Aug 05 2008
Is the Universe Logical?
Yes.
But I suppose you want a somewhat longer answer. This question comes up frequently among thoughtful skeptics, and also among critics of science. The critics often use a challenge to logic as a way of promoting relativism and the claim that we cannot really know anything. If all pretense to knowledge is ultimately vain and self-deception, they argue, then science holds no special position with regards to truth about the natural world. Therefore any crank notion is just as good as the mainstream scientific consensus.
When this line of reasoning is applied to logic (rather than the empiricism of science) the argument generally takes the form of – how do we know that logic, as currently defined, is correct? Perhaps it is just the way our brains work. A related question is – can the rules of logic be different in a different universe? Did we learn the rules of logic by observing our universe?
Here is a recent question on this topic from the SGU forums:
There is one challenge to materialism, though, that’s been giving me some trouble lately, so I’d love it if Dr. Novella could address it. This is sometimes called the Argument from Reason, and the basic claim is that materialism can’t make sense of reason and logic. If rational thought is nothing more than specific brain events, in what sense can those brain events be true, valid or sound, and other ones (e.g., brain events associated with logical fallacies) false, invalid or unsound? What is there to distinguish the brain thinking of modus ponens from the brain thinking of the fallacy of affirming the consequent? Thus, it would seem that the very logic and reason that is used to argue for materialism (as well as other conclusions) is undermined by materialism. If materialism is true, then it can’t be true (or false, for that matter).
The answer to these questions comes from understaning what logic is – it is simply an internal system, exactly like mathematics. Logic and math do not directly describe the outside world – therefore they are independent of the natural universe. They are systems of thought that require only internal consistency.
However, they also proceed from fundamental principles or assumptions that are so fundamental it would be absurd not to accept that they are true. At the very least they state their assumptions – in essence saying that if we assume these principles to be true, then various conclusions must follow.
For example, 1+1=2. This is true by definition – but the system of math indicates that it must always be true. It is fundamentally true. If you have one apple and I give you one apple, you have two apples.
Logic does the same thing – starting with the simplest statements that seem as if they must be true, and then carefully proceeding from there. For example, two true statements cannot contradict each other – they cannot be mutually exclusive. In other words, two true statements must be able to both be true at the same time. We can then build on such principles to more complex and subtle logic, but logic that is just as valid. Just as we can eventually get to calculus, building upon more basic mathematical principles – we can also derive fairly complex logical rules from simpler ones.
Valid logic cannot – by definition – be invalid. If the system is internally consistent and satisfies all fundamental rules, then it works.
Because such systems require only internal validity, I do not think that there can be a universe in which they are not valid. Therefore, 1+1=2 everywhere, even in a universe with different physical laws (if that is even possible).
But logic an math also do describe the real world. This does not mean, however, that they are dependent upon the physical world. Rather, they can be used to describe the real world because they are tools that can be used by empirical investigation – science. Science can use math and logic to construct its models of how the universe works. Scientific statements must be logically valid and mathematically correct, so math and logic help scientists arrive at conclusions about nature that are valid.
A scientific conclusion, however, requires more than math and logic – it also requires empirical data about the physical world. Therefore scientific conclusions, while they can be completely valid, may not be true if the empirical data is flawed. All scientific conclusions are also tentative, because all data is tentative.
To directly address the question above about materialism – the premise of the argument is that materialism is dependent upon logic, which is in turn dependent upon our material brains, and therefore materialism cannot confirm itself. But the second premise is not true – logic is not dependent upon our brains, it is what it is, an internally consistent system. Materialism is dependent upon logic only to the extent that, as an argument, it must be logically sound. But materialism is also an empirical claim about this universe, and it is therefore based to some extent also on observation. As an approach to understanding nature, materialism has worked well and continues to be very fruitful. It also does not violate logic, which is a minimum requirement for any conclusion.
For any claim to truth about physical reality we can therefore make two types of analysis. The first is about the logic of the claim. If it involved invalid logic, then the claim is not sound. This does not mean the conclusions are false, but it does mean we have no reason to accept it. A claim can therefore be rejected entirely on the basis of invalid logic.
