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Consider the example of causal determinism. It can be phrased in many ways, all with identical meaning:
- The idea that "every event, including human cognition and behavior, decision and action, is causally determined by an unbroken chain of prior occurrences” (Van Inwagen, 1983).
- The world is governed by (or is under the sway of) determinism if and only if, given a specified way things are at a time t, the way things go thereafter is fixed as a matter of natural law. (SEP)
- Everything has a cause.

My question is in reference to people who hold that the lack of complete understanding in a particular field can invalidate a positive claim. Continuing with the example of determinism, one of the most oft-used counter-arguments is the Heisenberg uncertainty principle. This is the principle that claims "precise inequalities that constrain certain pairs of physical properties, such as measuring the present position while determining future momentum of a particle. Both cannot be simultaneously done to arbitrarily high precision. In other words, the more precisely one property is measured, the less precisely the other can be controlled, determined, or known." Everyone knows that the principle cannot give free will, but some suggest that it invalidates determinism. How?

In the same regard, the fundamental nature of quantum mechanics is said to be indeterminate, that is, the measurements of an observable at the quantum level is said to have an indeterminate value. Stated more simply, the value is not determinable via our current methods of observation. This is another "lack of knowledge" position, just as the first one is.

Do these kind of "lack of knowledge" positions invalidate or otherwise lessen the strength of determinism as a theory? I'm having difficultly conceiving why there is any conflict. A lack of knowledge or understanding simply means we need to find out more before we know for sure. Some of the greatest minds of quantum theory asserted this (Einstein, Rosen, Podolsky). In fact, they wrote a paper where they went on to say that there must be "hidden variables" which haven't been accounted for which allow for strict determinacy. That was in 1935. 76 years later (as of this post), some physicists have seemed to have ruled out "local hidden variables", but global hidden variables and other explanations are still very much on the table. Again, we just don't know enough yet. It doesn't seem to follow that uncertainty about certainty can disprove certainty.

I have one further example that might help clarify: As you know, given the nature of science we may very well never be 100% absolutely, objectively "certain" about anything; but that doesn't mean all our theories are invalid. For example: I am uncertain that my aunt's apple pies are made with handpicked apples. I don't see how my uncertainty about the nature of the apple pies has any effect whatsoever on the actual possibility of the composition of the pies. Either the apple pies are made from handpicked apples, or they aren't. My uncertainty about it does not make either possibility more or less probable.

Keep in mind my question is about the general ability to use a "lack of knowledge" claim to invalidate a positive claim. Determinism/apple pies are just examples. Feel free to use whatever thought experiment or intuition pump that serves you best.

Note I wanted to avoid using the term "negative claim" because it's thrown around a lot and doesn't quite capture the essence of what I mean by a "lack of knowledge" claim; at least insofar as I see it being used today. E.G., some people think "There is no flamingo on my desk" is a negative claim, merely because it posits the non-existence of something. To me, anything which asserts a knowledge of the existence or non-existence of something is a positive claim. A "lack of knowledge" claim, on the other hand, is one which acknowledges an uncertainty or "non-knowledge" (if you will) of something. I will consider revising my question and simply stating my definitions at the top if people think it will aid in clarity.

Here is some background info with regard to my first example:
http://en.wikipedia.org/wiki/Quantum_indeterminacy
http://en.wikipedia.org/wiki/Uncertainty_principle
http://en.wikipedia.org/wiki/Hidden_variable_%28physics%29
http://en.wikipedia.org/wiki/Indeterminism#Quantum_mechanics
Einstein, A.; Podolsky, B.; Rosen, N. (1935). "Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?". Phys. Rev. 47 (10): 777–780.

  • interesting findings 10/04/2012 – stoicfury Oct 5 '12 at 5:01
  • On rereading your question, short answer: Yes obviously, insofar as that "positive claim" implies some "complete knowledge." See more below. – Nelson Alexander Oct 19 '15 at 15:22
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Keep in mind my question is about the general ability to use a "lack of knowledge" claim to invalidate a positive claim. Determinism/apple pies are just examples.

In that case, let's start with your specific examples, and then move on to the general case.

You claim that:

I don't see how my uncertainty about the nature of the apple pies has any effect whatsoever on the actual possibility of the composition of the pies. Either the apple pies are made from handpicked apples, or they aren't. My uncertainty about it does not make either possibility more or less probable.

