Thursday, October 04, 2007

Physical Abstractions

Over at Victor Reppert's blog, I've been confronting a form of the argument from reason (AfR). The AfR takes many forms, but the basic scheme is to say that there's something about the process of inference that makes it impossible to explain with any naturalistic model.

In this particular case, the AfR argues that inference is invariant across all possible universes, and that means that inference is physics independent. The argument then says that a thing that is physics independent is non-physical, and, therefore, no naturalistic theory can explain that thing.

I find it easy to see that this argument fails because I can cite counterexamples. The best one I have found so far is the concept of a plasma. A plasma is a high-density, high-temperature state wherein bound states in a medium lose their identity, and the medium becomes a soup of bound-state components and force-carriers. An ionic plasma is an ionized gas, of the type you find in a neon light. In an ionic plasma, atoms become unbound, and you get a soup of electrons, ions, and photons.

However, long after we learned of ionic plasmas, we discovered that there might be quark-gluon plasmas (QGP). In a QGP, we have a soup of quarks and gluons instead of bound nuclei. The physics of QGP, known as quantum chromodynamics, is completely different from the physics of ionic plasmas, which are electromagnetic.

This means that plasma is an abstraction that is physics independent. Indeed, we can imagine very different universes that would support plasmas. Yet, if the ability of an abstraction to apply across universes with different physics were a sign that the abstraction were non-physical, we would have to conclude that plasmas were non-physical. Clearly, plasmas are physical phenomena, and so the premise about the physical portability of abstractions is false.

Here is a systematic dismemberment of the argument. The argument goes like this:

1) We can abstract the possibility of other lawful universes.

2) In every abstraction of a lawful universe, there is a different set of laws.

3) However, every such universe contains common set of laws that establish non-contradiction. (Without these, the laws would predict an outcome and its negation, and not be laws at all.)

4) The conditions under which one classifies an inference as valid are common across every universe. In other words, inference is a specification that is independent of all the laws in the universe except the common logical laws.

5) Premise: Assume that minds in our universe are the result of physical processes of our universe.

6) Any physical system that meets a non-physical criterion must be portable across universes without changes.

7) Minds in our universe would cease to function if physical laws were changed. That is, changing physical laws of our universe without changing anything else in our universe (e.g., the structure of brains), would result in systems that no longer meet the specification for a mind that makes correct inferences.

8) Physical minds are not portable across universes without breaking the criterion or requiring redesign.

9) Therefore, due to (6), assumption (5) is incorrect.

This argument fails because (6) is false.

(6) is false because we can imagine more counterexamples like the following. A "hammer" is an example of an abstract, non-physical criterion that can apply to matter. A hammer is something that amplifies hardness and pressure with kinetic energy. Hammers can exist in a great many universes. Consider a universe slightly different from our own, one in which Iron is a liquid or a gas. An Iron hammer in this alternate universe would no longer meet the abstract criterion for being classified as a hammer. However, in the alternate universe, we could make a hammer with a brass head that meets the abstract criteria. Clearly, physical specifics do not have to be portable across universes for there to be physical implementations in other universes. There will certainly be universes that cannot support hammers, but this is not important.

There's another confusion buried in the argument. What does it mean when we say that correct inference is fixed in all lawful universes? Presumably, these other universes do not actually exist, so we are not referring to physical universes. Rather, we are referring to abstractions. We are saying that if we create an abstraction for another universe, that abstraction is subject to rules of inference. Hence, the very portability of inference is not across physical systems, but across abstractions of physical systems. That is, a mind needs to be able to port inferences across its own abstractions. Here's the experiment. If I create a physical implementation of a mind, and that mind creates abstractions for other universes, then that mind must be able to apply rules of inference to its abstractions of other universes. That's the burden a physical mind has to meet.

19 comments:

Darek Barefoot said...

DL

Thank you for detailing your objections to my argument.

Please allow me to once again restate my argument in (more or less) its original form:

The physical world is described by bodies of rules, the laws of nature. In theory, at least, there is a body of fundamental laws of nature, the ideal laws of physics, which the laws of our standard model of physics approximate. Some of the laws of nature are contained in secondard bodies of rules, such as the laws of thermodynamics, chemistry, optics, and genetics. Given the emergence of the processes described by secondary bodies of rules from processes described by the fundamental rules, the secondary bodies of rules are determined by and dependent upon the fundamental or primary rules. Naturalism holds that all that is real is contained within the same causal context, and therefore that the laws of physics are the bedrock description of reality. (I realize that you may reject some of these propositions, but I think that many if not most scientific naturalists would be on board so far.)

Some of our thought processes are described by what are commonly known as the rules of inference. These rules describe the way that conclusions are derived from premises, and allow us to classify sequences of thought as either logically sound or fallacious. I believe we can now formulate as follows, given naturalism:

1) All bodies of rules that describe secondary processes are determined by and dependent upon the fundamental rules of nature, the ideal laws of physics. For example, the rules of chemistry are determined by and dependent upon the ideal laws of physics.

2) Logical thought processes (i.e., instances of reasoning) are secondary processes within nature and are emergent from more fundamental processes.

3) Logical thought processes are described by the rules of inference.

4) Therefore, the rules of inference, like the laws of chemistry, optics, etc., are determined by and dependent upon the laws of an ideal physics.

This is the first part of my argument. The second part turns on what is entailed by a secondary body of rules being determined by and dependent upon another, primary body of rules. I content that determinacy and dependency entail that there is some conceivable change in the primary rules that would result in a change in the secondary rules. For example, Kepler's Law describes orbiting bodies. Kepler's Law is determined by and dependent upon the Law of Universal Gravitation, so that there are conceivable changes in the LUG that would change Kepler's Law. If no conceivable change in LUG could alter Kepler's Law, we could not claim that Kepler's Law is dependent upon the LUG. Notice that my contention is not that any conceivable change in a primary body of laws will result in a change in a dependent body of laws, but that there must be some conceivable change in the primary laws that would change the secondary laws in order for dependency to exist.

