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Four fallacies evolutionists make when arguing about biological function (part 1)

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First of all, I want to apologize for shamelessly copying the title and structure of a recent post by VJ Torley. VJ, I hope you will pardon me: imitators, after all, are an undeniable mark of true success! 🙂

That said, let’s go to the subject of this post. I have discussed a little bit about biological function in my previous posts, and I have received many comments about that topic, some of them from very good interlocutors (I would like to publicly thank here Piotr and wd400, in particular). From my general experience in this blog during the last few years, I would like to sum up some of the more questionable attitudes and arguments which I have witnessed most frequently from the “other side” about this concept. Indeed, my purpose here is to catch not so much the specific arguments, but rather the general perspectives which are behind them, and which I believe to be wrong (that’s why I call them “fallacies” in the title).

So, here we go. First the whole list, then we analyze each individual point.

1. The fallacy of denying the objectivity of function.

2.  The fallacy of overemphasizing the role of generic function.

3. The fallacy of downplaying the role of specific function.

4. The fallacy of completely ignoring the highest form of function: the procedures.

I will deal with the first three issue in this post, and with the fourth in a later post.

1. The fallacy of denying the objectivity of function.

This attitude takes the form of an obstinate resistance to the concept itself of function, as though it were something which does not exist. So it happens that, as soon as we IDists start talking about functional specification, there is always someone on the other side ready to question: “Yes, but how do you define function?”. Or to argue that function is just a subjective concept, and that it has no role in science.

Many times I have simply answered: “Hey, just look at some protein database, like Uniprot. You will easily find, for each protein listed there, the voice: “Molecular function”. And usually there is one or more functions listed there. Is that bad science? Are you going to write to the people who run Uniprot asking them what do they mean by that word?”

rusty-185531_640The truth is that practically everybody understands perfectly what function means, and the attitude of denying the concept is just that: simple denial, motivated by the (correct) conviction that the concept itself of function is definitely ID friendly. .

However, the more sophisticated among our interlocutors will not deny function in such a gross way, but they will probably try to argue that the concept is obscure, vague, ill defined, and therefore not reliable. Here we find objections such as: “What do you mean exactly with the word?” or “To what kind of function do you refer?” or “Function can change according to how we define the context”. There is some truth in these thoughts, but in no way such objections are a real problem if we treat the concept of function correctly.

For example, in my previous post “Functional information defined” I have given the following definitions:

I will try to begin introducing two slightly different, but connected, concepts:

a) A function (for an object)

b) A functionality (in a material object)

I define a function for an object as follows:

a) If a conscious observer connects some observed object to some possible desired result which can be obtained using the object in a context, then we say that the conscious observer conceives of a function for that object.

b) If an object can objectively be used by a conscious observer to obtain some specific desired result in a certain context, according to the conceived function, then we say that the object has objective functionality, referred to the specific conceived function.

I will stick to those definitions.

So, function can be objectively defined, even if some reference to a conscious observer conceiving and recognizing it is always necessary.

It is perfectly true that different functions can be defined for the same object. There is no problem there. It is also true that functions can be stratified at different levels. Uniprot correctly lists “molecular functions”. So, for example, hexokinase has the molecular function of binding ATP and phosphorylating glucose or other hexoses, That is what I call the “local function”, the immediate biochemical effect of the molecule. But we can also say that the role of hexokinase is to start the glycolysis process and therefore contribute to the extraction of energy from food in the form of ATP, a role which would not be immediately obvious from the local function (which, instead, consumes ATP). This is a meta-function, because it describes the role of the enzyme in a wider context. We can say that the local function contributes to the meta-function.

In ID theory, local functions are specially interesting when we try to compute the functional complexity of a single protein. For that, we must refer to its immediate biochemical effect. But the meta-function is specially interesting too, when we try to analyze the complexity of a whole system of molecules, such as a protein cascades. In this kind of analysis, the concept of irreducible complexity is very important.

The important point is: denying function, or denying that it can be treated objectively in a scientific context, is a fallacy.