The second type of analysis is the empirical support – the evidence. Does the evidence support or refute a particular claim. While logic can be black or white – it is either valid or not valid, evidence is never 100% for or against a claim, because data is never perfect. Regarding evidence we can only make tentative conclusions about the probability of being true or false. This probability can get very close to 100%, but never really achieve it.
In the end I think the question – is the Universe logical? – is not even a valid question. Logic is independent of the universe.
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43 Responses to “Is the Universe Logical?”
Materialism is the only possible way for the universe to work. For example, imagine the universe that Star Wars takes place in. In this universe, the force is a real explainable part of nature. To us it seems supernatural, but in the SW universe it follows consistent rules and can be learned and understood with enough time and skill. To them it is not supernatural. In much the same way, if magic were real, it would not represent a realm outside of the natural universe, it would represent a part of the universe we did not understand yet. As I once heard James Randi say, and I paraphrase, ” I would love for someone to prove psi, it would be a new science to study and try to understand”.
[...] into a kind of wishy washy Pascal’s Wager, “what if you’re wrong” gamut. Steven Novella has a great blog entry on this. The problem with this argument is that that it’s also a red herring. Even if they could [...]
But, if logic’s so cool…how come Kirk always beat Spock at tri-chess?
“Sacrificing all your pieces and wearing a dress was an illogical move Captain…I mean Jim.”
“Yep, and that’s why I’m the Captain “MR” Spock.”
[serious response : nice post DR. N]
I’m grinding my teeth here in abject jealousy at such a clear and concise addressment of such a universal question. What next? We learn Novella has a 98 mph fastball? *sigh*
Kudos on an excellent post, yet again.
So, logic is “independent of the natural universe” and is “not dependent upon our brains”. It seems plausible that “logic”, looking in on the physical universe from outside it, would confirm that the physical universe is indeed physical. But where is logic? Does it exist in a wider universe that contains logic, math and the physical universe. What else is in this wider universe?
You say logic and math are “systems of thought” but that they are “not dependent on our brains”. This seems to say that our brains express something that is not just a result of their physical functioning.
Interesting stuff.
“For example, 1+1=2. This is true by definition – but the system of math indicates that it must always be true. It is fundamentally true. If you have one apple and I give you one apple, you have two apples.”
But the two apples are not themselves ever exactly equal. So what you have is at best an approximate measure of appleness.
Logic also depends on inference, which in this case would have been that all apples are equal, and of course we know better – that the inference here is not valid. So perhaps the problem with measuring the universe is that we can’t know the validity of all necessary inference involved in doing so logically.
You might then say that while the universe is a priori measurable, we may not yet have perfected the tools by which we can “logically” do so.
juga: What I think Steve was implying is that logic is a system that holds true no matter what the circumstance. If you get to a conclusion that is wrong whether you’re talking about medicine, religion, UFO’s, or the universe and you used valid logic to get to that conclusion, then your premise (assumptions) must be wrong. So you can use logic with any system not just the universe, although, that’s what Steve focused on in this post.
Steve, I’m constantly getting into arguments with people about why logic is the only way we can describe the universe and everything we know, and I tell them (paranormal believers, pseudoscience believers, etc…) that it’s really not that the universe can’t be explained or understood any other way, just that science is the only method that has worked so far.
Am I wrong in saying that there is no real reason the universe has to be logical, there is just not any evidence that the universe doesn’t act in a logical fashion, and trying to discovered truths without logic has been futile?
Einstein had a good quote, something to the effect that as far as things are known to be true, it is not known if they apply to the universe and as far as things are known to apply to the universe it is not known if they are true or not.
This is the dichotomy between formal systems of mathematics and logic that Dr Novella is talking about and the actual universe. We don’t know “for sure” if they apply to the universe, but if an internally consistent system (mathematics and formal logic) doesn’t apply to the universe then no consistent system can apply to the universe.
I think that the universe is consistent and that the formal systems of mathematics and logic do apply to it. Exactly how remains unknown. I don’t think we need the appeal to incredulity that Dr Novella uses (“I do not think that there can be a universe in which they are not valid”), rather we are justified in using logic and mathematics as a default because logic and mathematics are internally consistent and so is any minimum system that must hold in any universe that has any type of consistency. If a system is not self-consistent it can’t hold anywhere.