The last part of my argument claims that we cannot conceive of a change in the rules of inference resulting from a change in the fundamental laws of physics. Therefore the rules of inference are not dependent upon the fundamental laws of physics--in contrast to laws of chemistry, optics, etc. Further, since this disconnect creates two distinct causal contexts for real events, the single causal context required for naturalism is refuted.

The implementation of certain laws of nature might change without the laws themselves changing. For example, we can imagine a world in which orbiting bodies that were much smaller or differently composed than those in our own nevertheless were still described by Kepler's Law. So a change in the implementation of the law or rule is not necessarily the same as a change in the rule itself.

Or is it? We might legitimately wonder whether, if Kepler's Law were differently implemented, it could still be called "Kepler's Law" in the strictest sense? We might also ask whether, if Kepler's Law were actually different because the LUG were different, we would be justified in calling the laws under discussion "the LUG" and "Kepler's Law." Perhaps we ought not to take for granted that we can imagine a world with different versions of the known laws of nature, because the different versions would actually be different laws entirely.

This ambiguity does not defeat my argument. I think we can imagine inhabiting a universe with all different laws. For example, it's easy to imagine that our universe obeyed strict Newtonian mechanics without relativity. Suppose we lived in a world where none of the laws could be identified with the laws that obtain presently. We can still imagine that these alternate laws would result in a coherent scheme of reality, and they would be organized in dependent layers with fundamental physical laws at the bottom. And among the laws, there would be a nearest equivalent of the LUG, nearest equivalents of the laws of electromagnetism, etc.

Of course, chemistry (or its nearest approximation) would be different, so our brains would function differently. But our thinking process in the imaginary world would still have to follow the rules of inference in order to make sense of our surroundings. We simply cannot imagine that thought could proceed other than according to the rules of inference and make sense of things--assuming the things could, in fact, be made sense of. And this, again, sets rational thought apart from all other secondary processes; the rules that describe it are independent of the laws of nature.

DL, you gave the example of plasma as an ionized gas versus plasma of quarks and gluons. You said that we still have a plasma state, although the physics is different in either case. I suspect that a degee of resemblance is all that is involved. The relationship between atomic nuclei and electrons resembles that between quarks and gluons to the extent that the plasma description be shared. But I am no physicist. I take it for granted that we can identify a certain special set of rules that uniquely describe plasma processes of both kinds. Does your example prove that plasma process rules are independent of fundamental laws of physics? Such that no conceivable changes in particle physics would alter plasma process rules?

Even if the same special process rules that describe ionized gas describe quark soup, we can imagine occupying a universe in which the fundamental laws yielded other plasma process rules than those we know--or rules that would be the nearest functional equivalents to those describing plasma processes. But we cannot imagine a universe in which the fundamental laws of physics of physics would yield alternate rules of inference or nearest equivalents to them.

As I pointed out before, the constituents of plasmas--whether ions and electrons or quarks and gluons--are otherwise described by fundamental laws of nature. But such cannot be said of the constituents of the reasoning process--premises and conclusions. Any physical object or event sequence that we might be tempted to identify as a "premise" turns out to be an artifact representing a premise.

In a different world, representations of atoms (diagrams, models) might be different because "atoms" would have different causal relations. Or, if there were nothing to identify strictly as atoms, there would be nearest functional equivalents of atoms. But representations of premises, though they might be different in another world, could not be different because they had different causal relations. Nor could there be such things as nearest functional equivalents of premises.

I agree with you that a case can be made for the laws of nature being abstractions, but if that case is pushed to its limit it too poses problems for naturalism. It tends to force a choice between the physicality of causal relations or realism regarding the laws of nature. That difficulty is different than the one I am trying to outline, however.

Doctor Logic said...

Darek,

Thanks for your comment.

I have two particulars I would like to focus on.

1) Every set of rules applies to something in some context. You say:

Some of our thought processes are described by what are commonly known as the rules of inference. These rules describe the way that conclusions are derived from premises, and allow us to classify sequences of thought as either logically sound or fallacious.

Implicitly then, a rule of inference applies to a sequence of thoughts in a mind. That means you must have a thinking system in order for the rules to apply. The rules don't apply to non-thinking systems. My analogy would be that one cannot have an illegal chess move in a non-chess context, e.g., in a cricket match.

We need to be very clear about this distinction. When we consider rules of inference applying to an uninhabited universe, we really mean that "a sequence of thoughts about an uninhabited universe" is subject to certain rules in order to be considered sound. We cannot mean to say that there are rules of thought in that uninhabited universe because there are no minds existing that would be subject to the rules. That is, if a universe does not support minds, it does not support proper rules of inference either.

In this light, your observation looks like a tautology: A proper mind is a thing that performs proper inferences. Any proper mind (in any conceivable universe that supports minds) will make proper inferences.

2) You are correct when you say that the rules of inference are not like physical laws, but I think you don't correctly connect this observation with naturalism.

The rules of inference determine whether or not a thought sequence is labeled as properly rational, but the rules of inference are optional. They do not force minds to be rational the way laws of atomic physics force compounds to adhere to the rules of chemistry.

Your argument relies on the faulty suggestion that naturalism takes all labeling conventions for optional states of affairs as emergent physical laws.

Consider that Carbon can be found in several different states, including diamond, graphite and C60. However, a "rule of diamonds" which describes proper diamond structure, does not cause diamonds to form. Diamonds are caused by atomic physics acting on certain configurations of matter. The "rule of diamonds" is a rule for recognizing diamonds. While naturalism may consider diamonds to be emergent, it does not consider the "rule of diamonds" itself is not emergent.

In naturalism, emergent laws represent the emergence of high-level must-be's from low-level must-be's. The rules of inference are not must-be's. That's why they don't depend on low-level physics in the same way that the laws of chemistry depend on low-level physics.

Darek Barefoot said...

DL

You raise excellent points.