2.  The fallacy of overemphasizing the role of generic function.

This is generally what I call the concept of “any possible function”, which is so often invoked by darwinists as a reason to believe in the power of natural selection and of the neo-darwinian RV + NS algorithm.

The reasoning is more or less the following: as NS is not looking for anything particular, it will detect everything possible which is “useful”. IOWs, NS has no prejudices, and therefore it is very powerful, much more powerful of old good intelligent design, which is confined to intelligent options. That was one of Petrushka’s favourite arguments, but in different ways it has been proposed by many darwinist commentators here.

Now, I hate quoting myself again, but if you look at the above definscrapyardition of “function”, you will see that everything can be functional in some context. Function is not a rare thing, because, as already said:

If a conscious observer connects some observed object to some possible desired result which can be obtained using the object in a context, then we say that the conscious observer conceives of a function for that object.”

Now, as we can conceive of a lot of desires (that is certainly a very human prerogative), functions are very easy to get. In any context, we can use practically anything to obtain some result. That’s why I rarely throw away anything because, you know, “it could be useful, sooner or later”.

Does that reinforce the darwinist concept that “any possible function” is relevant?

Not at all. Quite the contrary. Just because possible functions are everywhere, it is easy to see that only some specific functions are really relevant in a specific context.

home-office-336377_640So, if I go to my attic, I can maybe find some use for any kind of junk that I may find there. But, if I happen to find a forgotten working computer there, I can certainly use it in a very specific way.

So, I would say that there is a great difference between finding some piece of wood which could perhaps be adapted to some use, and finding a working computer. The piece of wood is an example of “any possible function”, while the computer is an example of specific, complex function.

And, as anyone should understand, even if I find 1000 pieces of wood in my attic, that will not give me a working computer. IOWs, simple generic functions do not naturally add to a complex specific function.

So, why am I saying that darwinists tend to overemphasize the role of generic function?  The reason is simple: generic function is all they have, all they can deal with. Their only “engine of variation”, which is RV, can only, at best, generate simple generic function, nothing more. So, what do we do when we have only such and such?   We overemphasize the importance of such and such. Not because it is important, but because it is the only thing we have. An old fallacy, but always a common one.

3. The fallacy of downplaying the role of specific function.

The simple truth is that, especially in a system which is already complex, functional changes usually require complex interventions. Indeed, the addition of a truly new function to an existing complex system requires not only the complexity implicit in the function itself, but also the complexity necessary to integrate the new function in the existing system.

As already said, in the biological context there are two different ways to look at functions: what I call the “local function”, IOWs, the immediate biochemical activity of the molecule, and the “meta-functions”, IOWs, the general results of the activity of that molecule in the whole system.

Let’s take a molecule as an example: ATP synthase. A classic.

It is a very good example, because:

a) It is a very old molecule, already present in LUCA, before the archaea-bacteria divergence, almost 4 billion years ago.

b) It is a very complex molecule: it is made of two different parts, F0 and F1, each of them made of many subunits, and each subunit is a complex protein.

c) It is a very functional protein, indeed a wonderful molecular machine which transforms a proton gradient into stored biochemical energy in the form of ATP, working very much like a mill.old-windmill-96688_640

d) It is a very conserved protein. Let’s take only the subunits alpha and beta, which make most of the F1 part. a multiple alignment between: the human protein, the archaea protein (methanosarcina barkeri) and the bacterial protein (E. coli) showed 176 identities for the alpha subunit and 202 identities for the beta subunit. A total of 378 perfectly conserved aminoacid positions in just two of the many subunits of the molecule, along the whole tree of life.

e) Its local function is very clear: it synthesizes ATP from the energy derived from a proton gradient, transforming the flow of H+ ions into a mechanical rotation which in turn couples the phosphate molecule to ADP.

f) Its meta-function is equally clear: it generates the energy substrate which makes all cellular life possible: ATP.

Now, 378 identities after about 4 billion years during which all possible neutral mutations had time to happen mean just one thing: those 378 AAs must be there, and they must be what they are for the molecule to work.