And this is true--of apples. Observation of apples has no significant effect on apples.

Things are different at the quantum level, however. Observation of particles has a definite effect on the particles. Thus, any notion of determinism that relies upon the observability of particles has a problem, as the act of observing interferes with the experiment (and may alter what would have occurred had the observation not taken place.) So, certain attempts to demonstrate determinism are stymied by the uncertainty principle.

So, from there, we can move on to the general case:

My question is in reference to people who hold that the lack of complete understanding in a particular field can invalidate a positive claim.

The answer is that this can occur only in cases where "the lack of complete understanding" is of a structural (i.e., transcendental) nature and not of a purely contingent or accidental nature. In other words, where we are dealing with situations where X is viewed as a necessary condition for the possibility of Y, uncertainty about X can invalidate positive claims about the presence of Y.

In practical terms, you're unlikely to run into this problematic outside of the quantum level, or other unusual edge cases.

  • 2
    +1 I enjoyed reading your reply, and although I disagree with it, it greatly enlightened me. After all this time, I think I understand. The distinction you bring up X is necessary condition is an example of a positive claim, which would make sense: People who use the quantum physics arguments I mention actually think they are making positive claims, as opposed to admitting uncertainty. Thus, it still seems that logically a lack-claim cannot invalidate a positive claim; it's just that with determinism, opponents citing quantum physics think they are making appropriate rebuttals. – stoicfury Aug 11 '11 at 13:29
  • Glad you enjoyed it. Let me flesh things out a bit more, based on your response (and I should point out, by the way, that I am not personally interested in either determinism or quantum physics, so I don't have a dog in this fight.) If one were to define "determinism" in a manner that requires observation-- and there are some proposed definitions that do so-- quantum objections can be raised, such as "since observation is a necessary condition for the possibility of determinism, our inability to accurately measure both position and velocity of a particle renders determinism impossible." – Michael Dorfman Aug 11 '11 at 13:52
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    Yes. It appears that the second QM argument I brought up actually can be thought of as both a positive claim or a lack-claim, depending on how you look at it (the first one, the Uncertainty principle, is by definition a lack-claim). Now it makes sense why some perceive a conflict whereas others do not. And given the nature of the problem, it seems that there is no way to establish it for certain either way at this point. Thanks for your help on that, Michael. :) – stoicfury Aug 12 '11 at 15:31
  • Happy to be of help. – Michael Dorfman Aug 12 '11 at 16:05
  • If I have even the slightest grasp of quantum mechanics (and I don't claim that I do), @stoicfury's second argument can be both a positive claim and a lack claim at the same time. From a purely grammatical/logical point, it doesn't make sense to use 'both this or that', but that's me picking nits. – Agi Hammerthief Mar 7 '14 at 21:32
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In order to have a coherent discussion about quantum mechanics, it helps to have a pretty good understanding of quantum mechanics. I think you're unintentionally mischaracterizing the arguments for non-determinism in quantum mechanics.

Let's take one of very many weird results in quantum mechanics. You have polarized sunglasses, right? What happens with polarization is that a photon has one of two polarizations which are at 90 degrees to each other; if it is aligned with the sunglasses it can pass through, but if it is aligned at right angles, it can't. If you line up two pairs of sunglasses, it's only as effective as one: the photons that were aligned with the first pair are still aligned and pass through both. Now suppose you play a nasty trick on your photons: you rotate your second pair of sunglasses by 45 degrees. Guess what happens? Half the photons go through. Half of them are aligned with the new sunglasses, and half are at right angles. It's like the sunglasses made the photon choose: did you really secretly want to be 45 degrees to the left, or 45 degrees to the right, when you said you were vertical before? And you can do this over and over and over and over. If you have vertical sunglasses, then 45 degrees, then vertical again, the photon doesn't remember anything about its first "choice"; maybe it was a "vertical, then 45 degree, then 90 degree" photon, or maybe it was a "vertical, then 45, then vertical again" photon.

At some point, saying that the behavior is determined (but by nothing that we can measure, and even with a proof that there is (probably) not anything local we could measure) starts to be unwieldy. It's not a useful description of how the world operates. After all, we say that dice are "random" when we know perfectly well that classical mechanics tell us all we need to know to calculate how dice will land given initial conditions; it's just so complicated that we never bother. Likewise, if the polarization of photons really is deterministic, it's almost impossible to imagine that it matters. Hence, the sensible scientific conclusion is that some quantum mechanical processes are random (unlike dice, we cannot determine how they will go, have no leads on finding out, and have good evidence that our normal methods will fail).

