How Brutish are Brute Facts?

[harvey1]

QED and I started discussing this subject on the nature of brute facts on another thread in the Christianity sub-forum. However, I wanted to make this discussion a separate thread so we can fully explore this subject matter:

The cost of atheism is that we have to believe something is a brute fact that happens to be the most complex object we have ever observed. In fact, so complex is it, that we can't come anywhere close to emulating such a design using supercomputers and the like, yet you expect us to believe such a departure from parsimony as being parsimonious!

I have pointed out to you often that this argument carries no weight because the nature of discovery and human understanding is fickle. It is an indisputable fact that we frequently miss that which is right-in-front-of-our-noses because we are often using the wrong tools or mindset. This is, after all, what we keep accusing each other with in many of our discsussions. So I am adamant that we cannot use our lack of savvy to assess the possibility or complexity of an unknown entity.

Let me put your argument in a more formal form so it is easier for me to point out the fallacious nature of that argument:

1. Brute facts are needed in every ultimate explanation of the world
2. The brute fact for atheism is that there is a (meta)universe
3. There are no prescriptive laws that determine or restrict brute facts
4. We have no way to evaluate the complexity, likelihood, or probability of this (meta)universe brute fact to bring about universes such as our own
5. There's no reason based on (4) to believe that it ought to be obvious or simple to simulate a world which naturally produces complexity that in principle can bring about universes such as our own
6. The observable universe can naturally be explained in terms of a brute fact (meta)universe that is allowed to evolve over time such that at some point in this process our universe naturally appears
7. The brute fact (meta)universe, according to (6), is a natural explanation
8. Occam's razor requires that we believe the most parsimonious explanation--which translates into a natural explanation

...9C. The universe is a consequence of a brute fact (meta)universe needing no God to explain its existence: God is unlikely to exist

Now, I'm sure you would like to make changes to the above argument, however I think no matter how you change it, it is a faulty argument. For example, (3) appears to contradict (4). If there are no prescriptive law limitations that determine the brutish nature of your brute fact (meta)universe, then absolutely anything is possible even brute fact scenarios that do not lead to universes with sophisticated structures. However, if anything is possible, then we do have a means to gauge likelihood. We have many conceptions of behaviors that the (meta)universe could have exhibited as a brute fact behavior. There are literally thousands or millions of behaviors that we can imagine that would never produce a universe such as our own. Hence, it appears the likelihood of a (meta)universe having a behavior that evolves sophisticated structures as our own looks diminishing small compared to the large number of brute fact (meta)universes that would not do anything of the sort. Hence, (4) is false. If (4) is false, the (5) is false. If (5) is false, then this is not a parsimonious solution (7), and hence it violates Occam's razor ( 8 ), and therefore not only is your conclusion false, but any explanation that doesn't violate Occam's razor should be more likely to be considered true (e.g., a belief in an Omniscient Interpeter, God).

If the [meta]universe was to evolve, it had to allow complex structures to evolve. This behavior cannot be programmed, not anything close. I realize you think that there might be a set of behaviors out there that a 1-billion line cellular automata algorithm could accurately simulate which does the trick, but that still doesn't answer why the metauniverse didn't have a behavior that a 10 line cellular automata algorithm would describe (e.g., a "beacon" metauniverse). Why do we not live in a beacon universe? We know your answer: "because we don't." But, that is not a good answer.

Do you deny that the majority of the worlds cosmologists working today are willing to accept scenarios where this is not the only universe that ever existed? If it rarely came up for serious consideration, that might make it "not a good answer" but I think you'll find it is a better answer than that.

QED, you're mixing up this issue. Cosmologists proceed based on prescriptive laws that other universes are likely given those prescriptive laws (e.g., quantum cosmological laws, or inflationary laws due to quantum laws, etc.). What you are saying of a brute fact (meta)universe has absolutely nothing in common with these scientific theories. You aren't basing your views on any law. You are basing it on a brute fact that has no prescriptive law that determines its truth or falsity. In fact, it is very difficult for me to access how it is that a principle of parsimony is even a concern for you since a principle of parsimony would be a prescriptive law, and you say there are no prescriptive laws. So, why do you limit brute facts to a principle of parsimony as a prescriptive law? Of course, if you don't do that, then your view becomes an irrational view, and as we agree, if there is a rational explanation and an irrational explanation, we are obligated to give precedence to the rational explanation.

