Philosophical invariance: it's like the concept of symmetry in physics. I think that many philosophical ideas might be equivalent under certain transformations. Writing philosophical arguments in a more consistent and formal way might expose these symmetries.

Politics. It is time for Rumsfeld to go. Why do the Republicans insist on rewarding incompetence? How big a screw up do you have to make before you get fired, or resign in shame?

Overheard...

She's just being intransigent...Intransigent? I though that meant homeless?

No, that's indigent.So what are native Americans?

They're indigenous.

Who knew doctor(logic) liked cute fuzzy bunnies! They're delicious!

## 18 comments:

Who knew doctor(logic) liked cute fuzzy bunnies! They're delicious!

http://catandgirl.com/view.php?loc=333

Love it!

DL:

The symmetry of a

physicalbeing or system is a characteristic of that being or system such that a particular aspect of that being or system is preserved under some change. For example: roll a billiard ball across a pool table and (assuming it’s clean, unmarked, undamaged, symmetrical, and materially uniform). To an observer only interested in physically-accessible knowledge of that billiard ball, it looks exactly the same after the change… within the framework of our imposed assumptions.The symmetry of a

mathematicalbeing or system (which is NOT arealbeing that exists outside and independent of the person considering that mathematical being—but IS reducible to real beings, i.e., the rim of a tire is in the form of a circle) is also a characteristic of that being or system such that a particular aspect is preserved under some change. For example, apply a specific rotation matrix to the formalistic representation of any geometrical entity (such as a hexagon), and that entity will “look” exactly the same as before the imposed operation.Note first: mathematical beings are NOT the same KIND of beings as real beings, i.e., a mathematical equation, while certainly existing in some mode or capacity (if it didn’t we wouldn’t be able to talk about it even in the abstract) is not the same thing as a real being that exists independent of your perception of it. Example: the equation of a circle does not enjoy the same mode of “beingness” as the rim of the tire it describes, and therefore the ontology of the two cannot be directly related. To claim that both the tire rim and the equation of a circle which describes the rim are the same KIND of being (as opposed to the simple-minded and idiotic claim that both ARE the SAME being), is to equivocate over their beingness—a monumental category error. (You’ve probably guessed I’m pointing to the grave error of equivocation you made at the Real Physics blog.)

Now, you claim that “ideas” (in this case, “philosophical” ideas) behave in essentially the same manner as the concept of symmetry in physics, or in other words, you believe a concept regarding physical systems or beings can be applied without qualification to ideas.

Note second: the concept of symmetry in physics ultimately relates to real beings. Just what is it you believe philosophical ideas ultimately relate to? Are these things directly relatable to real beings as if the two were the same KIND of thing? What particular notion of symmetry would you apply to concepts such as dignity, wisdom, fortitude, causality, purpose, free will?

You are certainly entitled to your opinion. However, it will remain at the level of a personal opinion until you demonstrate that you are, in fact, justified in drawing such a relation, and that such a relation governs in the same essential way ideas and billiard balls. Moreover, you betray the failed project of logical positivism lurking in your words: “Writing philosophical arguments in a more consistent and formal way might expose these symmetries.” Doesn’t that beg the question that you ASSUME (without proof or demonstration) “consistent and formal” is ONLY understood empirically and may be imposed in the same manner on ideas, which are NOT empirical as pertains to their ontological import?

You are NOT interested in understanding philosophical concepts per say. You ARE transparently interested in a vain attempt of “capturing” them with your limited tools of science and mathematics as applied by some vague notion of the scientific method (based on a positivist epistemological approach)—without demonstrating you can do so in the first place. Then, when you can’t capture something empirically, you deem such things “meaningless” or “incoherent” or “unintelligible.” Your

a priorinon-scientific commitments don’t permit you to think outside the box, and so once again you’re stacking the deck in your own favor.Holopupenko,

Thanks for stopping by to stimulate some thinking on this. I haven't really had time to think about this idea in any detail. I just posted a comment as a bookmark for future thinking.

I would be nicer to you, but every time I try, you throw it back in my face.

It is my claim that mathematics is an enumeration of consistent systems. If the world is consistent, then it is isomorphic to some (no doubt complex) mathematical system. Note that this doesn't mean that all laws are discoverable. Even where there are no detectable laws, the history of events can still be modeled by mathematics because those events would form some consistent structure with many axiomatic constants. In fact, physical laws are seen as symmetries in the mathematics describing the physical world.

The same applies to ideas. Ideas that are consistent (e.g., philosophical ideas) can be (and regularly are) modeled with mathematics. And they can also possess symmetries and laws of their own.