I'll take the second one first. The rules of oribtal mechanics can be restated so that they become rules for recognizing orbital systems. To the question, In what relations must what objects be in order to constitute orbital systems?, the answer will depend on the rules of orbital mechanics, which depend in turn on the fundamental rules of physics. Likewise, the rules for recognizing diamond, if stated in scientific detail, will make reference to a particular chrystalline form carbon assumes because of the fundamental laws of physics. In a universe where carbon atoms obeyed slightly different fundamental laws and therefore assumed different chrystalline forms, the scientific rules for classifying a form of carbon as diamond would be either different or else, perhaps, they could no longer be called rules for recognizing diamond. The covariance relation with the fundamental laws of physics would still hold, since those laws would determine what the rules for recognizing diamond would be.

Now, as to the first point, it is the case that not every logically possible universe contains processes that can be classified as "thought." And in those lacking thought, rules of inference indeed have no application. But logically possible universes in which thought occurs include those with just about every imaginable variation of the laws of nature.

If thought could be defined as a certain process occurring in brains or structures of brain-like complexity, then universes with laws that excluded brain-like structures would exclude thought and the rules of inference. The trouble is, humans were able to recognize thought, including the peculiar properties of rational thought, before the brain's processes and complexity were known. Knowledge of brain processes has not given us a better idea of what makes rational thought rational--or what makes thought thought, for that matter. To the extent that thought may require objects, logically possible universes where thought occurs will have to have potential objects of thought--that's about it. But I sympathize with naturalists who find this concept challenging.

Arguments from possible worlds can be useful, but they have their limitations. We can approach this issue from a different angle. Here is a famous quote from Einstein:

"As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality."

Einstein was taking a leaf from Hume and the analytic-synthetic distinction. He could have included the laws of logic and rules of inference along with the laws of mathematics. Conlusions based on sensory experience, such as reconstructions of the laws that describe the world disclosed by the senses, are always subject to a degree of doubt.

Basic mathematical laws, like rules of inference, are not subject to doubt because we cannot even imagine evidence of the senses that would disprove them. Mathematical principles that we might infer from sensory experience would be subject to doubt for that very reason--the same reason that laws of nature are subject to doubt.

We "observe" the certainty of basic laws of mathematics and inference in the course of thought, unlike observing nature with the senses. We can see that an otherwise unsupported apple dropped from the hand falls to the earth, but we can imagine it doing otherwise. We can "see" in our thought processes not only that 1+1 equal two, but that they cannot imaginably do otherwise. Seeing the apple is sensory whereas "seeing" the mathematical relation is not. Einstein implies that only the second type of "sight" can reveal certainty.

Hume first made this distinction. What neither Hume nor his disciples (such as Ayer) ever explained was how the necessity that cannot be sensed in natural processes can nevertheless be "sensed" in our thought processes, if thought processes are natural. There are times when, perhaps over a glass of soda, I am driven to accept a conclusion because it is logically necessitated by a premise or premises that I have been contemplating. Logical necessity is the reason that one thought--one "thinking state," we might say--is followed by another. The state of the glass of soda is changing too as outgassing causes bubbles to rise from the liquid. But the very fact that I must sense what physical state of the soda follows another and then doubtfully infer a law of nature to explain this sequence is proof, according to Hume, that logical necessity cannot be the reason for the succession of soda states.

As the soda is bubbling, so is my brain, in the sense that its chemical states are dynamically following one after another. But insofar as those states are potential objects of sensory observation--insofar as we classify them as natural, in other words--logical necessity cannot be the reason for any one of them succeeding any other(s). A physical sequence can represent a sequence driven by logical necessity (as in computation) but it cannot actually be one, anymore than a squiggle representing a number can actually be the number. We have an unbridgeable conceptual divide between rational thought and nature. Although Hume never explored this divide, Kant, who was inspired by Hume, glimpsed it. So although the Argument from Reason is usually traced back to Kant, in an important sense it owes to Hume's observations.

Now, I am not going to mount a further defense of Hume's point here. Your readers can do their own research and reach their own conclusions about it. Suffice it to say that his arguments for the lack of logical necessity in natural cause-and-effect are still generally considered formidable. And our discussion about possible worlds can be one way to get at this point. The laws of nature are inferred from sensory observation and are therefore not the way they are necessarily; the rules of inference are disclosed to introspection as being necessarily the way they are.

To preserve the hegemony of nature, we might interpret Einstein to say that the apparent certainty of the rules of mathematics (and inference) is not real at all. To put it another way, the apparent certainties absent from nature but present in thought are illusions generated by glitches in our programming. The trouble with this move is that it deprives all thought processes of their logical franchise--including the thought processes that give rise to a belief in naturalism.

To summarize, rational thought processes and natural processes are described by mutually exclusive bodies of rules. Therefore rational thought is not a natural process. If we reject the term "supernatural," then we might say metanatural or other-than-natural. The brain represents a somewhat mysterious interface between nature and a metanatural substrate of rationality. We can follow this in the direction of either theism or idealism, but either way it leads away from naturalism.

Doctor Logic said...

Darek,

I'll start with the issue of labels for recognizing possible states. My diamond example illustrated what I meant by labels for optional states of affairs, but, as you point out, that may not be very portable across universes.

However, I can make my point just as well (better, actually) with "solidity." We can imagine a wide range of possible universes that include solids. Yet solidity is an optional state. There is no "law of solidity" that forces all compounds to be solids. There may be conditions under which compounds form solids, but "solid" (or "properly solid") is just a label for a possible state. It is not a must-be. It is something recognized. It seems reasonable to me that the "solid-supporting" universes and the "thought-supporting" have comparable cardinality.

Basic mathematical laws, like rules of inference, are not subject to doubt because we cannot even imagine evidence of the senses that would disprove them.

I would disagree with this. They are subject to doubt, but our doubt is well-controlled, and therefore, arbitrarily small.