[Bugmaster]

Logical implication is a rule that functions in any consistantly defined universe since all bases for logic are necessarily the case in such a universe (namely such things as a=a, a (not =) (not a), a and (not a) = contradiction, etc).

Sorry, but what do you mean by "consistently defined" ?

I personally would contend that, in our own universe, the laws of logic and math exist solely as constructs in our heads. We use them to comprehend and organize the real world, but they in themselves are not real. If we wanted to, we could make up totally different laws of logic, and use them to comprehend the world in some different way; in fact, "fuzzy logic", which deals with probabilities rather than absolutes, does just that.

[harvey1]

I don't buy premise 2, since it is quite possible to have logical implication without causation.

Here's my reducio ad absurdum argument again:

1. A principle of causality does not exist
2. If there is no causality principle, then a consequent cannot follow from an antecedent
3. Therefore, the consequent is causally not related to the antecedent

In your example, there are consequents so there must be a causal relation subtly stated in your argument (I'll mention the reason why this is so). And, we see that there is. The brute fact is, "all even numbers in this universe have a vowel to the right of them." If there were no principle of causality in this hypothetical universe, then we could not state, "8 is an even number in this universe, therefore 8 has a vowel to the right of it."

The reason is that logical implication, as Bugmaster pointed out, is an abstraction. It must refer to something when talking about a universe. When you say, "then... therefore..." you are talking about that hypothetical world, in which case it is no longer just an abstraction, you are talking about a state of affairs.

This state of affairs expresses a causal relation when referring to the world (and it is an abstraction when referring to mathematics or logic). In the case of referring to the world, the causality enters because the brute fact itself requires a causal relation. That is, "all even numbers in this universe have a vowel to the right of them," and because this contingent fact is true (i.e., the statement of such a contingent fact corresponds and coheres with the state of affairs of there being even numbers in this universe having a vowel to the right of them), we can in fact conclude that "8 has a vowel to the right of it." If there were no principle of causality, there is no principle by which to base a progression from premise to conclusion. It would be impossible for there to exist a secondary consequent relation since the only way that relation could exist is if it is a result referring to something taking place in the hypothetical world.

[harvey1]

I personally would contend that, in our own universe, the laws of logic and math exist solely as constructs in our heads. We use them to comprehend and organize the real world, but they in themselves are not real.

I agree that logical implication must refer to some state of affairs. Although, I disagree with you that logic and math exist solely as constructs in our head. In my view, logic and math restrict what is possible given what is true of our world (e.g., given the laws of physics for our world). For example, if we assume that all of Euclid's axioms are true, then space is flat. That is, there are no possible worlds where space is curved, and all of Euclid's axioms are true. The reason is that a possible state of affairs (or possible universe) is dictated by the laws of that universe. A principle of causality (a primitive law) exists that forbids a possible universe that is not dictated by the laws of that universe. Logical implication refers to a state of affairs, and the state of affairs is caused by the logical implication. The logical implication reduces to a principle of causality (or God) which is primitive.

If we wanted to, we could make up totally different laws of logic, and use them to comprehend the world in some different way; in fact, "fuzzy logic", which deals with probabilities rather than absolutes, does just that

We could, and we often do, but then someone like Dyson would come along and show that there is a way to translate from one scheme to another which makes them equivalent. So, pi would still be pi, and the golden ratio would still be the golden ratio.

[Bugmaster]

Although, I disagree with you that logic and math exist solely as constructs in our head. In my view, logic and math restrict what is possible given what is true of our world (e.g., given the laws of physics for our world). For example, if we assume that all of Euclid's axioms are true, then space is flat. That is, there are no possible worlds where space is curved, and all of Euclid's axioms are true.

I think you are confusing three different things:

1). Our model of the real world
2). The tools we use to construct this model (that'd be the geometry)
3). The real world

When we want to model our universe in some way, we construct a model, saying, "to the best of our knowledge, space is flat". We then use some logic and math that we made up in order to solidify this model: "when I say flat, I really mean that parallel lines do not intersect, etc." Our model may be wrong, or it may be right, but it doesn't actually affect what's real and what isn't, no more than singing (just as an example) does. This illustrates the confusion between #1 and #3.