Anticipating an objection, I'll say that not everything is

initiallyquantifiable. For example, there was a time when temperature was not quantifiable. Before thermometers, we had to "feel" the temperature imprecisely, and temperature measurement was more subjective. Lack of precision, lack of objective measurement, and lack of computational power limit the richness of our mathematical models. However, what we do know about the world can be modeled with mathematics. That's why we can spot the contradiction in statements like "the summer of 1769 was the hottest in memory, but I remember the summer of 1767 was even hotter." The extent to which we can model a thing mathematically is the extent to which we can comprehend that thing.Now your beef seems to be that I limit my thinking to systems that can be modeled mathematically. Yet, as far as I can see, that covers all consistent systems. I'm not interested in inconsistent systems, and neither should you be. We cannot know anything about them.

The "box" within which I do my thinking contains all that is intelligible. Your statements boil down to the claim that my philosophy fails to comprehend truths about the fundamentally incomprehensible. But this is nonsense. How can there be truths about the fundamentally incomprehensible? Your problem is that you think one

cancomprehend the incomprehensible. And why would you hold to such an idea? Because unintelligibility is a prerequisite for religious faith.Note first: mathematical beings are NOT the same KIND of beings as real beings, i.e., a mathematical equation, while certainly existing in some mode or capacity (if it didn’t we wouldn’t be able to talk about it even in the abstract) is not the same thing as a real being that exists independent of your perception of it.To start with, mathematics does exist beyond my perception of it. That's why mathematics is considered to be an objective field of study.

Okay, let's talk about kinds of being.

Consider a physical flower. We have many sensations of this flower. We can see it, touch it, smell it, fixate upon it, and recognize it.

Each of these sensations is experienced. We can do each independently. I can smell a flower without first recognizing it as such. I can fixate upon the sight of the flower before realizing that it is the flower. I can even recognize a flower without sensing any aspect of it, just by recalling the concept.

When we analyze these sensations, what is apparent is that concepts are correlations between sensations. It is the subtlety of these correlations that enable us to distinguish between real flowers and photos of flowers, or between the idea of a flower and a plastic flower.

Indeed, even the sight of the flower is an intricate correlation of brightness and color.

So the only thing we get as real input to our philosophical research are these sensations, their correlations, and the recognition of their correlations. This applies to mathematics as much as it does to physical objects.

Now you want to say that there is something fundamentally different about certain kinds of sensations. But on what basis? Why is the idea of a flower (sensation of pattern recognition, the recalled experiences of flowers, etc.) fundamentally different from the physical sensation of a flower? It is

distinctfrom physical perceptions of the flower, but distinctness isn't ontological difference, otherwise we would have to say that the sight and smell of the flower were in ontologically different categories. Ontology would shatter into a million trivial pieces.The reason for your mistake is that your starting point isn't your direct experience of the world and of ideas. Your starting points are our most subtle, confused and complex sensations. Higher ideas like love, morality and rationality. The reason you start with these things is that these are the things you want to defend ideologically. For example, you have to find some way to grant morality a privileged status, or else you end up with naturalistic ethics - a thought which unreasonably disturbs you.

Your solution is to claim that moral facts are more than just correlations among sensations, and different from, say, physical objects. That while moral sensation occurs at the correlation of certain experiences, morality is somehow more. Alas, that's where your argument ends. It says that if moral facts weren't a different kind of thing, moral chaos and anarchy would erupt. Not only is this false, it's not even a philosophical argument.

Your strategy amounts to placing the most complex and least well-understood sensations into a bucket you call "ontologically different stuff". This strategy is nothing but a curiosity stopper. It says, do not search for explanatory (e.g., physical) correlations for these sensations because they are in my magic bucket. Actually, it's not your magic bucket. There are many metaphysicians (almost all of them devoutly religious) who share this voodoo pail.

So we see that the limitation isn't in my thinking. My thinking can, in principle, encompass everything intelligible. No, the limitation is in your own thinking because you unjustifiably wall off certain concepts as fundamentally beyond rational and scientific explanation.

DL:

It is my claim that mathematics is an enumeration of consistent systems.It may be “your claim” but with no demonstration of the soundness of arguments supporting it (as opposed to merely proof of any argument’s validity), it remains your personal opinion. The onus is on you to convince us.

The If the world is consistent, then it is isomorphic to some (no doubt complex) mathematical system.Again, why? On what basis do you draw this conclusion?

Note that this doesn't mean that all laws are discoverable.Huh? Are you intentionally asserting (rather pessimistically, I may add) that since some laws can’t be “discoverable” (i.e., “verifiable” to employ your term), that they nevertheless exist in some capacity? If so, you’ve just undermined your whole logical positivist position. Try again…

Even where there are no detectable laws, the history of events can still be modeled by mathematics because those events would form some consistent structure with many axiomatic constants.Point 1: You may want to try again, for it is a contradiction to claim a law may not be “dectable” and yet able to be modelled mathematically: to model something mathematically means to take in “detectable” data, to correlate that data, and from this to produce some mathematical formalism which (at least partially) reflects—i.e., models—an underlying “law” governing that system.