This is a very good example of a very specific and complex function. In a complex context (cellular life), where the function is useful because there are a lot of individual processes whic h depend on ATP to exist. It is not the piece of wood in the attic. It is a supercomputer, an amazing molecular machine.

Well, are darwinists  curious, concerned or worried because of such specific complex functions which can be found in the old attic of OOL? Not at all. They are confident that they can be readily dealt with. There is an appropriate tool, usually called “the just so story”. For a good example, just read the Wikipedia section about ATP synthase, the part under “Evolution of ATP synthase”. Have fun.

The problem is: complex functional proteins simply cannot be explained. So, why should we think that they must be explained? After all, we can find so many generic functions in our attic: small variations in a gene which can give antibiotic resistance through one or two AA mutations, small changes in the affinity of an existing esterase which confer a nylonase activity through a couple of mutations, the selective spread in specific populations of the heterozigote state of drepanocytosis (one mutation) which gives some resistance to malaria. With all those good pieces of wood which can be used to fix some old chair, who cares about those stunning supercomputers which crowd our attic? They are just there, let’s not be fastidious about the details.

Well, that’s enough for the moment. We will discuss the “procedures” fallacy in next post.

 

 

 

Comments
GP: Back in the OP, you identified four key fallacies -- all of which I agree are relevant:
1. The fallacy of denying the objectivity of function. 2. The fallacy of overemphasizing the role of generic function. 3. The fallacy of downplaying the role of specific function. 4. The fallacy of completely ignoring the highest form of function: the procedures.
To recognise the existence, identity and significance of complex specific function and associated organisation and information requires one to acknowledge the reality of organisation, information, cause-effect chains and design as well as empirically reliable signs of design. Not to mention, the willingness to allow inductive logic on cause-effect patterns as observed to have its say. In a world where selective hyperskeptics in lab coats are only too willing to dismiss causality and linked first principles of right reason, want to pull a universe out of a quantum foam hat they wish to relabel as nothing, wish to assume that blind chance and mechanical necessity have magical powers to create FSCO/I regardless of search space challenges, and so forth, we do need to identify that problem. Similarly, there is a gross extrapolation problem where minor changes suddenly take on the guise of proof that much bigger and search space challenged changes are practically certain. We see refusal to recognise what pop genetics is telling us about fixation of mutations, and more. Let's just mention deep isolation of protein fold domains in AA sequence space. I think at root, objectors need to take a long hard look at how they have been reasoning, with Johnson's warning in the back of their minds:
For scientific materialists the materialism comes first; the science comes thereafter. [[Emphasis original] We might more accurately term them "materialists employing science." And if materialism is true, then some materialistic theory of evolution has to be true simply as a matter of logical deduction, regardless of the evidence. That theory will necessarily be at least roughly like neo-Darwinism, in that it will have to involve some combination of random changes and law-like processes capable of producing complicated organisms that (in Dawkins’ words) "give the appearance of having been designed for a purpose." . . . . The debate about creation and evolution is not deadlocked . . . Biblical literalism is not the issue. The issue is whether materialism and rationality are the same thing. Darwinism is based on an a priori commitment to materialism, not on a philosophically neutral assessment of the evidence. Separate the philosophy from the science, and the proud tower collapses. [[Emphasis added.] [[The Unraveling of Scientific Materialism, First Things, 77 (Nov. 1997), pp. 22 – 25.]
KFkairosfocus
July 12, 2014
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F/N: It is plain that we are dealing with a case of a network of mutually reinforcing fallacious thought; a problematique. So, when we press objectors at one level, there is a resort to ever deeper levels of fallacy-driven differences, ultimately rooted in doubts about or outright rejection of first principles of right reasoning, especially sufficient reason, modes of being, causality, identity and non-contradiction. This, we must recognise and highlight for what it is. Frankly, this is an intellectually bankrupt age, living on and rapidly consuming the heritage of the past. We need to wake up to that fact, face it, then set out to renew our civilisation's intellectual culture and linked moral culture -- duties of care to accuracy, truth, fairness etc are directly coupled to genuine reasonableness. KFkairosfocus