In studying a physical system, we use induction and assumptions about simplicity, control and isolation. For example, we might say that an object falls according to certain laws "neglecting air resistance." Or neglecting any of countless other factors that might interfere.

In mathematical systems, there is still doubt, but there is no menagerie of interfering factors. The systematic error is in us, not the math. This doubt manifests itself in any complex proof. For example, many attempts were made to prove Fermat's Last Theorem, and it often took months to verify, with verdicts about the proof's validity oscillating between confirmation and falsification. Even in adding 1 + 1 to get 2, we might have made an error, but the uncertainty in that result is now so small as to be insignificant.

The laws of nature are inferred from sensory observation and are therefore not the way they are necessarily; the rules of inference are disclosed to introspection as being necessarily the way they are.
...
To summarize, rational thought processes and natural processes are described by mutually exclusive bodies of rules.


I don't think this argument is working because you're not isolating inference from mind (which we know are independent).

Let me see if I can state your argument in a better form.

1) There are physical laws and there are necessary laws of logical inference.

2) The laws of logical inference are not physical.

3) From time to time, minds can see the laws of logical inference and utilize them.

4) Therefore, minds are causally connected with the non-physical.

5) Therefore, minds are non-physical.

Is this your argument, or have I mangled it?

Darek Barefoot said...

DL

I would put the argument more as follows:

1) Naturalism entails that all real processes are potentially described by rules that are the laws of nature.

2) Rational thought is a real process.

3) Therefore naturalism entails that rational thought is potentially described by the laws of nature.

4) The laws of nature are not the way they are out of logical necessity.

5) The rules of inference are the way they are out of logical necessity.

6) In processes described by rules that are not the way they are out of logically necessity, the succeeding of one state by another cannot occur due to a logically necessary relation between states.

7) In processes described by rules that are the way they are out of logical necessity, the succeeding of one state by another can occur due to a logically necessary relation between states.

8) The process of rational thought is described by the rules of inference.

If these steps hold up, then rational thought falls outside of nature. Of course, we can debate the definition of nature. Above, I hold nature to be that which is described by rules for which scientific laws are at least useful approximations, or laws that are have the same character as scientific laws. I believe that naturalists and secularists ordinarily would find little to argue with there, but definitions can be debated endlessly.

As for the certainty of mathematical laws, I agree that we can be mistaken particularly about complex mathematical relations. But if 1+1=2, they do so necessarily. If Fermat's Last Theorem is correct, it is logically necessary that it is. General Relativity and String Theory, by contrast, even if true are not true out of necessity. We can try to question the entire concept of logical necessity, but that would be a rocky road to take. Let's assume for the moment that there are necessary truths, such as 1+1=2 and the Socrates Syllogism.

How is it that we can know some truths as necessary? We do not observe them to be true with the senses. We find ourselves compelled as a result of rationally attending to them. Notice--as a result. There is a temporal sequence of mental states involved. Logical necessity entails that an agent who attends to premises--who rationally comprehends them as the ground for a conclusion--is constrained out of logical necessity as to the conclusion(s) he or she will reach.

The otherwise unsupported apple moves toward the earth when my hand releases it. There is a a state that succeeds another. But there is no logical necessity that constrains the succeeding state. I observe that the apple moves toward the earth with the senses. All of this is entailed by 4 and 5 above.

I realize that you have trouble seeing rules as exerting force. But if rules are genuinely descriptive and do not exert force, they nevertheless characterize the nature of the force that is at work.

I think your example of solidity is only helpful to your case to the extent that you depart from a specifically scientific, law-based description and move toward the phenomenology of solidity--that which gives rise to an experience of something as being solid. Law-based, "scientific" descriptions were my focus, and if we stick with them it is far from clear that my argument is undermined by your example.

Doctor Logic said...

Darek,

I really think that we need to distinguish between minds and logical necessities.

Let's suppose for argument's sake that logical and mathematical theorems are non-physical. Given this supposition, theorems and syllogisms follow necessarily in light of their definitions, and they follow timelessly. The premises and conclusions in, say, the Socrates Syllogism would not have time coordinates.

Logical necessities would then be as much a part of the landscape of reality as physical reality (albeit constant, non-physical parts of reality).

However, minds do not parse syllogisms and theorems timelessly or instantaneously. Minds explore logical necessities the way bodies explore physical terrain. It takes time to wander over the terrain, and it takes time to explore logical necessities. Furthermore, there's no logical guarantee that a mind will successfully navigate a syllogism or theorem. There's no force that guarantees that behavior, so the rules of inference do not coerce minds the way physical laws coerce bodies. Indeed, it seems that physics coerces minds as they wander over that territory of logical necessity, with physics sometimes tripping up the mind.

At the very least, I think you'll have to admit that minds and rules of inference are independent things. An argument that shows logical necessities to be non-physical does not show that minds are non-physical.

In principle, there could be all sorts of evidence for non-physicality of mind. If we could instantaneously see arbitrarily complex logical relations, you would have excellent evidence for non-physical minds. Yet, we don't see that. Our ability to reason through proofs is limited by physics. Everything we do is limited by the physics of computation.

If minds were infallibly logical, you would also have good evidence to bolster your case that minds are non-physical. Minds are not infallible, and frequently make mistakes.

To me, all this is extremely convincing evidence that minds are wholly physical. It's just implausible to me that, of all the possible dualisms, dualism of human mind is that rare type that looks exactly like a physical mind.

Logical necessity entails that an agent who attends to premises--who rationally comprehends them as the ground for a conclusion--is constrained out of logical necessity as to the conclusion(s) he or she will reach.

This is a tautology.

A rational agent is one who strictly adheres to definitions and rules of rational thought.

So it is by definition that the rational agent is constrained by logical necessity as to the conclusions that he or she will reach.

The key point is that minds are not strictly rational. That means that the rules of rational thought are not laws at all. They are a recognizeable quality, and the only thing that makes them special is that such qualities are necessary for people like us who engage in this sort of analysis. Rational thinking is not necessary in a physical universe the way, say, obedience to the Second Law of Thermodynamics is necessary. However, rational thought is still possible in a physical universe, and an imperfect rationality fits the data much better.