Point 2: Clearly, it is not the mathematical formalism describing the behavior of the modelled system that “governs” the behavior of that system. How can a mathematical description actualize anything? It cannot, for to claim so would be to claim that the equation describing the free fall of a steel sphere from the Tower of Pisa CAUSES the steel ball to behave the way it does. Things have been falling long, long before equations describing freely-falling bodies were correlated from observed data. (Even Stephen Hawking, bless his honest soul, admitted this when he asked, “What breathes fire into the equations?”—which is precisely the opposite of what you claim: you directly impute causal efficacy to mathematical formalisms that describe the behavior of physical phenomena.) Are you maybe suggesting (which you later do quite directly) that mathematics exists in some capacity apart from us? Given the admission that you have no philosophical

bona fides, you might be forgiven for not realizing this is pure Platonism…Point 3 (most crucial): you confuse the mathematical formalisms developed to describe phenonena with the underlying nature of the phenomenon itself. You assume the world around us is mathematically structured, and assume further that this is ALL that is required to describe nature. Witness your claim: “

… not everything isinitiallyquantifiable.” That’s sheer speculation: EVENTUALLY for you EVERYTHING will be quantifiable? Are you sure you want to be promoting such a faith system? This ispreciselythea priorinon-scientific presupposition that drives the rest of your views: it is axiomatic and beyond question. Funny how that doesn’t square with the Descartes quote in your masthead. You’re obsessing on a deep belief that verifiability IS THE SAME THING AS empirical verifiability (they are NOT the same thing), and that empirical verifiability alone counts as meaningful knowledge.The same applies to ideas. Ideas that are consistent (e.g., philosophical ideas) can be (and regularly are) modeled with mathematics.Without any demonstrated basis for doing so, you equivocate “ideas” to be the same KIND of being as every other existents. That’s incoherent. (To be clear, you’re NOT asserting a freely-falling ball IS an idea, you assert a freely-falling ball is the same KIND of thing as an idea.) I can gather physical data for a freely-falling body and correlate that data into a mathematical description. What possible data can you correlate mathematically to NECESSARILLY and SUFFICIENTLY describe the idea of evil, or fortitude, or justice, or patience,

ad nauseum? You so strongly demand verifiable evidence (limited by the failed methodology of logical positivism) from every other person, yet you cannot provide a speck of evidence or argumentation to support your own assertions. You have such a deep faith that a mathematization of everything WILL EVENTUALLY happen, yet despise and belittle religious faith.And so, mimicking your

modus operandi, I demand verification of only two assertions you make:(1) provide a mathematical model for the IDEA of evil that NECESSARILY and SUFFICIENTLY describes it;

(2) If you cannot do so, at least provide verifiable evidence and sound argumentation that supports your deep-seated faith that all existents will eventually be mathematically modeled.

I limit my thinking to systems that can be modeled mathematically. Yet, as far as I can see, that covers all consistent systems. I'm not interested in inconsistent systems, and neither should you be. We cannot know anything about them.Point 1: Please define “consistent” before asserting all “consistent systems” can be mathematically modeled. (You cannot refer back to mathematics to do so for that would be a circular argument.) But if you can’t refer to mathematics to support your argument, then this implies there’s something else (some other way apart from mathematics or mathematical modeling) by which to draw conclusions… which means goodbye to your whole project.

Finally, Point 2: Without appearing to necessarily defend “inconsistent” systems, you miss an obvious point when you assert “

we cannot know anything about [inconsistent systems]” To make such an assertion is itself to admit you know something about them, i.e., that one cannot know anything about them. That’s as a blatant a contradiction as one can achieve: I bow before your cognitive dissonance.To start with, mathematics does exist beyond my perception of it. That's why mathematics is considered to be an objective field of study.Really? Mathematics “exists” beyond your perception of it? Where? Which of the five senses can locate it for me so that I can put it away for safe-keeping, knowing it will be there (and always was) when I'm not "looking"? If it can’t be detected by the five senses but must be reasoned to by employing the data obtained by the five senses, what does this say about the mode of “existence” of mathematics, i.e., does mathematics exist in the same manner as, say, the steel sphere falling from the Tower of Pisa? Provide verifiable evidence of it, and also demonstrate to me that mathematics existed before man walked the face of the earth.

So the only thing we get as real input to our philosophical research are these sensations…Bravo! Finally, it’s admitted that while our thinking begins with sensory knowledge, not all knowledge IS sensory knowledge. However, you’ve left out a crucial aspect of your claim: by plunging ahead you fail to categorize just what “philosophical research” is in the first place. Any analytical philosopher (especially a logical positivist) would demand you define your terms. So, say you have your sensory knowledge—which you’ve obtained from the “real” world. Great. Now, what exactly is the nature of the philosophical knowledge you gain by reflecting on this sensory knowledge? You imply quite strongly they are not the same thing. I agree… but what EXACTLY is philosophical knowledge? Is it the same KIND of knowledge as sensory knowledge, i.e., is it somehow materially-based and is this the NECESSARY and SUFFICIENT condition to understand the essence of philosophical ideas? If so, why can’t I get philosophical knowledge directly from my senses? If not, you have some explaining to do… In any event, please provide verifiable evidence supporting your arguments.