Sorry apparently my brain had trouble decompressing the last paragraph I wrote, but I think you get the idea. Also, I tell people science and the use of well designed experiments is really the only way to come to a probable truth about any topic in medicine especially because of the complexity of the biological system.
I use this analogy, and would like to see if you think it’s valid: I tell people about the evolution of the understanding of the atom from Bohr to Schrodinger and how complicated things can be to describe the interactions on the atomic level. And to understand and mathematically describe the atomic interactions and then interactions with proteins and eventually the entire body and then on to the interactions of individual biological systems is entirely too complicated to describe on a purely logical basis of mathematics and we must invoke experimentally tested data to use as a premise whereby we can make logical jumps from.
Do you agree?
Roy, it is true that no two apples are exactly alike, but this is irrelevant. All that matters in that example is that the two apples satisfy the definition of a complete apple. Even if one apple was 1000 pounds and the other was a few ounces, you would still have two apples.
What if it’s consistently chaotic?
If math and logic were just ‘other ways of thinking’, then how come we have computers and technology? None would be possible without math and logic. What technical (non-artistic) accomplishments required other ‘ways of knowing’? If your ‘way of knowing’ does not corroborate with the real world, it cannot produce real results, like technology.
If ‘magic’ were a legitimate way of knowing, like in Lord of the Rings, then it would be able to produce useful technology, like magic rings and walking forests. So far these things remain in fiction.
So far, the best that the ‘other ways of knowing’ have come up with in any technical field is the exploitation of the placebo effect (which is in medicine), which is just a trick played on the mind. In the end, isn’t that what true magic is?
Superdave, you would still have two apples, but would have proved nothing by that example except that one and one are two. Hardly an example of qualitative or quantitative measurement.
Actually you wouldn’t “prove” one and one are two either – because by using apples you would have failed to demonstrate the definition of “two.”
Roy, I still disagree. All you have you have to do is define an apple and then take two of them. The apples do not need to be exactly the same if you only take the perspective that what defines them as apples are equal between the two.
If I add one and uno together I still have deux. That the languages used to represent each number are not the same does not mean the ideas and quantities they represent are different.
But this is not about defining apples, it’s about using apples as an example of how logic might be applied to a qualitative and quantitative analysis of the makeup of the universe. The underlying assumption in these “one and one are two” examples is that mathematics is an accurate system of quantitative and qualitative measurement, and that logic, to the extent that it is based on mathematics, is therefor similarly accurate.
The relevance of pointing out that no two apples are equal is that we will find that almost any other set of two apparently identical natural or material objects to be measured will not be exactly equal.
Any “truths” to be derived from such measurements will be at best an approximation.
Is the universe therefor logical? Yes, if we accept this as highly approximate to the truth.
Roy,
I disagree. Mathematics is not a system of measurement – but a formal system for manipulating numerical values. That 1x +1x = 2x is not dependent upon any measurement – it is an abstract concept that is valid because it is internally consistent. Measurement is only required when you apply mathematical concepts to physical reality – and therefore the description of physical reality will be dependent upon those measurements, but not the underlying system of math.
Also – some things are a matter of definition, not measurement. The application of math to apples is not really limited by measurement but by the ambiguity of the definition of apple. If the definition is metaphysically unambiguous, then 1 apple + 1 apple always equals 2 apples. This statement is mathematically valid and is therefore true to the extent that the definition of “apple” is unambiguous and contains all apples and excludes all non-apples.
Steven,
But as using it to demonstrate a function of logic, you have zeroed in on the very reason why the application of logic cannot do more than determine a degree of approximate truth.
And I think you are also wrong in saying mathematics is not a system of measurement, because that’s exactly what a formal system for manipulating numerical values is meant to accomplish. It may not be ONLY a system of measurement, but that wasn’t my contention.
The apple analogy is mathematically valid, but in my view represents the quintessential of logical fallacies as well. Because the inference to be drawn in your example was not valid.