Darek Barefoot said...

DL

>>"Logical necessity entails that an agent who attends to premises--who rationally comprehends them as the ground for a conclusion--is constrained out of logical necessity as to the conclusion(s) he or she will reach."

This is a tautology.<<

To a degree, yes, like many specimens of logic. What would make my statement trivial is an equivalence between rationally comprehending the premises and accepting the conclusion. But plainly they are not the same thing. Accepting the conclusion follows by necessity from comprehending the premises, but "to comprehend the premises" is not another way of saying "to accept the conclusion." We have a sequence in which logical necessity plays a role that it does not play in the sequences of natural processes.

It would be easier to play down the rules of inference if we could simply redefine the words "truth," "rationality," "premise," "infer," etc. and make up new rules of inference to match the new definitions. Some people may think that is possible, but I doubt that you and I are among them. The rules of inference are immovable. Sometimes they lead us to conclusions we would rather not reach. We might as well try to budge Gibraltar as to change them.

The "power" of any rules is a bit mysterious. The laws of optics don't grab us by the collar and force us to grind lenses. If we decide to grind lenses, the laws of optics don't force us to grind effective ones. If we try to grind effective lenses and fail to do so, the laws of optics can tell us where we went wrong. The laws of optics do dictate to us how we must grind lenses if they are to affect light in certain ways.

Likewise, the rules of inference do not force us to think rationally. If we fail to arrive at sound conclusions or fail to construct a cogent argument, the rules of inference can tell us where we went wrong. The rules of inference dictate to us how we must think in order to move closer to the truth instead of farther away from it. There are processes to which rules of thought have no application. But the rules have application to all processes of thought to the extent that they determine whether any sequence of thought is rational or non-rational, sound or fallacious.

I suspect that we both endeavor hard to stick to the rules of inference in our arguments, just as a grinder of lenses attends closely to the laws of optics in order to get the result he or she desires. If these rules were mere assumptions, we would be tempted to question or challenge them. But they are not, so we don't.

No, I don't think we can claim that the rules of inference are not rules. Preserving naturalism means arguing for compatibilism. Thought processes, perhaps, are described by both the laws of chemistry and the rules of inference. Processes can, after all, fall under multiple sets of rules--but only as long as there is interdendence among the rules. Organic reproduction can be described both by the laws of chemistry and the laws of heredity, but only if one set of laws is dependent upon the other. That's why the stubborn independence of rules of inference is such a problem for naturalism.

We could specify rules in the form of graphic equations. A line can be described by one equation in two-dimensional space and yet be independently described by another equation for movement in three-dimensional space. This model might work. Except in this analogy, naturalism claims that only the two-dimensional space is real. Natural processes are defined by their description within the system of laws of nature. To the extent that a process is described by rules that exist independent of natural laws, that process falls outside of nature. That does not mean that brains are not physical. It does not mean that we do not need functioning brains to think. It means that when brains are functioning at a certain level, something else begins to occur--thought--that transcends the interlocked system of nature. What does this transcendence imply? That's another issue. But if nothing else, it definitely implies that naturalism is an incomplete description of of reality.

Doctor Logic said...

Darek,

Sorry for taking so long to respond.

It seems like we're not getting past something.

You agree that the rules of inference do not impose necessities on minds because they do not compel us to think rationally.

On the other hand, naturalism says that the world is governed by rules that impose necessities (and what is left is random).

Then you say:

Thought processes, perhaps, are described by both the laws of chemistry and the rules of inference.

Were thought processes necessitated by both sets of rules, naturalism might indeed have a problem. However, the action of physical minds is necessitated by physics, not by the rules of inference. Not all thought processes are rational.

So there is no problem for naturalism. It's perfectly plausible that physics could cause a mind to favor the rules of inference because proper execution of the rules of inference generally provides a survival advantage. Such a loose, unnecessary coupling can explain the connection between physical minds and rules of inference very well.

One other thought. I think we're looking at a sort of cognitive-anthropic effect. Any being capable of appreciating the arguments here (or naturalism), must value the rules of inference. However, that does not mean that the rules of inference are necessary in general. They are necessary only for beings practicing rational thought, and rational thought isn't necessary.

Darek Barefoot said...

DL

I also apologize for being a bit slow to get back to this.

>>You agree that the rules of inference do not impose necessities on minds because they do not compel us to think rationally.<<

Well, yes and no. I was trying to avoid muddying the waters by needlessly bringing volition into the discussion. I might claim that the laws of physics do not compel me to play golf, but that if I choose to play golf, the laws of physics will compel me to hold and swing the club a certain way in order to hit the ball. But, for the sake of argument, physics may compel me to choose to play golf and so I am compelled altogether hold the golf club a certain way.

Likewise, if I attend comprehendingly to certain premises, then my conclusion from them must be a certain way. I may even be compelled rationally to a conclusion I would rather not reach. If laws of physics (in the form of biochemistry) compell me to comprehend the premises, and comprehending the premises constrains the conclusion, then physics must indeed be constraining me to think rationally on those occasions when I do so. But for that to be the case, the rules of inference again would have to be dependently interconnected with the laws of physics--which they cannot be.

Notice that in philosophy of science discussions nomological description and nomological necessity are more or less interchangeable or at least inseparable.

Doctor Logic said...

Darek,

Please let's avoid the tautological statement that "when I think rationally, I necessarily think rationally." That statement can be made about any contingent event.

Consider an actual natural law like conservation of electric charge. This law says that in any closed system, the net charge in the initial state equals the net charge in the final state. This is true for all initial conditions. I don't care which initial state you give me, the final state will have the same net electric charge.