The reason for your mistake is that your starting point isn't your direct experience of the world and of ideas.That’s a straw man… in fact, it’s a lie: and you know it. Remember (at the very least) the example I provided of stealing candy from a baby? Did I not begin with direct sensory input, and then from this reason to the concept of “injustice” as perpetrated by the man stealing the candy that we “see” based on sensory input? (How could I reason to “seeing” (i.e., understanding) “injustice” without having first experienced through the five primary senses the real world actions of the man?) Are you claiming I FIRST provided the concept of injustice and THEN provided arguments to support this? In fact, you do:

“The reason you START (emphasis added) with these [higher ideas] is that these are the things you want to defend ideologically. For example, you have to find some way to grant morality a privileged status.”Well, please provide directly-referenced, verifiable evidence of my making such a claim… otherwise admit to what it is: the convenient rhetorical device called a lie. I should have anticipated you employing lies to present your case…Your solution is to claim that moral facts are more than just correlations among sensations, and different from, say, physical objects.Apart from being improperly phrased (probably intentionally so), do you realize how absurd your implication is? Let’s reverse your assertion and point it back at you to bring out that absurdity: “Your solution is to claim that moral facts ARE MERELY correlations among sensations and that they are the same KIND of thing as physical objects.” (We’ll leave aside the obvious howler you claim above that (eventually) all ideas (including moral facts) will be mathematically modeled.) Again (per the above comment), if you believe that moral facts ARE reducible to physical objects, then why do I need to reason to moral facts? Why can’t I simply know them directly from my senses? On the other hand, if you believe moral facts are not simply reducible to physical objects, then (again) you’ve undermined your entire position.

… you unjustifiably wall off certain concepts as fundamentally beyond rational and scientific explanationSilly, if not sad, for it begs the issue: you ASSERT without justification that ALL concepts CAN be NECESSARILY and SUFFICIENTLY explained by the modern empirical sciences. Please provide sound argumentation to support and verify this assertion. Note: you may not employ any knowledge obtained from the modern empirical sciences to justify the epistemological efficacy of the modern empirical sciences—that’s a circular argument.

It says that if moral facts weren't a different kind of thing, moral chaos and anarchy would erupt.Another lie: please provide directly-referenced, verifiable evidence that I ever claimed this. Otherwise, stop lying… or does the relativism for which you argue permit you to lie in presenting your case? My advise: if you relish engaging in intellectual battles, please don’t lie and please don’t enter the field unarmed (which you admit to, by the way, in terms of a lack of philosophical

bona fides)—that’s a common courtesy to be rendered to your interlocutor and your readers.It is my claim that mathematics is an enumeration of consistent systems.

It may be “your claim” but with no demonstration of the soundness of arguments supporting it (as opposed to merely proof of any argument’s validity), it remains your personal opinion. The onus is on you to convince us.

I'm convinced and I am sure that most mathmeticians are also convinced. Holopupenko what are your credentials in mathmetics?

You seem to indicate that unless one has credentials in a given area of study that one should not be permitted to engage others on the topic.

Alas, poor Holopupenko. He can dish it out, but he can't take it.

Putting words in another persons mouth isn't so tasty when yours is the mouth in question, huh? Live by the sword, die by the sword, baby.

And spew all you like about "bona fides". The proof of the pudding is in the tasting, and your pudding is defective.

Really? Mathematics "exists" beyond your perception of it? Where? Which of the five senses can locate it for me so that I can put it away for safe-keeping, knowing it will be there (and always was) when I'm not "looking"?Five senses? We've been over this a dozen times now. I am talking about experiences, of which the five senses are associated with a

subset. Besides, why would you think that things that appear to exist beyond our perception must register directly on the five senses? Electrons don't. Neither do individual photons. Nor magnetic fields. Did electrons predate human life? I think they did.So whether we are mixing compounds together to uncover chemical laws, or pushing symbols around in our heads to uncover laws of computation seems to make very little difference. The point is that we get reliable results when starting from specified inputs.

Russell and Whitehead demonstrated that one can derive mathematics from logic, so saying that mathematics is an enumeration of consistent systems is not controversial. Look at it this way: if you wanted to show a complex system was consistent (or inconsistent), how would you do it?

I cannot prove that the universe is consistent, but then I don't have to. It's not one of my claims! I just assume that the universe is consistent.

Some phenomena in the universe maybe truly random (e.g., radioactive decay). In that case, there are no further laws to be discovered about them. But this doesn't mean we cannot mathematically describe past random events such as observed decays. I'm sure we've both done this in a physics lab.

