With respect to contradictions: What I meant to say (though unclearly) is that I am deeply committed to the principle of non-contradiction. If there is compelling and clear evidence that two assertions that appear to contradict (or at least to lead to a contradiction) are true, I am willing to consider that I may be making a mistake in resolving them to a contradiction or that I have overlooked some distinction that makes them not be contradictory.

For example, Aristotle thought that the existence of a void would lead to contradictions–at least if we also allow that there are bodies in or passing through that void–but this was because he fundamentally misunderstood the nature of movement and the way in which bodies occupy space. He thought he had a rigorous proof (several, actually) that there is no void, but that is because he was working with inaccurate concepts.

Maybe I am inconsistent. I don’t know; I have a lot of questions I have yet to work out.

I tend to think that we have concepts that we form (somehow), and once we have those concepts we can, by carefully analyzing those concepts and the relationships between them arrive at conclusions that are pretty darn certain and rock-solid (although it is also possible to make mistakes, as is clear in math). But even once we get those solid conclusions, there remains the question of whether our concepts actually correspond accurately to the real world. So for example, Euclid had a concept of spacial extension, and by analyzing that concept and other related concepts (line, point, curve) he derived with great rigor his whole system of geometry. But the issue is whether the concepts he was working with accurately describe the actual world. His system describes euclidean space very well, but whether the space we actually inhabit is euclidean is another question altogether.

Here is perhaps the best example I can come up with off-hand of something that looked rock-solid but ended up being wrong: There was a time that people–very smart people–would have said that having different orders of infinity was nonsense, and asserting that there were was contradictory. The infinite is–by definition–unbounded, not limited. Well, what is unbounded and not limited can’t be compared. For one thing to be less than another just is to say that it is limited and bounded. Thus to say that one infinite is less than another infinite seems necessarily to bound the lesser infinite, which contradicts the very meaning of infinite: The unbounded thing is bounded.

Yet, of course, we now know that there are different infinities that genuinely infinite and yet that can be meaningfully compared as greater and less. It is hard to look at a case like that and not draw a pessimistic induction.

Still, once faced with that, I’m not willing to admit that the principle of non-contradiction doesn’t hold. I will insist that there was a mistake in the original proof that showed that one infinity can’t be less than another. Our concepts were, somehow, too simple. It seems to me that the correct solution to the apparent contradiction is to note that countable and uncountable infinities are both unbounded, but in different ways. A crucial but very subtle distinction in a key term had been overlooked. The number of points within an inch, and the number of inches on an infinitely long ruler are both unbounded but in fundamentally different senses of ‘unbounded’, but the proof acted as though ‘unbounded’ is an univocal term.

Which metaphysical assertions are you inclined to accept as true?

It’s a good question. I’ve never tried to catalogue them.

I’ve already said that I accept the principle of non-contradiction, and that I think it is metaphysical. I think there are probably some assertions about causality (like, nothing causes itself, or a cause cannot be after its effect). I’m inclined to accept principles related to sufficient causality: Nothing comes from nothing, or suchlike.

I’m not sure if this is even possible, but I like to think that I at least try not to have any metaphysical opinions, let alone presumptions taken to be necessarily true

That’s the thing, I’m not sure that it is possible not to have some metaphysical beliefs, while also retaining sanity. Take the principle of non-contradiction. Is that not, underneath it all, metaphysical? If these beliefs turn out to be false, can we trust reason at all? Can we use reason at all? Or–channeling Kant with a dash of Quine–could we ever acknowledge that it was false, or would we instead modify our other beliefs to retain the principle at all costs?

On Aquinas’s understanding (which I tend to think is basically correct), we start our rational lives with an intuitive grasp of these sorts of basic metaphysical truths (though we do not necessarily have a reflexive knowledge that we know them–a child knows the principle of non-contradiction, though he would never formulate it explicitly); we use them to build up our understanding of the world; but only at the end of our investigations can a lucky few explicitly do the sort of rarefied philosophy that is necessary to show that those truths (that underlie the entire edifice of our intellectual lives) are actually accurate (insofar as we even can, for some of them are genuine first principles that cannot be proven deductively, we can only show them dialectically). All deductive reasoning requires starting points; if we are reasoning deductively, we have axioms.

Sort of like how any child knows that 2+2=4, but it took Whitehead and Russell 379 pages just to prove that 1+1=2 in their Principia, and they didn’t show 2+2=4 until the second volume.

When we do eventually explicitly look at those metaphysical presuppositions, I think we are often making explicit presuppositions we have been intuitively and implicitly using as axiomatic all along, and we are examining them openly to see if they are indeed axios.

were the early 20th century German Supremacists beginning to question if 1+1=2 rather than admit defeat that they might have been not so absolutely precisely accurate in their measurements or thinking and language?