Dr. Novella,
This is the first time I’ve heard of this philosophical problem, but it seems akin to the problem of induction, if I’m interpreting the original question correctly. Is the issue that one cannot justify the use of mathematics or logic from a materialist’s set of axioms (alone)? I suppose, I’m struggling to find the problem. In particular phrasing like, “if rational thought is nothing more than specific brain events, in what sense can those brain events be true, valid or sound, and other ones (e.g., brain events associated with logical fallacies) false, invalid or unsound,” seems to suggest that truth, validity and soundness are properties of brain states, as opposed to properties of (abstract) arguments.
I agree attacking this from the perspective of mathematics and logic as internally consistent, formal systems used for explaining the world is a good method of counter argument. However, I’m always hesitant to completely strip the world/universe away as a source of mathematical development, not to say these were the thoughts you expressed. I’m not a mathematical realist, but I do think observation of the universe, and cognitive abilities, like the ability to subitize, led to mathematical axioms, and are justifications for those axioms.
>The answer to these questions comes from understaning what >logic is – it is simply an internal system, exactly like mathematics. >Logic and math do not directly describe the outside world – >therefore they are independent of the natural universe. They are >systems of thought that require only internal consistency.
How about this for a counter argument:
Logic and Math do directly describe the outside world and were created by the human mind as an abstract language to organize the outside world. They cannot survive independently of the existing universe because they would then have no meaning. Counting has no meaning if there is nothing to count.
>Because such systems require only internal validity, I do not think >that there can be a universe in which they are not valid. >Therefore, 1+1=2 everywhere, even in a universe with different >physical laws (if that is even possible).
I agree that the laws of logic and basic math are so universal that they would be valid no matter which universe we were in. But I feel this is true because these basic laws are so fundamental that they define existence itself, not because they are merely internally consistent. Basically what I am saying is if 1+1=2 was not true or if two true statements contradicted each other in some universe, then that universe just could not exist. Perhaps we should rename these really fundamental laws from “universal” to “transuniversal” or “existential”
.
Then the laws of mathematics and/or logic would only be different in different universes depending on the different complex organization properties in that particular universe. For instance, if human beings lived in a strange universe in which the precise shapes of objects was less important and the objects kept changing shape, perhaps the natural language for physics in that universe would be combinatorics rather than calculus. However basic mathematic principles would have to be exactly the same in both universes else the second universe would not exist.
In conclusion: Logic and math do directly describe the outside world as we see it (even though I have just asserted it and tried to show that it is possible to think universally holding on to this assetion. Actually proving it is a little more involved). The fact that they require internal consistency is more a property of the law of existence and the law of indentity than the law of logic. If it were possible to have (or even conceive of) universes in which contradictory statements were true and objects with the exact same basic properties behaved differently etc. then any conscious entity in such a universe would simply create a logic in its own head based on the rules of logic that govern that particular universe and the basic principles of that system of logic would indeed be different from the basic principles we consider inviolable and true even outside of the universe.
Sajid,
If in your universe, you find you can conceive of ones and twos, then one plus one equals two ones. In this universe, that’s less a truth than a calculative procedure. The devil is in the details of its application. If you are in a universe (such as this) where it appears nothing can be divided into exactly equal proportions, then whatever the purpose of this application, the results can be expected to be no closer than an approximation of whatever reality you are attempting to measure, depict, model or otherwise understand.
The inviolable and true are traditional concepts with an uncertain future.
Why did I not study LOGIC in college and why were you not a professor at my University?! In so much that I could be aware of my appreciation in the future from the delight I would find in your blogs and podcasts…
Great Post!
Jack Vance wrote an interesting short story (among many such) with the premise that conditions in the universe suddenly change so that logic no longer gives humans a survival advantage. Quantum uncertainty effects become amplifiedso that the results of any actions are unpredictable. If you want to go north, you might as well step west, or stay still, for example. Under those conditions, people who leap before they look do just as well as those who try to plan rationally. Nothing complex could have evolved in such a universe, but the premise is that this ocurred as a change to a previously more deterministic universe, such as our own. (I got hooked on science-fiction at a young age because at its best it explores ideas like these.)