Note that we can actually use different tools to construct models of the same thing. For example, electric current can be modeled either with complex numbers, or with lots of trigonometry functions; it's up to you to choose which tool you'll end up using. For another example, you could count things in base 10 or base 2 or whatever base you want; you don't change anything in the real world by switching to a different base. This illustrates the confusion between #2 and #3, as well as #2 and #1.

Logical implication refers to a state of affairs, and the state of affairs is caused by the logical implication.

I do not understand what this sentence means... Do you mean to say that I can move objects in the real world by thinking about logical implications in my head ? That can't be right...

We could, and we often do, but then someone like Dyson would come along and show that there is a way to translate from one scheme to another which makes them equivalent.

That's not entirely true. You cannot translate from fuzzy logic to regular logic, AFAIK, though it's been a while since I studied this.

In any case, the possibility of translating from one scheme to another does not automatically imply that these schemes are anything more than concepts in our heads.

[harvey1]

I think you are confusing three different things:

1). Our model of the real world
2). The tools we use to construct this model (that'd be the geometry)
3). The real world

Thanks for your elucidation. It will help in my reply, I think.

Our model may be wrong, or it may be right, but it doesn't actually affect what's real and what isn't, no more than singing (just as an example) does. This illustrates the confusion between #1 and #3.

True. However, there's something missing in your answer. In the case of quarks, the reason we say there are quarks is because there's a quark model. The quark model refers to particle interaction models which identify hadrons, muons, electrons, anti-particles, QED, etc.. The only access we have to the real world, is the model. In fact, the model tells us what is the real world. If the model is wrong, then we aren't talking about a real world, and our success at manipulating nature is based on false premises. So, our singing may not affect what's real, but if we don't sing, we have no idea what is real.

Note that we can actually use different tools to construct models of the same thing. For example, electric current can be modeled either with complex numbers, or with lots of trigonometry functions; it's up to you to choose which tool you'll end up using. For another example, you could count things in base 10 or base 2 or whatever base you want; you don't change anything in the real world by switching to a different base. This illustrates the confusion between #2 and #3, as well as #2 and #1.

Sure. And, we can use different language to describe a sunset. But, it is a sunset that is being described.

Logical implication refers to a state of affairs, and the state of affairs is caused by the logical implication.

I do not understand what this sentence means... Do you mean to say that I can move objects in the real world by thinking about logical implications in my head ? That can't be right...

We live in a causal world. That causal world obeys certain laws that humans have done a good job in modelling. The basis of any real world model is logico-mathematical implication. If the world all of a sudden didn't obey logical implication, then our ability to do science would cease. I'm saying that logical implication, or causal laws acting in the real world, are real. That is, they refer to a set of rules that reality plays by, and by knowing these rules that reality plays by we can directly see how one state of affairs can bring about another state of affairs. The rules cause one state to move to another state. We cannot by thought alone change the rules, thereby making a different state of affairs. The rules just "are" based on a chain of causal events that happened in the past (e.g., the big bang, symmetry breaking events of the laws of physics, etc.).

We could, and we often do, but then someone like Dyson would come along and show that there is a way to translate from one scheme to another which makes them equivalent.

That's not entirely true. You cannot translate from fuzzy logic to regular logic, AFAIK, though it's been a while since I studied this.

Okay, you're right. What I was referring to is the real world itself (i.e., the laws of physics), and I meant that we can construct the laws of physics using different languages (i.e., different formulations), but the formulations produce equivalent predictions. They can still be radically different interpetations that do not have every element that can be translated, but since their predictions are equivalent and we can translate the observables into the different formulations, the models themsevles are equivalent. For example, the Hamiltonian and Lagrangian are two different formulations, but they are able to provide the same results (just one may be more convenient than the other). On the other hand, there is evidentally a limit of how many formulations we can construct without reducing the formulation into its more recognizable form.

In any case, the possibility of translating from one scheme to another does not automatically imply that these schemes are anything more than concepts in our heads.