I can gather physical data for a freely-falling body and correlate that data into a mathematical description. What possible data can you correlate mathematically to NECESSARILLY and SUFFICIENTLY describe the idea of evil, or fortitude, or justice, or patience, ad nauseum?If it is the case that the mind is a physical system, then a simulation of the human body and brain will behave no differently than a real human (including its ability to sense justice and evil). The simulation will have to be exposed to years of simulated stimulation in a virtual world, but it's feasible. It's just complicated. I know, I know. It's in your magic bucket.

Time after time you incorrectly claim that I assert that everything can be explained using science and mathematics. (Hmm... what should I call such incorrect claims?) It's possible that some things cannot be explained with science and mathematics. However, then there is

no explanationfor those things! If you want to say that God or justice or love cannot be explained by science and mathematics, then you assert that they cannot be explained at all. But what is the use of such defeatism? Why gain satisfaction from the thought that certain things will never be explained?you confuse the mathematical formalisms developed to describe phenonena with the underlying nature of the phenomenon itself.Er, no. I do not confuse the word "lion" with the a physical lion. I don't confuse a flower with a rock. They are all distinct things. However, all of them are accessed via experience, and that's what they share in common. Philosophy is a meta-description of experience.

Again (per the above comment), if you believe that moral facts ARE reducible to physical objects, then why do I need to reason to moral facts? Why can’t I simply know them directly from my senses? On the other hand, if you believe moral facts are not simply reducible to physical objects, then (again) you’ve undermined your entire position.Error. You assume that if heads and tails are both sides of the same coin, then either heads is tails or tails is heads - as if their commonality renders them indistinct.

If chemistry is reducible to atomic physics, why do I need to reason to atomic physics? That depends. If all I want to do is use the little chemistry I already know, then I don't need to reason to anything deeper. Yet we don't know the value of knowledge we don't have. Knowing about, say, the periodic table helped us explain chemical properties and devise new materials and technologies like, say, nuclear reactors.

Our observations of morality (e.g., how we feel when someone takes our stuff, or when we punish them for theft) are much like our sensation of heat from a flame. The difference is in the complexity of the correlation. Reasoning to a moral course of action involves predictions about the outcomes of our actions and an integral over our moral feelings about those outcomes. For example, it may be morally distasteful to let someone steal from someone else, but it might be more morally distasteful to get someone killed in trying to stop the theft.

We find that heat is transmitted to the nervous system by pain receptors. Clearly, moral feelings cannot be mediated by something so physically simple, but there's no reason to believe that it isn't mediated by some mechanism in the physical brain. Morality is certainly coupled to physical reality.

If I understand your position (you're usually too busy being uncivil to have the chance to speak of your own views), it is that morality or evil are things that float "out there" like flames in the ether, and our souls have simple moral pain receptors. This seems a rather circuitous route to travel in order to prevent us from reducing feelings to physics. Not that it's ruled out a priori. The problem is that even if it isn't ruled out, I don't see how it buys you another ontological category. You just end up with parallel (yet coupled) physical systems.

What we have are experiences and connections between them that recursively are also experiences. Every experience exists, but that notion of existence is trivial. The common (non-trivial) notion of existence is a correlation of a mental model with actual experiences. The idea of Bigfoot exists trivially because I experience the idea directly. What is non-trivial is whether Bigfoot exists as a physical entity correlating strongly with my idea of him. Asserting that Bigfoot exists

predictsthat there will be specific correlations of sensation.This exposes talk of metaphysical substances as confusion and oversimplification. It makes no more sense to see existence as being made up of a handful of different ontological kinds than it does to think of the world as earth, air, fire and water. Explore the correlations. That is all.

sartresamigurumi:

My

bona fides? A Ph.D. in nuclear engineering from MIT, an MA in Soviet Studies from Harvard University, a B.S. from in nuclear engineering and physics from RPI, an MA in Thomism from the ICU through Notre Dame, additional formal language studies in the former Soviet Union. (Mathematics (including mathematical analysis) is the bread-and-butter of nuclear engineering and physics.) Would you like to cross intellectual swords with me as well, or are you just as unarmed as DL? Of course anyone is welcome to participate in these discussions no matter their formal training and experience. But, those who admit to having nobona fidesshould have the courtesy to consider the fact that they (like DL) don’t have a clue about certain philosophical ideas – ESPECIALLY when bandied about in such ameaturish ways AND rammed down people’s throats as the truth.DL:

You have intentionally refused to provide references in support of the lies propogated in your previous comments. That speaks volumes. It’s convenient to keep silent in the face of your lies, isn’t it?