A flaw in the story that occurs to me now is that the macro physical manifestations of uncertainty described in the story ought to apply also at the neuron level, whereas some of the people in the story still retained the ability to think logically – but then again there was not complete chaos in the macro world either. Anyway, the story itself may not have been completely logically consistent, but it was an interesting story.
As an example of logic and mathematics that is consistent but does not apply to this universe, how about n-dimensional geometry (for suitable values of n)?
I also recall an anecdote about Euler that might be tangentially related to this topic, but this comment is tangential enough already.
For a good explanation of why 1+1=2 one should read Russel and Whitehead’s “Principia Mathematica”
This was a three volume work, with a fourth volume proposed but never finished. I’m told it was to be called the Uncertaintia Principia, subtitled, The New Quantum Apple, but then what do I know.
[...] Is the Universe Logical? [...]
One last comment about the conclusion reached in this post that “Logic is independent of the universe” That, unfortunately is the exact opposite of the case. Logic was and is dependent of and on the nature of the universe for its birth and growth and present status. Logic is essentially the method by which our brains, and those of the life forms we evolved from, sought to predict and anticipate consequences of their actions based on the probabilities associated with prior experiences and expectations under then observable circumstances.
The nature of the universe dictated the development of that process, and the resultant ability to predict the onset of natural events and results of tampering with and manipulating natural forces and materials confirmed the efficacy of the state of our logical systems, as well as triggering improvements of those systems as their ability to anticipate the workings of nature improved.
And our logical processes will continue to evolve dependent on our success in understanding natural events and causes – and science itself is part of that process.
Is the universe logical? The universe IS the blueprint from which our logic is derived. Our logic cannot or could not exist for long independent of the universe that continues to form it.
Roy:
As Dr. Novella said, 1+1=2 is part of an axiomatic system that humans have defined to be true based on abstraction. That is, when we notice a property of an object (external or even internal ideas), we inherently look for patterns and then assign symbols that precisely defines that property if it were a separate object (which it’s not, it’s just a property) from all the objects. Unfortunately, the object “two” doesn’t exist as you are eluding to, but as defined through mathematics, it details a property that holds when for a set of objects in which one of those objects is housed together with another of those objects. In this case, it is said that the property of “two-ness” holds. That property should hold no matter what objects in which I have two.
That’s just an internally consistent system created by humans for humans. It’s consistent, because no matter what symbols are used to denote our “2″, the resultant statements used to define the notion of “two” when combined will be a logical tautology.
Locke, Berkeley, and Hume have great literature on these subjects (Hume providing the most interesting perspectives IMO).
Roy:
Yikes, I didn’t mean it would be a logical tautology. I meant it would just follow the definition of consistency, which is that it would always be possible for all the statements describing “two” to be true (the different symbolizations to describe two would not contradict each other, or stated another way, one symbolization being true wouldn’t disallow another symbolization from being true).
lurchwurm, I studied Locke, Berkeley and especially Hume at UC Berkeley in my youth. They came along before Darwin, and clearly to Darwin’s benefit, except his findings were not to theirs. The concept of “two” exists in calculating systems of organisms that were not known to have any direct connection to humans in Hume’s day.
Humans may think they created it, but at best they recognized it in the abstract.
In any case, you are missing the point, if you think I was objecting to the tautological depiction. I was pointing out the inaptness of the particular inference expected to be drawn with regard to correctly depicting the universe.
Roy:
Also, in response to your quantification issue. That’s an interesting point. In this case, two is describing a discrete set, because we are counting things, not quanitifying some continuous property of the object. With “two” in a counting problem such as ours, an object is included into the set to be considered for “two-ness” by meeting the basic properties that define the object in question (in this case apples, no matter the size, mass distribution, etc..). And we know at least those basic properties exist in nature, because a peoperty is not axiomatic until it’s agreed upon by most of the people intimately involved with that object (those who study the nature of that object). The axiomatic defintions might not precisely define an apple as it occurs in nature (Hume addressed this issue in his discussion of necessary connection vs. probabilistic connection: great thinker that Hume!), but if it’s agreed upon, we can rest assured that at least the observed basic properties defining the object are most probably true. Once we agree upon what it means to be an apple, we can define what it means to have two apples. It simply means we have one object that satisfies our agreed-upon definition with an another object that satisfies that same definition.