The problem I have with this statement is that if true, then the only means by which a model can be selected is based on its observational success. However, we know that's not true since there are aesthetic factors and parsimonious factors that models are selected for. In addition, as I mentioned above, models tell us what the real world is (e.g., in the case of particle physics), we are so far away from using our direct sense perceptions that if the models are not true depictions of the world, then there is no way to account for the success of particle physics. For example, the Eightfold way introduced by Murray Gell-Mann would be totally unreasonable to suggest that it was an invention given its simplicity and mathematical nature. True, someone could construct a model that gave us information of a missing particle yet to be discovered, but the simplicity and beauty of the correct theories demonstrate that nature is in certain respects simple and elegant. If we look at engineering as an example, even for simple drawings we don't see nearly the simplicity as this Gell-Mann model describing quarks and all fermion particle interactions. That would strongly suggest that our models are about truth.

[Bugmaster]

I've labeled your statements below, for easy referencing:

a). The only access we have to the real world, is the model. In fact, the model tells us what is the real world. If the model is wrong, then we aren't talking about a real world, and our success at manipulating nature is based on false premises...

b). And, we can use different language to describe a sunset. But, it is a sunset that is being described...

c). We live in a causal world. That causal world obeys certain laws that humans have done a good job in modelling. The basis of any real world model is logico-mathematical implication. If the world all of a sudden didn't obey logical implication, then our ability to do science would cease.

d). I'm saying that logical implication, or causal laws acting in the real world, are real. That is, they refer to a set of rules that reality plays by, and by knowing these rules that reality plays by we can directly see how one state of affairs can bring about another state of affairs.

Firstly, I think your statements (a) and (b) are in conflict with each other. If the only way we can know the real world is to use our model, then we cannot say, "in reality, all our models describe the same sunset" -- at least, we can't say that with certainty. The best we can hope for is, "to the best of our knowledge, there's something in this world that behaves very similarly to our sunset models".

I'm not sure what you mean by a "logico-mathematical implication" in statement (c). If you mean something along the lines of "a->b; a; therefore b", then you're not entirely correct. Science deals with probabilities, not "hardwired" boolean implications. However, I would obviously agree that science uses math and logic to build its models. However, when you say, "we live in a causal world", what you really mean is, "the world seems to work according to certain rules that fit our causality model". You're still talking in terms of models, just as in (a).

However, I don't see the justification for jumping from (a), (b), and (c) to (d). Statement (d) doesn't merely state, "our models seem to work", it says, "at least one of our models -- the implication -- describes the real world with 100% certainty". To me, this sounds pretty close to dualism, since implication is not the kind of thing that you can see or smell or measure in any way. Thus, the claim "implication is real" sounds quite extraordinary to me (along with other claims, such as "F=ma is 100% true for all cases"), and I'd need extraordinary evidence before I can believe in it.

On the other hand, there is evidentally a limit of how many formulations we can construct without reducing the formulation into its more recognizable form.

Is there really ? I haven't thought about this in depth, but it seems like I'd be able to construct any number of formulations of the same laws. At least, in the trivial case: for example, there's an infinite number of integer bases for math, and thus I could count objects in an infinite number of ways.

In any case, the possibility of translating from one scheme to another does not automatically imply that these schemes are anything more than concepts in our heads.

The problem I have with this statement is that if true, then the only means by which a model can be selected is based on its observational success. However, we know that's not true since there are aesthetic factors and parsimonious factors that models are selected for.

I would personally say that aesthetic and parsimonious factors are just heuristics that reduce the number of models you have to actually test (since testing is expensive in terms of time and money). Science ultimately is all about observational success; it doesn't matter how elegant your model is, you still need to test empirically in the end.

we are so far away from using our direct sense perceptions that if the models are not true depictions of the world, then there is no way to account for the success of particle physics.

I wouldn't call particle physics "true"; I'd only call it "pretty damn accurate". There's a big difference there. Newtonian mechanics is also pretty damn accurate in most cases.

but the simplicity and beauty of the correct theories demonstrate that nature is in certain respects simple and elegant. If we look at engineering as an example, even for simple drawings we don't see nearly the simplicity as this Gell-Mann model describing quarks and all fermion particle interactions. That would strongly suggest that our models are about truth.