There's no such law regarding rationality. It is not the case that any initial state will produce a rational inference by the time it reaches the final state. We can only say that if the initial conditions are favorable, then rational inference will occur. If that were the standard for a law, then I can declare a law for any contingency I want, so as long as I require favorable initial conditions. For example, there would be "rules of irrationality", because if I set up the initial conditions right, no inference (or wrong inference) will result.

That means that the rules of rational inference are not physical laws. If minds are brains, rational thought is something that can/might happen, and such thoughts will be decoupled (or loosely-coupled) from pure physics.

You seem to argue that the rules of inference are different from other contingencies because we cannot rationally find those rules to be otherwise. The problem with your argument is the word "rationally," which confines us to initial conditions in which the rules of inference hold. It's no surprise that systems whose initial state is normatively rational will necessarily find that the rules of rational inference ought to be the case for any thinking system.

The rules of rational inference only have value when the initial state is specially pre-selected to value rational thinking (like we do), and that makes rationality contingent and merely loosely-coupled to natural law.

Darek Barefoot said...

DL

>>If that were the standard for a law, then I can declare a law for any contingency I want, so as long as I require favorable initial conditions.<<

The laws of chemistry do not apply to all physical states. They do not apply to high energy particle collisions in an accelerator, for example. Certain initial conditions must be present in order for a process to be described under the laws of chemistry, and the laws of chemistry are "helpless" (if I can use that word) to bring those conditions about. Those conditions come about due to processes that are described by more fundamental laws of physics. I suppose we could say that this is tautological: when a process is chemical, it can be described under laws of chemistry and vice versa.

To put it differently, there is a narrow frame of reference withhin which the laws of chemistry seem to constrain physical states. Alternatively there exists a broader frame of reference within which it seems as if certain processes simply begin to occur, for non-chemical reasons, and then proceed in such a way that they can be described in chemical terms. From within the narrow frame of reference, the laws of chemistry seem to have genuine power to constrain states in certain ways. From a broader frame of reference that includes more fundamental non-chemical processes, the "laws of chemistry" seem more like descriptions than constraining forces. The real power seems to lie in the laws that obtain all the way across this more general frame of reference.

We can apply this reasoning using the laws of heredity or genetics to define the narrow frame of reference and the laws of chemistry to define the broader and more fundamental frame of reference. Speaking strictly within the confines of reproductive dynamics, the laws of heredity seem to exert real force. Placing heredity in the context of chemical interactions along chromosomes, the laws of heredity seem merely like convenient descriptions of a narrow class of processes that sometimes occur and sometimes do not--for reasons entirely outside the laws of genetics.

Notice that when we pass from one frame of reference to another, compulsion seems to evaporate into mere description. But we do not as a result conclude that processes are only loosely interconnected, just the opposite. The laws of chemistry seem merely descriptive in the context of fundamental physics precisely to the extent that they are dependent upon more fundamental physical law. No "loosely" about it. The laws of chemistry are the way they are solely because the laws of fundamental physics are the way they are.

Naturalism tempts us to put reasoning processes into this hierarchy. It would belong within (or above) chemistry or perhaps organic chemistry. When we are within the frame of reference of systematic thought, how the premises are apprehended determines the nature of the conclusion reached from them. But step back into the frame of reference of chemistry, and this seems merely descriptive of the way things happen when certain conditions come about--for reasons having nothing to do with rationality. Again, this picture requires that the rules of inference are the way they are because the laws of chemistry are the way they are, just as the laws of chemistry are the way they are because the laws of fundamental physics are the way they are.

Doctor Logic said...

Darek,

Those conditions come about due to processes that are described by more fundamental laws of physics. I suppose we could say that this is tautological: when a process is chemical, it can be described under laws of chemistry and vice versa.

This certainly is tautological which is why a scientist would never say this.

A scientist would say that when energy levels are low, matter density is high, and matter composition is stable, then you get the laws of chemistry. That's not a tautology.

A geneticist would say that any process that has sexual reproduction with genes will exhibit the laws of heredity. She will also say that cells with DNA are mere examples of such systems. This is not tautological. It would be tautological if she said that "when a system obeys the laws of heredity, it can be described by the laws of heredity."

The interesting part of the action is in saying under what conditions higher-order rules emerge from lower-order ones.

But step back into the frame of reference of chemistry, and this seems merely descriptive of the way things happen when certain conditions come about--for reasons having nothing to do with rationality.

There's no reason why the laws of chemistry ought to reflect the entities described by rationality.

Indeed, chemistry does not contain in its fundamental rule-set anything about heredity. In fundamental chemistry, there is no such thing as a mother, father, replicator, child, gene, sex or survival attribute. The thing that permits us to reduce human heredity to chemistry is our ability to conceive of (and test for) chemical configurations that implement mothers, fathers, genes, etc.

So, if human rationality reduces to chemistry and physics, we ought not expect fundamental physics to refer to thoughts about ideas, thoughts of propositions, thoughts of truth, perception, etc. We should only expect to one day identify the physical implementation of thoughts. And there may very well be many such implementations just as there are many implementations of typewriters or wings or hereditary systems.

Again, this picture requires that the rules of inference are the way they are because the laws of chemistry are the way they are, just as the laws of chemistry are the way they are because the laws of fundamental physics are the way they are.

Note that these layers are only fixed and locked when we have specifically fixed the implementation at every layer boundary. In general, every lower layer may have multiple possible implementations of the upper layer, and at every upper layer we can imagine alternative physics at the lower level that provides an implementation. That's where your cross-universe portability comes from. That's why the layers are fluid until the specifics are filled in.

Upward Example: Just because heredity is implemented by DNA in humans does not mean we could not implement heredity for another context in some other chemical fashion.

Downward Example: If all I tell you is that I have a hereditary system, you don't know what kind of lower level the system is implemented upon (nor even which physical universe forms the basis of the lower level). For all you know, it is running on a computer simulation made in another universe with radically different laws.

Darek Barefoot said...