July 12, 2014
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Mapou, an earlier response was eaten, probably by my ISP. Pardon delay. I seek to give you some guidelines that speak to concerns without further distracting thread from main focus on fallacies. I note that whole numbers, fractions and the real numbers can be defined, based on place value notation without reference to concrete material objects. Recall, we go {} -->0. {0} --> 1, {0,1} --> 2 etc, then we get fractions a/b, then we define special ways to represent numbers as WHOLE.abcd . . . like 19.78. Between any two place value based numbers [think decimals like 19.78123 . . . ] we can interpolate a third, i.e. we have a meaning for continuum. Like a perfect rope not like rungs on a ladder with gaps you cannot stand on. Using sqrt -1, we may define an orthogonal axis so we define a plane of numbers z = x1 + i*x2, xn being a real number. We map the i*x axis to y. In such a plane, the eqn y = m*x + c defines a line. And, as all of this is conceptual, it can be ideally continuous, and lines have no thickness, they are strung together locations. Points, are locations, they are not blobs. All of this can then be applied to our world, recognising the limitations of reality relative to an idealised concept. So, we can think of getting area under a curve as a limit of a process of slicing it up into stripes that are thinner and thinner. In the limit, we arrive at the area. And, we thus have a meaning for the infinitesimals used in Calculus, dx, dt, etc. Non-Standard analysis may help you. KF KFkairosfocus
July 12, 2014
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SB: Recall, the injection of non-Euclidean geometries was used rhetorically to distract attention from the point that there are impossible beings -- entities that are infeasible as core attributes contradict, by coming up with equivocated redefinitions and contexts that twist all into pretzels. Such geometries are interesting in their context, but obviously what they call a square is not a square in the ordinary sense as already described, what they call a straight line is not a straight line in the ordinary sense and so on. If P had said, the analogue of a square or the analogue of a straight line or the like, that is different, but the above just shows tat we are seeing an equivocation based red herring led away to a strawman in a context where we saw a major outcome on the issue of first principles of right reason and the linked matter of causality. Notice, behind the cloud of distractive discussion, that pivotal matter seems to have now vanished from attention. I doubt that that is an accident. Let us take due note, and only respond tot he distraction insofar as it is relevant to highlight it as yet another example of fallacious reasoning. KF PS: Observe, Wikipedia:
In non-Euclidean geometry, squares are more generally [--> Notice, shift of context from the normal one] polygons [--> Also redefined to not imply straight line based sides, oops, straight line is also redefined] with 4 equal sides and equal angles. In spherical geometry, a square is a polygon whose edges are great circle arcs [--> not straight lines] of equal distance, which meet at equal angles. Unlike the square of plane geometry, the angles of such a square are larger than a right angle [--> Tell that to manufacturers of roofing squares and carpenter's squares]. Larger spherical squares have larger angles. In hyperbolic geometry, squares with right angles do not exist. Rather, squares in hyperbolic geometry have angles of less than right angles. Larger hyperbolic squares have smaller angles
Where obviously "polygon" has been redefined from being an object with straight line sides, straight line has been redefined form being actually straight, etc etc. Distance, too, and being in a plane, and more. The point is the whole purpose here is distractive based on an equivocation fallacy. Brightening up the pink paint mix to make yellow, by adding yellow paint. "It depends on what the definition of is, is."kairosfocus
July 12, 2014
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StephenB, I'm not going to stretch this off-topic thread ad infinitum. If you want to educate yourself, I recommend an excellent, pretty elementary and reader-friendly introduction to non-Euclidean geometry by Stefan Kulczycki (originally written in Polish in the 1950s but still re-published in English): Stefan Kulczycki. 1961. Non-Euclidean Geometry. Oxford: Pergamon Press. A convenient brief introduction (with illustrations, links, and more bibliography) can be found here: http://www.math.cornell.edu/~mec/mircea.htmlPiotr
July 12, 2014
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424 should read, "So, do you have a single definition for a non-Euclidian circle and a non-Euclidian [square] or do you not?"StephenB
July 11, 2014
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Querius @423. Thank you. I hope that I am not running out of ways to explain why reason must lead and scientific evidence must follow.StephenB
July 11, 2014