Either that, or there's something about us humans that makes it very easy for us to break down complex natural phenomena into simple, elegant chunks, in order to understand them better. I think both explanations are at least equally plausible.

[harvey1]

I've labeled your statements below, for easy referencing:

a). The only access we have to the real world, is the model. In fact, the model tells us what is the real world. If the model is wrong, then we aren't talking about a real world, and our success at manipulating nature is based on false premises...

b). And, we can use different language to describe a sunset. But, it is a sunset that is being described...

c). We live in a causal world. That causal world obeys certain laws that humans have done a good job in modelling. The basis of any real world model is logico-mathematical implication. If the world all of a sudden didn't obey logical implication, then our ability to do science would cease.

d). I'm saying that logical implication, or causal laws acting in the real world, are real. That is, they refer to a set of rules that reality plays by, and by knowing these rules that reality plays by we can directly see how one state of affairs can bring about another state of affairs.

Firstly, I think your statements (a) and (b) are in conflict with each other. If the only way we can know the real world is to use our model, then we cannot say, "in reality, all our models describe the same sunset" -- at least, we can't say that with certainty.

In the case of a sunset, our main "model" is our own personal experience. However, we can use that main model to also construct other models of the same experience (e.g., poetry of a sunset). We use our personal experience to extend our knowledge to scientific models which may be very distant from personal experience. If the model is very far removed from personal experience (e.g., the detection of quarks), then we cannot rely on personal experiences at all. Therefore, our notion of real is dictated by the model and not the main model of our perceptions (at least directly). That's why (a) and (b) are not in conflict.

The best we can hope for is, "to the best of our knowledge, there's something in this world that behaves very similarly to our sunset models".

This is like saying the best we can hope for is, "to the best of our knowledge, there's a world for us to know that behaves very similar to the world our senses bring to our awareness." For example, if I were to learn how to speak Swahili, I might wonder whether I'm really learning Swahili, or just a good approximation of Swahili. Yet, if I am speaking Swahili, and understanding someone who speaks Swahili, and they say that they understand me, then on a principle of charity I have to assume that I indeed am speaking Swahili and that my colleague really does understand me when I say something in Swahili (e.g., "that a rabbit just ran by"). Now, it's always possible that I am not learning Swahili correctly--my word for rabbit is wrong, and even my Swahili friend doesn't think it's a rabbit in the first place. However, I am forced by this principle of charity to believe that I speak and understand real Swahili, and that my colleague really speaks and understands what I say and has the same definition of rabbit as I do.

Similarly, we are forced by a principle of charity to assume that there really is a world outside of ourselves. Of course, we cannot defeat extreme skepticism without having some kind of unproven belief, but this belief is justified even if it is unproven. There is room in this argument to include scientific models as being caused by real features of the world. It's true, we can't say for certain that our models are true, since there's always something that can be left out (just like my Swahili colleague might mean something different by his Swahili terms), but as an interpretation we are justified in believing that our language is from the same source (i.e., a result of the real world).

I'm not sure what you mean by a "logico-mathematical implication" in statement (c). If you mean something along the lines of "a->b; a; therefore b", then you're not entirely correct. Science deals with probabilities, not "hardwired" boolean implications. However, I would obviously agree that science uses math and logic to build its models. However, when you say, "we live in a causal world", what you really mean is, "the world seems to work according to certain rules that fit our causality model". You're still talking in terms of models, just as in (a).

Again, we have no reason to doubt that the world conforms to causal laws. Even probablistic laws are causal laws, just with an added feature in that they are not deterministic laws. For example, Born's postulate is a causal law, it's just not a deterministic law in the sense that we cannot predict the actual precise value of P(x). Let's put it this way, we have no more reason to doubt Born's postulate than we do each other's existence. Therefore, we are justified in some unproven beliefs by the mere fact that all of our beliefs are based on something as being unproven. Under certain special circumstances, some of the equations of physics (within the domain that they apply), justifies our belief in their reality as being the way they are because of some direct or indirect causal feature of the world (i.e., the way the world actually is). In the same manner, our personal experiences justify our belief in the reality of those experiences as being the way they are because of some direct or indirect causal feature of the world (i.e., the way the world actually is).