DL

>>A scientist would say that when energy levels are low, matter density is high, and matter composition is stable, then you get the laws of chemistry. That's not a tautology.<<

It is if "stable" refers to forms that are recognizable by the roles they play in chemical reactions--for example, if "atoms" are defined as objects with, among other things, the property of being able to form certain types of bonds. Otherwise we have to imagine objects that are recognizable as atoms, yet are incapable of forming bonds in the ways necessary for chemistry.

>>A geneticist would say that any process that has sexual reproduction with genes will exhibit the laws of heredity.<<

This is tautological if "sexual reproduction" and "genes" are in fact defined within the context of the laws of heredity. Equivalent to, "a geneticist would say that any process that has the entities referred to in the laws of heredity will exhibit the laws of heredity." Otherwise, we have to imagine "sexual reproduction" and "genes" that are recognizably such but do not take the roles they do under the laws of heredity.

Now, suppose you are correct. There can be low-temperature, stable forms of matter whose interactions cannot be described by the laws of chemistry. There can be what we would recognize as "sexual reproduction" and "genes" that nevertheless are not described by the laws of heredity. By analogy, that means that there could be what we would recognize as "premises," "truth," and "conclusions" that nevertheless would not be described by the rules of inference.

At any rate, perhaps we have this much settled:

1) There are processes that are described by the rules of inference.

2) The rules of inference stand in relation to the laws of chemistry in substantially the same way that the laws of chemistry stand in relation to the laws of particle physics.

Note that these two points by themselves allow for your claim of multiple realizability. You say that the laws of chemistry are multiply realizable and likewise that the rules of inference are multiply realizable. So, whatever else, can you agree with 1 and 2?

Darek Barefoot said...

DL

Excuse me. I should have made clear in my last post that the two claims I listed are what naturalism necessarily leaves us with, not that I am ultimately advocating the second of them. The process of thought in human beings requires brain activity, and brain activity is undeniably chemical in nature. Given naturalism, "thought" must stand in relation to "brain" much the way that "photosynthesis" stands in relation to "leaf" and "respiration" stands in relation to "lung." Even if all these processes could be realized non-chemically, to the extent that we know them as physical processes we know them as chemical processes.

Doctor Logic said...

Darek,

I wrote a number of paragraphs describing why I was uneasy moving forward, but when I finished I realized where our disconnect is (so I'll skip the paragraphs I wrote :)).

Our disconnect is that the rules of inference are moral laws, not physical/natural ones.

At the level of thought, the entities are propositions, inferences, concepts and generalizations. All of these entities are thoughts. The rules of inference is that set of thought transitions that maintains non-contradiction and identity.

This means that the chemical analogue of the rules of inference would be something like the list of substances that burn exothermically in air. The "rule of exothermic burning" says which species of substance one needs in order to have exothermic burning, or what processes one must follow to make such substances.

Just as the rules of inference don't constrain irrational minds to be rational, the rules of exothermic burning do not constrain inert substances to burn exothermically in air. Both sets of rules describe possible states, desirable states perhaps, not necessary ones. They are both oughts.

If you want thoughts consistent with logic (generate heat by burning substances in air), then you ought to think according to the rules of rationality (burn substances according to their flammability).

I think this is the key issue we have been missing. The rules you are talking about are moral rules, not physical ones. Physics tells us which stuff burns and which stuff doesn't, but it doesn't say there's a rule that one ought to have flammable stuff. It can only tell you what stuff to burn if you wanted to generate heat.

Similarly, a physical model of the mind would tell us that there are logical thoughts and illogical ones, but it doesn't say there's any absolute rule that one ought to think rationally. Evolution may point to survival advantages of rational thinking, but survival isn't an ought either. At best, physics will describe why we feel we ought to achieve a goal, but it won't say we objectively ought to reach it. It will tell us what physical thought sequences we ought to follow if rational thinking is desired.

Darek Barefoot said...

DL

I'll get to your point about values in a moment.

>>At the level of thought, the entities are propositions, inferences, concepts and generalizations. All of these entities are thoughts. The rules of inference is that set of thought transitions that maintains non-contradiction and identity.<<

Perhaps you mean that the rules of inference constitute a set of types of thought transitions. And the rules of inference develop the application of principles such as identity and non-contradiction in interesting ways.

>>This means that the chemical analogue of the rules of inference would be something like the list of substances that burn exothermically in air. The "rule of exothermic burning" says which species of substance one needs in order to have exothermic burning, or what processes one must follow to make such substances.<<

One of the ways that rules can be thought of is as descriptions of relations. Special relativity describes certain relations between mass, time and velocity. General relativity describes relations between mass, space and acceleration, among other things. The laws of electromagnetism describe relations between charged bodies. We could set up "rules of exothermic burning" that would describe those relations between chemical substances that are evident in certain instances of combustion.

The rules of inference describe relations among premises--or, we could say, between propositions or ideas or thoughts about how things are or how they might be. When we survey thought sequences, we see them falling into types and patterns, just as with physical events. How do we identify or classify these types of sequences? The rules of inference provide an answer. The process of classification is non-trivial because the types are real and objective. We are not picking out thought sequences to form a subset consisting of thought sequences we happen to pick out.

So far there are some key resemblances between laws of nature as describing relationships and rules of inference as doing so. However, the rules of inference are necessary in a way that relativity, laws of electromagnetism, and even our hypothetical rules of exothermic burning are not. There is both similarity and distinction.

Let's say we have actually formulated our rules of exothermic burning. Why do our "rules of e.b." look the way they do? One answer would be that they could not be otherwise. In other words, we could deny that the question makes any sense. But if e.b. relationships are part of the broader scheme of nature, the question does make sense because it has an interesting answer. The rules of e.b. have the shape they do because there are underlying physical laws that determine e.b. relationships--laws that describe more than just e.b.

Note that the fundamental laws that give the rules of e.b. their shape are fundamental precisely because they explain not only e.b. but non-e.b. relationships. They put e.b. into a broader physical context. The formulations of Q.M. are fundamental to the laws of chemistry because they pertain to more than chemical relationships; they place chemistry into a broader context.