My main approach to your unsubstantiated claims is to pose questions BASED ON YOUR STATED POSITION back at you, and in all the blogs you’ve participated in (to which I’ve witnessed) you’ve haven’t answered your own assertions as they apply to your own ideas. I don’t give a hoot whether you accept my philosophical position. What is fairly demanded of you, however, is to apply your ideas back upon themselves for the CONSISTENCY you claim to so dearly love. Yet, you cannot do so. The logical positivism project has been abadoned by many, far more knowledgeable and experienced people than you (including your alleged hero, Ayer) precisely because it is INCONSISTENT (in fact, self-defeating)… and yet you continue to chant the CONSISTENCY mantra unabated and unsubstantiated. Your track record is not good: you’ve either been removed from participation in at least one blog, have been properly castigated from descending to emotional

ad hominemagainst those who dare to hold different views from yours, or other participants have basically relegated you to incoherence. And then the pitiful complaints start of “not being nice to you.” Oh dear, I guess we need to hold a pity party…Here is an example of why your lack of philosophical

bona fidesleads you to make ignorant claims:“Russell and Whitehead demonstrated that one can derive mathematics from logic, so saying that mathematics is an enumeration of consistent systems is not controversial. Look at it this way: if you wanted to show a complex system was consistent (or inconsistent), how would you do it?”So, here is a very badly-needed history lesson for you (in the interests of full disclosure, this is extracted from my thesis… by the way, do you ever formally defended a philosophical thesis?):In 1900, David Hilbert provocatively challenged mathematicians and logicians to prove that the consistency of the axioms of logic. Russell and Whitehead took up the challenge and, during 1910-13, published their famed

Principia Mathematica. But later Russell relented—lamenting, with some self-aggrandizement, “I wanted certainty in the kind of way in which people want religious faith. I thought that certainty is more likely to be found in mathematics than elsewhere. But I discovered that many mathematical demonstrations, which my teachers expect me to accept, were full of fallacies, and that, if certainty were indeed discoverable in mathematics, it would be in a new field of mathematics, with more solid foundations than those that had hitherto been thought secure. But as the work proceeded, I was continually reminded of the fable about the elephant and the tortoise. Having constructed an elephant upon which the mathematical world could rest, I found the elephant tottering, and proceeded to construct a tortoise to keep the elephant from falling. But the tortoise was no more secure than the elephant, and after some twenty years of very arduous toil, I came to the conclusion that there was nothing more that I could do in the way of making mathematical knowledge indubitable.” [Bertrand Russell inPortraits from Memory(G. Allen & Unwin, 1956) as quoted in Philip J. Davis and Reuben Hersh,The Mathematical Experience(introduction by Gian-Carlo Rota), Houghton-Mifflin: Boston, MA, 1981), page 333.]Russell was forced to this conclusion not based upon his own realization but with the unsolicited (and quite unexpected) assistance of Czech-born mathematician Kurt Gödel who, in a paper entitled “Formally Undecidable Propositions of

Principia Mathematicaand Related Systems I” presented on 24 November 1930 and published in 1931, showed that the Hilbert system was unattainable: by their very nature such attempts to radically neuter the epistemic cycle by an axiomatization of mathematics were futile. Gödel shocked mathematicians and logicians (and later physicists) by proving that within any given branch of mathematics, there would always be some propositions that cannot be proven either true or false using the rules and axioms of that mathematical branch itself. The unfortunate upshot for logicists such as Russell (but which certainly breathed the fresh air of reality into the failed project known as logicism) was that the CONSISTENCY of mathematics can be proved only in a language which is stronger than the language of mathematics itself. [Memo to DL, that is why you MUST demonstrate the soundness of your arguments without resorting to mere mathematical notions of consistency…] More specifically, Gödel’s First Incompleteness Theorem proved that any formal system deep enough to support number theory has at least one statement that is not decidable: even if we now that the statement is true, the system cannot prove it—which means it is incomplete. The Second Incompleteness Theorem is closely related to the First: it is not possible to prove, from within any complex formal system, that it is self-consistent—which means that from a given set of premises which are known to be true, nonetheless some things cannot be proved in mathematics. [The essence of Gödel’s Theorems may very briefly summarized as (1) Mathematics is mechanically (or algorithmically) inexhaustible (or incomplete), (2) No formal system of mathematics can be both consistent and complete, (3) Any consistent formal theory of mathematics must contain undecidable propositions.] [Memo to DL: this tosses your fundamentalist belief in “consistent mathematical” systems as the only ones that are meaningful or coherent into the trash bin, and (again) exposes the utter ignorance of your approach.]One might be able to prove (again, as opposed to demonstrate) every conceivable statement about numbers within a system of mathematics (or propositions and rules within a system of logic) by going outside the system to come up with new rules and axioms, but by doing so one would only end up creating a larger system with its own unprovable statements. For example, number theory cannot be complete: no matter what axioms are chosen as a basis for number theory, there will always be some true statements that cannot be deducted from them—even though they may be provable within the larger context of symbolic logic. But since symbolic logic is itself an abstract collection of rules (beings of reason), it itself is incomplete.