However, I don't see the justification for jumping from (a), (b), and (c) to (d). Statement (d) doesn't merely state, "our models seem to work", it says, "at least one of our models -- the implication -- describes the real world with 100% certainty". To me, this sounds pretty close to dualism, since implication is not the kind of thing that you can see or smell or measure in any way. Thus, the claim "implication is real" sounds quite extraordinary to me (along with other claims, such as "F=ma is 100% true for all cases"), and I'd need extraordinary evidence before I can believe in it.

I'm not suggesting that we know we have modelled logical implication in its purest form. For example, let's say that category theory is the actual language of reality, but let's say we are using set theory. In that instance, (d) is saying that set theory is indirectly referring to the language of category theory in an approximate fashion. However, there is an objective account of logical implication (i.e., in this example, category theory) that make up the real causal laws.

Of course, category theory, set theory, and every other formulation known to humans may be far removed from the primitive causal laws as they really are, but due to this principle of charity I mentioned above we are justified in believing that our sense of logical implication is a set of rules that reality plays by. We can pretty much know they are not the ultimate set of rules, but we are justified in believing that they are a set of rules that are causally related to the fundamental truths of the world (e.g., a principle of causality).

Is there really ? I haven't thought about this in depth, but it seems like I'd be able to construct any number of formulations of the same laws. At least, in the trivial case: for example, there's an infinite number of integer bases for math, and thus I could count objects in an infinite number of ways.

I'm talking about equivalent languages that are non-reducible. We can reduce or translate base 10 to base 2, and so on, but we may not be able to reduce category theory into set theory (or vice versa), but we can show how they can produce equivalent expressions of mathematics. I don't believe there's an infinite number of fundamental formulations. If so, then where are they? Set theory, although we can build all kinds of varieties (e.g., ZF, Neumann, etc.) is still a set theory. Similarly, if there are an infinite number of equivalent formulations of physics besides Lagrangian, Hamiltonian, Newtonian formulations, then where are they?

I would personally say that aesthetic and parsimonious factors are just heuristics that reduce the number of models you have to actually test (since testing is expensive in terms of time and money). Science ultimately is all about observational success; it doesn't matter how elegant your model is, you still need to test empirically in the end.

This seems to run contrary to the Quine-Duhem thesis which states that:

In words, the failure of some theory implies the failure of at least one of its underlying hypotheses. It is always possible to resurrect a falsified theory by claiming that only one of its underlying hypotheses is false; again, since there are an indeterminate number of such hypotheses, any theory can potentially be made compatible with any particular observation. Therefore it is in principle impossible to determine if a theory is false by reference to evidence.

I wouldn't call particle physics "true"; I'd only call it "pretty damn accurate". There's a big difference there. Newtonian mechanics is also pretty damn accurate in most cases.

In the domain where the theory is applicable, there is something true of these theories, otherwise they would only be lucky. For example, imagine a computer program that churned out random theories of the world. Imagine also, an army of robotic physicists each equipped with a lab that could make any real observation/experiment conceivable. The program churns out theories that make predictions, and just as quickly the robotic physicists test the theories. The theories that make correct predictions are published, and the theories that are wrong in their predictions are deleted from the harddisk. Now, in such a hypothetical world, these "physicists" are bound to produce theories that agree with observation, by definition. However, the theories themselves may be completely non-sensical. With enough hypotheses tacked onto a random theory, observables can be found to agree with what is observed. The theories have no basis in reality whatsoever because they don't reduce or expand into more comprehensive theories as current physics theories do. They are randomly connected.

Since this is not what we see in actuality, the idea behind anti-realism must be false. Hence, the models of science are mostly true, i.e., approximately true.

Either that, or there's something about us humans that makes it very easy for us to break down complex natural phenomena into simple, elegant chunks, in order to understand them better. I think both explanations are at least equally plausible.

I don't think postulating something internal to humans is a reasonable explanation. Engineers can reverse engineer a complex system, and the system is almost always a very complex explanation as to how it works, completely outside the grasp laypeople and engineers who are working on other projects. Even people on the same project are not able to grasp the generalities on a different but related component. Cosmologists, though, as they reverse engineer the causes of the universe, can utilize the quantum laws and general relativity laws to explain in principle just about everything we see. In fact, particle accelerators can recreate the environment of the universe when it was a trillionth of a second old. None of that makes a lick of sense if scientific anti-realism is correct.