Computer systems have to follow these same rules and look at the results produced by these great machines. Once an engineer determines the overall nature of his computer system through the circuits he’s chosen to implement, he can begin to define axiomatically what it means for a signal to be considered logically “true” or “false”/ eletrically “high” or “low” (the primitive way that a computer processes information). The way he determines the cut-off voltage levels that define “high/true” or “low/false” will depend on the circuitry (nature of the system). He then tweaks the circuitry to look for the voltage levels he’s described. If the data coming into the system has data on the voltage boundaries, he might get false high’s or low’s, which means he might need to tweak his axiomatic voltage system to account for the new observations.
This is why scientists and mathematicians work really hard to rigorously define any axiomatic systems. If you read a mathematical analysis book, you’ll notice that axioms can sometimes take up entire pages to account for cases that might produce contradictions (inconsistencies).
Roy:
I was just saying that humans define axiomatic systems that define the best way to describe “two” in ways they can understand. “Two” can be seen as describing things in the universe, which speaks to the nature of the universe. As Hume (as you know) said, we cannot know “any secret powers” of objects that might exist behind the scenes, but we can define what is observable and create strong inductive arguments for the existence of a property. And once we get a strong correlation from statistics on our data with the inductive conclusion we are striving for, we approach an almost 100% (never 100, obviously) confidence in that aspect of nature. We shouldn’t take the inability of 100% confidence to say we can’t describe the universe with logic, but rather that we must always account for the fact that our system of logic does not allow us to deductively validate inductive statements. But our axiomatic systems are internally consistent, and as our axiomatic systems are internally consistence and the fact that they define strong confidences in aspects of nature we have studied, we can confidently say the universe follows the rules of logic.
That’s all well and good, but all I pointed out was that the results as applied to the universe could never be more than a highly approximate depiction. Which I think is what you just said as well.
(And if you like, I’ll refer you to some papers in my library making reference to those very axiomatic inconstancies.)
Why? One of the answers lies in the observation that the universe is infinitely divisible. I could also refer to the problems presented by quantum mechanics, uncertainty principles, and other ruminations of the physicists that Dr. Novella is not all that enamored with.
Bottom line, the universe IS logical, which may in itself be a tautology, given that it’s the source of the logic that we somewhat arrogantly assume was our independant creation.
And I’ll make a counter suggestion to you that you look a bit more into the subject of inference that is the heart and soul of logic, and without which mathematics would not have been intuited as well.
http://en.wikipedia.org/wiki/Inference
We’re knocking out these items a bit too fast, as my last response was to your previous comment, but what the hell, we can infer what I might have were I to answer the latest.
Oh and if when I mentioned studying Hume, the inference left was that I remembered everything he said, it would not be valid.
That’s why I keep a library.
Roy:
Yeah, I have the same problem. I’ve kept all my notes from my second year of CS work (I”m currently a year away from a BS in CS, BA in Philosophy from UC – Santa Cruz; however, as a side note, I’m a returning student having done an 8 year stint in the Navy). I just have Hume more on the brain, because my Empiricists class was last quarter
He along with my continued listening to SGU over the past two years has solidified my interest in the philosophy of science and mathematics.
I think I know where you’re coming from now. We don’t know 100% if the Universe is logical. My response is that you may be right, since we don’t have intimate knowledge of all parts of the universe. However, our continued observations through science are showing more and more that the universe does follow our system of logic, because when we apply the axioms we’ve used to predict effects from causes and manipulate (technology) the varying objects in the universe, those effects are consistent with our internal system of logic we’ve created.