[

Memo to DL: That you are ignorant of this is all the more stunning since you bandy about half-truths as if they were full truths, and do NOT understand what philosophy and its relationship with other form of knowledge is all about.]Here’s a perfect example of intellectual cowardice on your part:

“I cannot prove that the universe is consistent, but then I don’t have to. It’s not one of my claims! I just assume that the universe is consistent.”You ASSUME?? That means you abandon any attempt to understand that assumption: no explanation is necessary, it’s a brute fact, “I don’t have to prove it!” And yet, you hypocrite, you despise and attack people of faith for any possible assumptions or understandings they have?!? Mixed together with your hypocrisy is your ignorance of logical positivism: even these bozos would laugh you out of the room for your “assumption.” “Assumption?!?” Give me a break: how self-admittedly closed-minded can one get?Here’s one that demonstrates your lack of deep immersion in the understanding of what physics is (remember, you’re discussing this with an MIT Ph.D. nuclear engineer and a

bona fidephilosopher):“Some phenomena in the universe maybe truly random (e.g., radioactive decay). In that case, there are no further laws to be discovered about them. But this doesn’t mean we cannot mathematically describe past random events such as observed decays. I’m sure we’ve both done this in a physics lab.”Do you have a clue as to what you just said?!? Do you understand what “random” means or “chance occurrence”? Here’s the ontological definition of chance occurrence: at least two causally-independent yet intersecting lines of causality. It’s more solidy-based than your mere mathematical descriptions, yet you cannot permit yourself to step out of your mathematicized, logicized, black-and-white box. You strongly suggest some events are “random” by their very nature, which is ludicrous and certainly explains your ignorance of WHAT randomness is rather than just HOW to describe randomness using mathematical formalisms. We use the bionomial distribution to ultimately derive mathematical formalisms that provide outcomes OVER MANY EVENTS for the toss of a penny. But this does NOT mean the NATURE of the flipped-penny phenomena is RANDOM, which (again) you imply, i.e., you rely solely on mathematics to define the ontological nature of beings. That’s sheer ignorance. The penny’s motion is NOT random by its nature: we must resort to statistical formalisms because we DON’T KNOW how to account for all the intial conditions, boundary conditions, and intermediate impacts on the flight of the penny (i.e., how greasy were the fingers of the person flipping the penny, air currents in the room, geometrical mass distribution of a particular penny, etc., etc., etc. In fact, the motion of the penny is quite well determined by physical principles. But just because we can’t account for them and are forced to employ statistical shorthand does NOT mean the motion of a penny is BY ITS NATURE random. (Please don’t start with me on quantum fluctuations: if you can’t seem to understand something as simple as the alleged “randomness” of a penny, then you should not have been granted any degrees in the first place.)

Here’s an example of self-contradiction:

“Time after time you incorrectly claim that I assert that everything can be explained using science and mathematics… It’s possible that some things cannot be explained with science and mathematics. However, then there is no explanation for those things!”Huh? I claim you make an assertion, you deny it, and then conclude the assertion is correct?!? Think before you spew.There rest of what you say is even worse than these examples, and not worth anyone’s time.

You may have the last word…

come on, doc, answer h's questions. you're evasive, you're not convincing, your ways are fundamentalist. answer the questions.

Sorry Holopupenko, your Ph.D. in nuclear engineering is trumped by my Ph.D. in high-energy theoretical physics. And Thomism? I suppose there might be one or two older and more obsolete philosophies you could have wasted your time studying...

How can you be so consistently wrong? Let me count the ways.

1) Quantum Mechanics and Randomness

As I've seen you do before, you completely mischaracterize quantum mechanics. Quantum mechanics is, as far as we can tell, totally random. Not only have we found no hidden mechanism beneath quantum events, there are theorems placing severe limits on the very possibility of hidden-variable accounts of quantum phenomena. It's nothing like flipping a coin. Einstein said that "God does not play dice with the universe." He was wrong.

There's probably no way to determine whether certain types of events are truly or random or have only a random appearence. That does not mean that we can arbitrarily rule out the possibility of true randomness.

Look at your own "ontological definition" of chance occurrence. If some property of an event is not caused (e.g., photon direction in positronium decay), then it would also be random by your definition. Or would you like to add riders to your definition?

And don't take that "random events are ludicrous" tone with me, as if I'm the only person on the planet who thinks this is the case. Most quantum physicists are happy to consider quantum events as truly random. Your physics, like your philosophy, is obsolete.

2) What's the difference between these two statements?

a) For all X, X can be explained by science and mathematics.

b) For all X, X can be explained if X can be explained with science and mathematics.

Not (a) => Not (b)? I don't think so.

Maybe you should go back to school and get another degree. In logic this time.

3) Modeling Random Events

Had you read what I wrote initally, you would know that I was primarily talking about modeling history. It doesn't matter whether the coin flips are actually deterministic or random. After they have been flipped, I can represent the results mathematically (e.g., an array of results, H, T, T, H, T, H, H...). We can also model future possibility with distributions, but that's not particularly relevant to the point that I was making.