[Bugmaster]

In the case of a sunset, our main "model" is our own personal experience.

I don't think that differentiating between personal experiences and other models is useful. After all, in my personal experience, the little yellow ball of the sun sets below the flat horizon. However, our current model tells us that the Sun is a mass of incandecent gas, a gigantic nuclear (*) furnace, where hydrogen is turned into helium, etc. Personal experience is just data for the model; looking at the Sun is no different (scientifically, at least) from reading a voltmeter.

(*) shouldn't the lyrics say, "thermonuclear" ?

This is like saying the best we can hope for is, "to the best of our knowledge, there's a world for us to know that behaves very similar to the world our senses bring to our awareness."

I would wholeheartedly support that statement. After all, I could be in the Matrix and not know it. It's extremely unlikely, but it's possible.

That's exactly what the principle of charity says. It doesn't say that the most parsimonious explanation is absolutely true; it just says that we should assume it to be true and move on, if we want to get anywhere.

Let's put it this way, we have no more reason to doubt Born's postulate than we do each other's existence.

I am actually not sure what Born's Postulate means (to my shame)... My quantum-fu is weak.

Anyway, I completely agree with you regarding unproven beliefs and the principle of parsimony. However, I disagree that abstract concepts, such as rules of logic and numbers, necessarily fall into the same category as scientific models.

I'm not suggesting that we know we have modelled logical implication in its purest form.

Unlike scientific models, implication does not leave room for error -- either you assume it, or you don't. Additionally, implication itself cannot be verified against anything in the real world, and neither can category theory. That's because the implication does not refer to any objects in the real world; it just refers to logical statements.

In other words, when you say, "F=ma", you're making a statement about the behavior of physical objects, such as rocks. You can go outside and test their behavior any time you want, and the results of the test will not depend on any definitions you have or have not made. Quantum physics also works in this way, only it requires more expensive equipment than just rocks.

Implication, on the other hand, deals with logical statements. You cannot go outside, pick up two logical statements, and see what they do. You can't test the implication against anything, because it's just something you assume to be true by definition.

Thus, I don't think you can use parsimony to conclude that the logical implication actually exists in some dualistic realm out there, because implication is fundamentally different from scientific theories. Yes, it's used as a building block in those theories, but nonetheless, it deals with a different subject entirely.

I don't believe there's an infinite number of fundamental formulations. If so, then where are they? Set theory, although we can build all kinds of varieties (e.g., ZF, Neumann, etc.) is still a set theory. Similarly, if there are an infinite number of equivalent formulations of physics besides Lagrangian, Hamiltonian, Newtonian formulations, then where are they?

We are getting into the realm of mathematics here, which, as I said above, deals with an entirely different subject than physics. Still, in pure mathematics, your statement doesn't work. I might as well ask, "well, if there's an infinite number of real numbers, then where are they ? List them for me !" You'd need some kind of a valid mathematical proof to determine whether "there's an infinite number of fundamental formulations", one way or the other... that's getting a bit off-topic, though.

In words, the failure of some theory implies the failure of at least one of its underlying hypotheses. It is always possible to resurrect a falsified theory by claiming that only one of its underlying hypotheses is false... Therefore it is in principle impossible to determine if a theory is false by reference to evidence.

I'm not sure this is right. If my theory predicts that this rock will float upward, and the rock falls downward, then my theory is false. You can always modify the theory, saying something like, "oh, only magnetic rocks float upward, not regular rocks", but the original theory is still false.

Now, in such a hypothetical world, these "physicists" are bound to produce theories that agree with observation, by definition. However, the theories themselves may be completely non-sensical. With enough hypotheses tacked onto a random theory, observables can be found to agree with what is observed. The theories have no basis in reality whatsoever because they don't reduce or expand into more comprehensive theories as current physics theories do. They are randomly connected.

Wait a sec, are they connected or aren't they ? If they are connected, then the robo-physicists can be augmented with an optimization scheme: keep the theories that explain the most phenomena at once. For example, let's say we have two phenomena: P1 and P2. We also have two theories: T1 predicts P1, and T2 predicts P2. When the computer randomly generates T3, which explains both P1 and P2, the robo-physicists will throw away T1 and T2 and keep T3.