Now, back to your question: knowing that you don't know something is, of course, not a reason to say that something is false, or true, or unknowable. But when you're trying to come up with a compact predictive framework to describe observations, the theory that lets you best deal with those things you can know, and lets you adequately work around that which you don't (or can't--even if you don't know whether it's "don't" or "can't"), is the superior theory. Once that theory is shown to agree with many observations over long periods of time and under a wide range of conditions, it is pragmatic to accept that theory as true in the scientific sense (i.e. in the sense that it is "true" that you cannot fly by flapping your arms).

  • Accepting a theory doen't mean accepting all interpretations of that theory necessarily. Especially those interpretations that refuse realism and locality. – Alberto May 11 '16 at 19:40
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I think you are asking two different questions here. One is, does what we know about QM mean that determinism is false? The answer to that seems to be: it depends to some extent on your interpretation of QM. However, on any interpretation it is the case that there are fundamental limits to our ability as observers to predict outcomes. Even with the maximum theoretically available information we can't do better than calculate probabilities of various outcomes.

The other question is, does the fact that we are uncertain about something mean that it is not determinately true one way or the other? As your apple example shows, the answer is no. The fact that you don't know whether your aunt's pies are made with hand-picked apples doesn't mean there is no fact of the matter. For a start, your aunt probably knows. Here the uncertainty is not some fundamental theoretical uncertainty that arises from QM, but the common or garden variety of uncertainty that we suffer from all the time because we are finite beings with limited information and limited ability to process it.

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The quantum mechanics distinction is not between "global" variables and "local" variables, but rather between "distant" variables and "local" variables. Bell's inequality proves that quantum effects cannot be accounted for by locally acting variables not yet understood. Because "entangled" particle pairs share quantum effects (I am mangling the quantum mechanics description a bit for brevity) at a distance (farther than a light speed message can travel in the time under consideration - what Einstein called "spooky action at a distance") in ways that cannot be predicted except in a general statistical manner we are left with no ability to specifically predict the behavior of the entangled particles, nor can we expect that the unpredictability is due to current ignorance of some effect that will surface in the future (no hidden local variables). This lack of predictability does not appear to me to relate in a meaningful way to what I understand to be the issue in determinism - namely, does will have a role in determining the future. The fact that we cannot predict an outcome does not lend any support to a thesis that outcomes are determined by will. Casual readers are often led astray by the terminology used in quantum mechanics. Terms such as "observer" and "measurement" appear to open the door to will having a causal role, but that is misusing the terms - in no way do these terms imply willful control of outcomes, they only specify times when unpredictable outcomes might become known.

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Your pie is made of Schrodinger Apples, and whether or not they are "fresh" remains, as far as I know, a question very much up for grabs, among physicists and metaphysicists alike. And possibly futile.

But I'm not sure your question needs to bring in QM at all. Argument from an "absence of knowledge" is indeed an element of induction and a crucial assumption of science.

The argument that everything or, indeed, anything is "causally determined" is a claim of complete knowledge. Some Laplace machine can work out every possibility, with no room for randomness, "clinamen," or miraculous intervention. Modern science (since statistical thermodynamics) never makes such absolute claims (no matter what individual scientists may say).

Thus the demonstration of a "lack of knowledge" does indeed "disprove" not any particular theory, but any claim that the theory implies concerning "complete knowledge." Thus the inductive compromise. The theory is "true for now," until its direct predictions are falsified. But it can never claim "complete knowledge," even internally, and is thus validly limited by any and all claims of "incomplete knowledge."

As an aside, the whole acceptance of "lack of knowledge" is central to the modern project. A good example is the way in which ancient maps were always filled up with fanciful dragons, chimera, netherworlds, and whatnot. It was only with modern exploration that maps became marked "Unexplored," thus inviting empirical research. This is the cartographic innovation comparable to Kant's noumena. Until the "lack of knowledge" is admitted as a limit into the arguments, we have the futile contentions of a prior assertions.

How many of today's QM arguments fall into this realm of futile antinomy remains to be seen. Hidden variables may turn up. Or we may find that we act like Berkeley's God, splitting universes or endowing states-of-affairs with existence by what we now innocently call "observation."

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