4) Russell, Whitehead and Gödel

You might be able to pull the wool over the eyes of some folks, but not me.

Gödel's theorem tells us that certain mathematical systems are either inconsistent or incomplete. But who cares about completeness? What limitation is placed upon us by, say, our inability to prove the Goldbach Conjecture true, if it is, in fact, true? None of any great significance.

You write as if philosophy trumps mathematics when philosophy is bound by the theorem as much as mathematics is. If you can represent the natural numbers with your philosophy, and you use consistent rules of manipulation in coming to philosophical conclusions, then your philosophy is equally bound by the theorem.

We are all held hostage by the consistency of mathematics. If it were discovered that mathematics were deeply inconsistent, then it would be impossible to reason consistently about anything that had sufficient complexity.

So you implicitly assume the consistency of mathematics throughout your own philosophy. If logic is broken, then you can hardly give a convincing logical argument for any of your non-trivial philosophical claims.

The only remaining question up for debate is whether the system is complete. And, again,

I don't care!Completeness is irrelevant to my claims because I'm not saying that science and mathematics can decide or determine every true proposition. My point, for the nth time, is that science and mathematics provide the only basis for what we can know, but do not provide a guarantee that all truths can be known.5) Assuming Consistency

You have strong words about my assumption that the world is logical. Yet, the assumption that the world is logical is one you yourself make. And this assumptions, is nothing like traditional theistic assumptions which are useless, illogical and unjustified.

There can be no explanations for global consistency. That would rely on logic and be circular. So logical consistency is an assumption that has to be made before

anyargumentation takes place.6) Blog Behavior

Your comments about my blog behavior are calculated to mislead. I have only been banned from one blog, and that's Telic Thoughts. I was banned from there because they felt my comments (and those of other critics of ID) were spoiling the "pleasant and fruitful atmosphere" they were hoping to achieve. I was not cited for ad hominems. In fact, it was

who was cited for ad hominems by the admins at Telic Thoughts, not me.youIn our recent discussion at Real Physics, you claimed I made ad hominem statements. And what were these statements? Criticisms of the medieval Church. I'm sorry, but it's not an ad hominem to criticize a totalitarian, military dictatorship.

Again, how should I refer to these misleading statements of yours? I guess I'll be generous and call them "mistakes".

DL:

Despite your paranoia, I have NEVER posted any comments at Telic Thoughts. (Where is your verifiable evidence?) Again, you're letting your little conspiratorial wheels spin out of control.

As for your other comments: unbelievable... I've got to admit, you've stunned me. That is why I give you the final word.

dr: you make no sense at all. h shouldn't respond. no one should waste time answering you. do you know what obfuscate means?

Holopupenko said...

DL:

Despite your paranoia, I have NEVER posted any comments at Telic Thoughts. (Where is your verifiable evidence?)

.....................

http://telicthoughts.com/?p=360

I suggest that you start using a more generic tag if you insist on deception.

Sartresamigurumi & DL:

I stand corrected, humbled, and repentent: I honestly forgot because I was confusing Telic Thoughts with Tu Quoque. Please accept my brain fart and apologies.

Oops! That last message didn't quite turn out the way it should have... the last sentence should read: please accept my apologies for the brain flatulence...

Ah, so you meant to say:

Despite your paranoia, I have NEVER posted any comments atTu Quoque. (Where is your verifiable evidence?)An interesting excuse because what you claim to have "honestly" wanted to say was an even more egregious deception. The "studio audience," as you like to put it, can go to Tu Quoque and see if they can pick out which commentator just happens to be another Ph.D. nuclear engineer with a passion for Thomism and a penchant for emphasis with uppercase instead of HTML.

Non-apology not accepted.

DL:

Your paranoia is again getting the best of you. That you reject a sincere apology is your problem, not mine. Why? Because you’re chaining yourself to hatred. That you misunderstood (because of your self-imposed blinders) is also your problem. If you had stopped to think (!) for a moment that I was focused on the many exchanges at Tu Quoque, Real Physics, etc., and because of this simply forgot about Telic Thoughts exchange, you would have realized what was meant. Whether you accept this is, again, your problem.

All this serves as clear confirmation that your disordered will is driving your narrow-minded, dogmatic worldview. It also serves as confirmation that your hatred (as reflected in these exchanges and your various other postings) for those who disagree with you is eating you alive. It also confirms the hypocrisy of lecturing and preaching moral relativism on the one hand, while on the other hand crying absolutist “foul!” if you feel personally slighted. It betrays emotivism at the highest levels. You have become the very monster against which you so self-righteously rail.

Be assured, I will continue to hunt down and expose the dysfunctional ideas you promulgate. In the mean time, please seek help.

Holopupenko,

Oh, I see. I'm paranoid and obsessed, and that's why you stalk me in the blogosphere (and promise to continue doing so).

Talk to the hand!

P.S. Your pants are still on fire.

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