Since this is not what we see in actuality, the idea behind anti-realism must be false. Hence, the models of science are mostly true, i.e., approximately true.

This is kinda what we see in actuality. We have electromagentism, and the electroweak force, and gravity, but we don't yet have electromagneweakgravity. We're getting there, but we're not there yet.

In any case, I never once said that I support anti-realism. On the contrary, I would completely agree with your statement about the models of science above. I simply don't think that logical implication is a scientific model.

I don't think postulating something internal to humans is a reasonable explanation. Engineers can reverse engineer a complex system, and the system is almost always a very complex explanation as to how it works...

This is a false analogy. Complex systems that are subject to reverse-engineering are constructed by humans. Thus, they would be built up of simple blocks, because humans tend to build systems like that to begin with, because (according to me, at least) humans find it easier to think in simple blocks.

Nature, however, was not built by humans, and thus is not subject to this analogy.

Anyway, again, let me restate my claim: I absolutely support scientific realism, but I deny that implication is a scientific theory, because its subject matter is logical statements, not real-world phenomena. Thus, there's no need to convince me that materialism is true, I'm convinced already :-)

[harvey1]

I absolutely support scientific realism, but I deny that implication is a scientific theory, because its subject matter is logical statements, not real-world phenomena. Thus, there's no need to convince me that materialism is true, I'm convinced already... I disagree that abstract concepts, such as rules of logic and numbers, necessarily fall into the same category as scientific models (...) Unlike scientific models, implication does not leave room for error -- either you assume it, or you don't. Additionally, implication itself cannot be verified against anything in the real world, and neither can category theory. That's because the implication does not refer to any objects in the real world; it just refers to logical statements (...) Implication...deals with logical statements. You cannot go outside, pick up two logical statements, and see what they do. You can't test the implication against anything, because it's just something you assume to be true by definition. Thus, I don't think you can use parsimony to conclude that the logical implication actually exists in some dualistic realm out there, because implication is fundamentally different from scientific theories. Yes, it's used as a building block in those theories, but nonetheless, it deals with a different subject entirely. (...) I would completely agree with your statement about the models of science above. I simply don't think that logical implication is a scientific model.

Let me draw an analogy to chess. Scientific models are like chess opening strategies (e.g., Réti Opening). Logical implication are the chess rules themselves. Now, if you accept that analogy, how can you be a realist about the Réti Opening, for example, but anti-realist about the rules themselves? The Réti Opening is based on the rules actually being the way they are. If the rules of reality are invented (which in this example they are since we are talking about chess), then how is the scientific model (Réti Opening) also itself not an invention? Now, if we happened to observe a chess-duplicate structure, and we noticed that the Réti Opening was a very popular event for this structure, why are we not entitled to say that this structure plays by the rules of chess, and that is why the Réti Opening is popular? I could very well imagine a chess analyst (a field of "mathematics" ) coming along and giving a proof that shows why the Réti Opening is probablistically more effective than many other possible moves. Why wouldn't that be sufficient reason in believing that chess rules (or the logical implication of chess) are real given that we find that structure in the universe?

[Bugmaster]

[Let me draw an analogy to chess. Scientific models are like chess opening strategies (e.g., Réti Opening). Logical implication are the chess rules themselves. Now, if you accept that analogy, how can you be a realist about the Réti Opening, for example, but anti-realist about the rules themselves?

Ok, I'll admit that my chess-fu is weak, as well. I'm not sure I can fully understand the analogy, but I don't think it applies.

Chess is an entirely made-up game; the rules for it were created solely by humans. Scientific laws, however, aim to describe the workings of the physical universe, which is independent of us humans.

Let me try and draw a little diagram to describe what I mean:

Code: Select all

   
  Things that exist only in our heads   |    Things that exist independently 
 ---------------------------------------+--------------------------------------
                                        |
  Our models of physical laws   -------------->  Physical laws 
    Mathematics                         |
    Logical implications                |
  Chess                                 |
 ---------------------------------------+--------------------------------------

EDIT: Sorry, I hit the Submit button by mistake. See continuation below.