You are free to do that. Although I said all along, I’m not interested in philosophy for its own sake. My real work is mathematics (with elements of physics and computer science), and my philosophy is simply the way that I explain the ideas to myself and to other people. My defense of my philosophy is “it works for me”, that is, I find it helpful for my own research.

If I can at least correctly explain my viewpoint to you, then that’s good enough.

The point is not to be able to declare dogmatically that the theory is correct, the point is to have an exact specification of the way the world might be.

On the contrary, in my view, what has an exact specification is the rules that the world follows, and not necessarily its state.

As a generalization of the concept of probability, the significant thing about noncommutative probability is precisely that it abandons the view that the probabilities are associated with a determinate (not determinist) set of possibilities.

Yes it does. That’s why I love it.

The priors, guesses about the state of the world, or epistemic strategies of rational agents can be inconsistent-until-conferral as you describe, without impugning their rationality, but those things are not knowledge.

I concede that there is a legitimate wrinkle about what one ever might have meant by knowledge. Beliefs that are rational, predictive, and reliable are at least hard to distinguish from absolute knowledge. Maybe I would concede that absolute knowledge does not exist, although as an expedient, I’m happy to call “RBR beliefs” knowledge.

Again, it’s important to remember that if you have a whole society of rational agents whose perceptions all commute, then there will be an appearance of absolute knowledge.

So long as something like the Bohmian option exists

Again, the Bohmian option is no different as a predictive theory, it’s only a different pedagogy. It does serve to show that the actual theory of quantum probability might well be complete. After that, the only question is which pedagogy you like best.

Greg, I think I understand well enough what you are saying but I reject the philosophy of it as pernicious and retrograde. Specification of an “absolute ontology” is a minimal standard for any theory which has pretensions to finality. The point is not to be able to declare dogmatically that the theory is correct, the point is to have an exact specification of the way the world might be. The focus on epistemic states rather than possible states of the world is pernicious because it allows this point to be obscured. I do not understand why theoretical physicists, who have more reason than anyone to think that the world might be completely knowable (in outline if not in all its particulars), would settle for such a thing, but noncommutative probability combined with the epistemic focus offers a way to do it.

As a generalization of the concept of probability, the significant thing about noncommutative probability is precisely that it abandons the view that the probabilities are associated with a determinate (not determinist) set of possibilities. If one’s focus is ontological, this is immediately perceived as a problem, because you want to know what the actual states of the world are supposed to be in a given theory. If states are epistemic, this is apparently not so clear, which is why I wish Bohm had prevailed over Bohr.

John, I agree with Carl regarding Gettier; he did not falsify the definition of knowledge as justified true belief; he simply exposed (though everyone should already have known this, at least since Hume) that many beliefs which we are accustomed to thinking of as justified are not so, strictly speaking. From the perspective of philosophical skepticism, there is very little knowledge, and it seems that it’s the difficulty of justification which mostly makes it so - there are always too many other empirically indistinguishable possibilities.

And Scott A., I owe some sort of response to your mention of Galileo. Galileo may have expelled a host of baseless apriorisms from the scientific method, but I have to wonder whether he would endorse a theoretical approach which apriori makes a virtue of incomplete descriptions.

Greg, you also say: The knowledge of two different thinkers does not have to be consistent unless they can confer. If it isn’t even consistent, then it was never knowledge! - unless you think that the world can be self-inconsistent. The priors, guesses about the state of the world, or epistemic strategies of rational agents can be inconsistent-until-conferral as you describe, without impugning their rationality, but those things are not knowledge.

As for sentient quantum computers rejecting absolute ontology on the grounds that they must be able to conceive of their interlocutors as being in superposed states - so long as something like the Bohmian option exists, they will have no need to reject absolute ontology. Again, I want to distinguish between epistemic uncertainty and ontological indeterminacy. A rationality based on quantum priors is not a problem. But an anti-ontology is.

I very recently discovered your excellent blog. I know very little about quantum computing, or the related advanced physics, and I’m looking forward to using your blog as a learning resource.

One of my personal interests is to understand the mathematics that underlies such things. I just read lecture 1 in this series, and I’m wondering what prerequisite math subjects would you recommend to help me get started with this quantum stuff, and to follow the lectures with a bit more understanding? I’ve got an engineering background and made it to introductory linear algebra years ago. I enjoy studying and reading about math as a hobby now, so no matter how daunting the task, I won’t run away with my tail between my legs!

Scott

Your phrase “`justified’ means justified in a relevant sense” is a surely a darn tricky standard to apply, whether the context is math, science, engineering, politics, … or even marriage, as Dave Bacon is no doubt finding out!

Lance Fortnow’s thread on the Continuum Hypothesis illustrates how subtle these issues can be, even when physics is (seemingly) not involved.

Gottier’s article actually settled a philosophical question … an event that is almost unique in the annals of philosophy.

The answer, by the way, is “no”. But as Hemingway’s Jake Barnes says, ““Isn’t it pretty to think so?”

Well you say belief, while I say knowledge. The distinction is important, because knowledge is that part of belief which is reliable.

Otherwise your assertion is at least on the same terms as my remark, but I don’t agree with it. The knowledge of two different thinkers does not have to be consistent unless they can confer. When it isn’t consistent, there does not exist a common actuality. But by the rules of quantum probability, when two different thinkers can confer, then their knowledge is always consistent.

This is a counterintuitive conclusion, because in human society, people can always confer. There is never a need for one person to assume that another is in a quantum superposition. But in a society of qubits, that is exactly how things would stand. If there were sentient quantum computers — conceivably they will exist one day — I’m sure that they wouldn’t philosophize about the incompleteness of quantum probability. Instead, they would reject absolute ontology, which is it what it sounds like you are digging for.