To address the infinite divisibility issue, I’ll introduce a thought experiment. Assume that we have axiomatically defined every object in the known universe (disregarding infinite divisibility for the moment), but because of the deductive limitation on induction, we only have 99.99999999999999999999999999999999999999999% confidence that the universe is logical. Does one then conclude that there is undiscovered phenemenom left to discover, or that simply, the rules of inductive logic disallow 100% verifiability? Now, add in infinite divisibility. Because we’ve already dealt with macro and micro objects at this point, we are talking about changes in matter that would beyond micro. Would that extra amount of matter actually contribute new information about the universe, and also, can you actually imagine an object that would have infinite divisibility? I personally can only imagine changes in matter that would be observable by our most powerful microscope. Past that, I wouldn’t be able to place any confidence in the matter extending on beyond that point.
The infinite divisibility is part of the larger conundrum that we intuit as necessarily true but conceptually incomprehensible. Take the smallest bit of matter that you can imagine and then imagine that it can be divided into a series of infinitely smaller pieces, as there’s no way we can visually conceive that this would be either possible or impossible.
(That’s my version of the problem off the top of my head.)
You might say that to the extent we use symbolism in our abstractions, this system fails us when faced with questions about the nature of the universe or cosmos, and the apparent necessity to assume or presume that it has no boundaries, no beginning, will never end, consists of matter that could not have come from nothing and yet there could not have been a nothing that preceded it, that is not only infinitely large but even worse, has to be, correspondingly, infinitely divisible. For starters.
The point being that our logical systems have not yet evolved (and may never do so) to allow us to do more than guess at what we might find if and when we either start to get some answers, or learn that we had not yet been able to even formulate the right questions.
Roy:
I’ll posit your infinite divisibility of matter for the sake of argument. Does that still show that parts of the universe wouldn’t follow from our system of logic? I would say no.
When you talk of inifinitely dividing matter, you are not adding new information about the universe, only that it’s possible to represent an ever-increasing smaller portion of the matter that we’ve already defined. But those smaller and smaller representations of matter will still have the basic properties of matter (mainly extension). It’s what allows us in calculus to think of the notion as a limit. Obviously, mathematicians don’t literally think that we keep moving closer and closer to a value (or neighborhood) infinitely many times. They are using language such as “as x approaches infinity,” because they are only interested in the fact that there’s an unlimited amount of error precision that can be allowed. If you choose some change in a variable, I can choose two values around that new value that will bound the value to the limited boundary point (the actual value of the limit). At each point, we can intelligibly represent each value, because no matter what point that we choose for error precision, we are still operating in a class of real or complex numbers (all defined by rules of logic and math).
In short, infinite divisibility is a tool for representation, not showing that parts of the universe are undiscovered.
It’s showing that we can make reliable predictions with our logical systems about things that, at the same time, our systems cannot yet describe. It’s hinting perhaps that particles may be our explanation of something that only simulates particle interaction. It’s hinting at a reality that is presently beyond the grasp of the type of mind that has so far been evolved on this planet.
I’m not hinting in turn at the supernatural, which is essentially a non-explanation of those things we cannot otherwise grasp. Supernatural adherents have remained in the dark ages when it comes to predicting and anticipating the behavior of nature’s forces.
Note for example that even by saying “nature’s forces” I have slipped into using terminology that hints at purpose, when the logic of science tells us there is no evidence of that purpose. But the logic of science does not otherwise contemplate the full scope of “purposefulness.”
It doesn’t postulate any such thing as a semi-purpose in nature, for example (and neither do I although it seems I just did).
Note that my position has been all along that the universe is logical, yet that’s statement itself implies a purposeful universe. But logic in fact may get its purpose only from the humans that have give that label to their calculating processes – as we don’t really know to what extent nature calculates anything. All we really “know” is that there seems to be a reliable progress of causes and effects that we can tap into.
We don’t know the source of what we call “cause,” however. Can we build computers that find that source for us? Perhaps, but will we even know when they find such things due to inability to understand what they have found?
This is a very complicated topic to say the least.
Novella said:
Because such systems require only internal validity, I do not think that there can be a universe in which they are not valid. Therefore, 1+1=2 everywhere, even in a universe with different physical laws (if that is even possible).