As soon as we ask why the rules of inference have the shape they do, the analogy breaks down. The answer that was unsatisfying in the case of e.b., that the rules simply must be so, seems acceptable in the case of rules of inference. On second thought, we might propose that the rules of inference are as they are because of the principle of non-contradition. But the analogy is still broken because the principle of non-contradition is not inferred from observation as are fundamental laws of nature. We bring non-contradiction to the process of inferring the laws of nature, so we can't very well claim that we derive it from that process.

All we have to do is invert our answers and try to explain the rules of e.b. as deriving in some interesting way from the principle of non-contraction. And we find that we cannot do so.

Your reference to values is interesting. An "ought" can be applied to either following a certain procedural rules based in laws of nature or following the rules of inference. But that does not speak to the necessity or lack of necessity that the rules have the form they do in either case.

Look, I don't mean to browbeat you. I am ready to call it quits if we are just going around in circles. I think we have done some genuine exploration of the issue, but at some point it turns into tomayto/tomahto and if we have reached it I'm willing to move on to more fruitful endeavors.

Bryan said...

Pun not intended, I trust.

Doctor Logic said...

Hi Darek,

I agree that there is some objective distinction underlying these oughts. One distinction may not be objectively better than another, but there has to be an objective distinction underneath.

On second thought, we might propose that the rules of inference are as they are because of the principle of non-contradiction.

This was my thought, sort of. I really mean that the laws of non-contradiction provides us with the objective distinction between consistent and inconsistent thought patterns.

But the analogy is still broken because the principle of non-contradiction is not inferred from observation as are fundamental laws of nature. We bring non-contradiction to the process of inferring the laws of nature, so we can't very well claim that we derive it from that process.

I don't think this objection works, for many reasons.

First of all, you are introducing a new criterion, namely, the manner in which the rule is inferred. I don't immediately see why that has any relevance.

Second, it is our experiments and experiences relating to EM that enable us to infer that EM distinctions exist. As we now know, we used our own electromagnetic construction to discover EM. That does not throw our discovery into doubt.

Third, if non-contradiction is the first law of any lawful universe, there's no reason to give it any particularly special status over the second, third, or Nth laws of such a universe. If minds are physical systems, that does not prevent them from inferring the laws of their universe.

Remember, the rules of inference are applied by properly thinking systems. Such systems generally prefer that thoughts are consistent by some measure. However, brains (and minds) don't have to be consistent thought-wise, even if they are consistent physically. The universal law of non-contradiction provides for the possibility of consistent thinking, and establishes a distinction between consistent and inconsistent thought. I don't see how the means of our discovery of universal non-contradiction is relevant the the physicality of minds.

Fourth, you seem to be suggesting that we invented the conception of non-contradiction, so there cannot be a law of non-contradiction that precedes us. I'm sure you see what's wrong your idea as I am reading it. Do you mean something else?

Darek, I don't feel browbeaten. :) I found our conversation quite stimulating, and I have a better understanding of the terrain. Thank you for participating!

Darek Barefoot said...

Bryan

I guess it depends on whether the tomato is a vegetable or a fruit. But that is not a question I care to pursue!


DL

>>First of all, you are introducing a new criterion, namely, the manner in which the rule is inferred. I don't immediately see why that has any relevance.<<

How we come to know about a thing is directly related to the kind of thing that it is. Examples are so numerous and obvious that I won't bother with them.

The rules of inference are necessary truths. Necessary truths are not inferred the same way as are contingent propositions. The LUG, the laws of chemistry, and the laws of EM are contingent, not necessary. The distinction between necessary truths and contingent propositions is a valid distinction, don't you think?

>>Second, it is our experiments and experiences relating to EM that enable us to infer that EM distinctions exist. As we now know, we used our own electromagnetic construction to discover EM. That does not throw our discovery into doubt.<<

The laws of nature are hypthesized, then the hypotheses are tested against experience for confirmation/disconfirmation/revision. Knowledge of some necessary truths is required for the testing process, not to mention the idea of testing in the first place. To the extent that we perceive mathematical principles to be necessarily true, we rely on them in evaluating hypotheses. We cannot claim that as we are evaluating a hypothesis by mathematical analysis of test results, we are simultaneously evaluting mathematical principles. Nor can we make that claim about the rules of inference.

Take the commutative law of addition. To the extent that it is a necessary truth, it is not subject to hypothesis, testing and confirmation. If we arrived at the CLA the same way we arrived at the LUG, it would be subject to progressive confirmation by experience. But the CLA is not subject to such confirmation, therefore we did not arrive at it the same way.

Earlier you mentioned earlier Fermat's Last Theorem. That theorem is not subject to scientific evaluation as if it were a hypothetical law of nature. There is no experiment that could confirm or disconfirm it. Instead, those of us with sufficient analytical skill must simply study it to see if it derives from other necessary truths.

>>Third, if non-contradiction is the first law of any lawful universe, there's no reason to give it any particularly special status over the second, third, or Nth laws of such a universe.<<

Again, if non-contradiction is a necessary truth, it is not a law of nature. Laws of nature are contingent. What experiment could be devised to confirm or disconfirm the principle of non-contradiction? Non-contradiction must be assumed in order to confirm or disconfirm contingent propositions.

>>Fourth, you seem to be suggesting that we invented the conception of non-contradiction, so there cannot be a law of non-contradiction that precedes us.<<

Not at all. I am suggesting that we do not know about non-contradiction the same way we know about the LUG, the laws of EM, Quantum Mechanics, etc.

Think of it this way: In the old British empirical tradition, nature is that which we sense. In modern scientific terms, nature is that about which we form hypotheses that can be tested against experience. Non-contradiction, the laws of mathematics and the rules of inference cannot be tested against experience; they are what make testing against experience possible.

To restate, laws that are necessary truths fall outside the definition of nature as that about which we form testable hypotheses.