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Piotr
Yes, the two sets partly overlap. Like, say, some integer numbers divisible by 3 are also divisible by 7, but there are also integers divisible by 3 but not by 7, and integers divisible by 7 but not by 3.
SB; Does this mean that some non-Euclidan circles have four equal sides and others do not?
It means that some circles in spherical geometry (considered as sets of points on a surface) are at the same time analysable as quadritalerals with four equal sides and four equal angles. The only circles that have this property are the so-called great circles of the sphere in question (a great circle is any circle that cuts the sphere into two equal hemispheres).
Analyzsable? I am not asking you how they appear or by what method they can be studied. I am asking your what they are, by definition. You can analyze a circle as a square all day long, that doesn't mean that is is, by definition, a square. According to your definition, a non-Euclidian square has four equal sides, and is different from some non-Euclidian circles, which do not. Conversely, non-Euclidian circle (that is not a great circle) does not have four equal sides and is different from a square. On the other hand, a non-Euclidian great circle, which would have to satisfy the definition of a circle and a square in order to be both, does have four equal sides. So it seems evident that some non-Euclidian circles (great) have four sides and some do not. Similarly, some non-Euclidian squares (by virtue of also being great circles) are the set of all points on a surface that are at the same distance from the center while others are not. So, do you have a single definition for a non-Euclidian circle and a non-Euclidian circle or do you not?StephenB
July 11, 2014
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StephenB@416 Nicely stated. - Yes, causality is a foundation of science (among other things, including repeatability). - In contrast, the primary foundation stone of Darwinism is speculative interpretation (among other things, including ideological affinity). Mapou, Non-Euclidean geometries depend on what one chooses to define and how many instances there are. Some geometries define only points---there is no such thing as a "line." In others, several lines are defined and "points" are not. Anyone read George Gamow's "One, two, three ... Infinity" when they were growing up? In it, Gamow describes an equilateral triangle with straight lines that each meet at a 90 (not 60) degree angle. Now how did he do that? ;-) -QQuerius
July 11, 2014
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StephenB
[Square: a polygon with four equal internal triangles and four equal sides].
Four equal angles, not triangles.
So, some non-Euclidian squares are circles and others are not?
Yes, the two sets partly overlap. Like, say, some integer numbers divisible by 3 are also divisible by 7, but there are also integers divisible by 3 but not by 7, and integers divisible by 7 but not by 3.
Does this mean that some non-Euclidan circles have four equal sides and others do not?
It means that some circles in spherical geometry (considered as sets of points on a surface) are at the same time analysable as quadritalerals with four equal sides and four equal angles. The only circles that have this property are the so-called great circles of the sphere in question (a great circle is any circle that cuts the sphere into two equal hemispheres). A great circle is also the spherical-geometry analogue of a Euclidean straight line, so you can say that in that type of geometry there are certain figures that are at the same time straight lines, circles, and squares (and, by the way, equilateral triangles, regular pentagons, hexagons, heptagons, etc.).Piotr
July 11, 2014
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Piotr
Do you really think I’m fudging definitions or making stuff up as I go along? It’s been mathematical common knowledge for a long time.
I don't think it is ever an imposition to ask a person to define his terms. To me, that's where everything starts. [Square: a polygon with four equal internal triangles and four equal sides]. [Circle: the set of all points on a surface that are the same distance from a given point O]. Thank you. I appreciate it. I am just trying to make sense of your other comment to Eric about non-Euclidian squares:
No, not in general (there are squares that are not circles, and there are circles that are not squares), but in spherical geometry every great circle is at the same time a square (or, to be precise, there are infinitely many squares identical with it, since you are free to choose any point on the circle as one of the vertices of a square.
So, some non-Euclidian squares are circles and others are not? Does this mean that some non-Euclidan circles have four equal sides and others do not?StephenB
July 11, 2014
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Gentlemen, please answer this question: is there such a thing as a line? Does it not assume continuity, i.e., infinite smoothness? Before one can talk about a line, one must prove that continuity is a scientific/logical concept. In my opinion, continuity is pseudoscientific nonsense. This means that lines, surfaces, circles, spheres, etc., do not exist. We only have approximations at the macroscopic level.Mapou