Godel proved that you cannot prove that axiomatized arithmetic is consistent, which leaves open the possibility that it is not. While you may start with a bunch of seemingly reasonable axioms (though anybody that has studied axiomatic set theory will realize some of them are not so intuitive or simple), unless you can prove that your inference rules (rules for making transitions from axioms to theorems) will never lead to an inconsistency, then you have problems. Unfortunately for those who want to rest their head on axiomatized mathematics, Godel proved that no such proof is possible.
Also, there exist deviant logics such as quantum logic, paraconsistent logics (in which contradictions are allowed: these were developed to handle liars paradoxes and such), constructionist logics (in which proof by contradiction is not allowed), and a bunch of other weird stuff.
How would one go about deciding which logic to use in a given situation? Is there one true universal logic that can decide? Or must a particular choice about what logical system to employ be sensitive to empirical and pragmatic considerations?
One of my favorite authors on these complicated topics is Penelope Maddy, especially her wonderful recent book Second Philosophy (which I briefly review here).
In it, among other things, she gives specific examples where classical logic fails, and discusses how all this relates to human cognition and the world.
I recommend Susan Haack, her latest being: Putting Philosophy to Work – Essays on Science, Religion, Law, Literature, and Life.
And her various books are also affordable.
[...] the Universe, has a fascinating blog of his own called NeuroLogica. In Tuesday’s post he asks Is The Universe Logical? [...]
Hi Dr. Novella, I just discovered your blog recently. I found this thread and it’s a topic that has been interesting me lately. I sort of agree with you and sort of don’t.
Before explaining, first let me say I’m not anti-science, logic, rationalism or that. I think our current scientific theories, evolution for example, are the best and only rational explanations we have. I think science is great because science works and isn’t based on mysticism or opinion.
Now, obviously we have no choice but to reason with each other using logic. How else can we communicate and convince without resorting to force? Something I’ll try to do now and probably fail, but hopefully you can correct me.
The example you give above about 2 true propositions not contradicting is true in logic, but it doesn’t follow that this logical truth binds the universe or reality. There may be some undiscovered property of some form of energy or matter that is contradictory in logic, but still get’s by just fine and we’ll never be able to logically grasp it. I can’t argue against the law of non-contradiction without affirming that law, but from this it doesn’t follow that the universe or some property of it is contradictory or not. How would we know?
Science can use math and logic to construct its models of how the universe works. This is correct, and the only good way of doing it. However, a model isn’t reality, it’s a construction that ‘models’ obviously. We have no way of ever 100% verifying that it, logic, maths and evidence, are reality and not just a good approximation. We can’t step outside the universe and check it, we can only keep testing hypotheses.
I found this quote from Bertrand Russell’s introduction to Wittgenstein’s Tractatus while trying to work out why some philosophers seem to claim that the universe is bound by logic:
According to this view we could only say things about the world as a whole if we could get outside the world, if, that is to say, it ceased to be for us the whole world. Our world may be bounded for some superior being who can survey it from above, but for us, however finite it may be, it cannot have a boundary, since it has nothing outside it. Wittgenstein uses, as an analogy, the field of vision. Our field of vision does not, for us, have a visual boundary, just because there is nothing outside it, and in like manner our logic world has no logical boundary because our logic knows nothing outside it…Logic, he says, fills the world. The boundaries of the world are also its boundaries. In logic therefore we cannot say there is this and this in the world, but not that, for to say so would apparently presuppose that we exclude certain possibilities, and this cannot be the case, since it would require that logic go beyond the boundaries of the world as if it could contemplate these boundaries from the other side also. What we cannot think we cannot think, therefore we also cannot say what we cannot think.
Anyway, none of this devalues science, as it keeps testing logical conjecture against the evidence, and keeps working. The only problem would be if a scientist dogmatically asserted that a theory was absolutely true and couldn’t be altered. To me, it’s a greater attack against religious arguments for God which start from everyday events, like cause and effect and argue that logically every effect must have a cause, the universe is an effect, ergo. Well, even if that logically follows from the premises, which I doubt, it doesn’t mean that the universe is bound by such a logical argument. As Hume (I think) said, our line is too short to plumb such depths.
Anyway, I hope I’ve explained myself and if you’ve got time, I’d like to read your thoughts.