July 11, 2014
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StephenB: I have already defined a square: a polygon with four equal internal angles and four equal sides. This definition works in both Euclidean and non-Euclidean geometries. A circle is the set of all points on a surface that are at the same distance r (called the radius) from a given point O (called the centre). Again, this works in both Euclidean and non-Euclidean geometries. Do you really think I'm fudging definitions or making stuff up as I go along? It's been mathematical common knowledge for a long time. Non-Euclidean geometries were discovered by Gauss, Lobachevsky and Bolyai about 200 years ago. By the 1850s Riemann developed a general theory of n-dimensional manifolds, geometries and their metric properties -- the formalism employed, for example, in general relativity.Piotr
July 11, 2014
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Piotr
Of course they are: the “straight lines” in question are geodesics (a line segment bounded by A and B is defined as the shortest path from A to B in the space we are considering).
Define a non-Euclidian circle and define a non-Euclidian square.StephenB
July 11, 2014
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Piotr: When is a straight line not a straight line? It depends on what the meaning of is, is. Please, confusion of identity through equivocation is a straight path to absurdity. KF PS: Kindly note that I gave something that will allow us to identify straight lines in accord with y = mx + c, above. We can extend to a 3-d space using the ijk unit vectors.kairosfocus
July 11, 2014
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Two men walk into a room and notice a red ball lying on the table that once wasn't there. Person A. Look, there is a red ball lying on the table. I wonder how it got there. Person B. What do you mean, "how did it get there?" Obviously, someone put it there. This argument is unassailable. It is self-evidently true. No amount of scientific evidence can affirm it or negate the point. The principle of causality is not based on science; science is based on the principle of causality. Now blow the ball up to the size of the room. Has the argument changed or lost any of its force? No. Now blow the ball up the size of a city, a country, the world, the cosmos. Has the argument changed? No. The only thing that has changed is the size of the ball.StephenB
July 11, 2014
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KF:
Are those squares based on straight line side...
Of course they are: the "straight lines" in question are geodesics (a line segment bounded by A and B is defined as the shortest path from A to B in the space we are considering).Piotr
July 11, 2014
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SB: That there is a sufficient reason for God, would not entail that we have compassed all there is of God in such a discussion. KF
Right. That is the point I was trying to express to Paul after taking his objection into account. (In other words, I don't think Feser needs to change his language [unless there is some other point that I am missing])StephenB
July 11, 2014
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KF at 411. Exactly. So many of the other side's arguments rest on equivocation that I've lost count.Barry Arrington
July 11, 2014
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SB: That there is a sufficient reason for God, would not entail that we have compassed all there is of God in such a discussion. KFkairosfocus
July 11, 2014
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Piotr: Are those squares based on straight line side, polygons -- specifically, a rhombus with a right angle vertex? If not, have we not equivocated the term square, which carries us right back to square one? And, are we not therefore on a side-track that -- however interesting in its own right -- does not undermine the basic point that when we see an entity A we may ask, why is it, and seek to understand in light of modes of being, with impossible beings having a problem of self contradictory core characteristics that block them from being feasible in any possible world? Such as, classically, a square circle, per the ordinary meaning of circles and squares? KFkairosfocus
July 11, 2014
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Eric Anderson:
Is a square identical to, in other words the same thing as, a circle in non-Euclidean geometry?
No, not in general (there are squares that are not circles, and there are circles that are not squares), but in spherical geometry every great circle is at the same time a square (or, to be precise, there are infinitely many squares identical with it, since you are free to choose any point on the circle as one of the vertices of a square.Piotr
July 11, 2014
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Paul @403, The more I think about it, the more I am inclined to go with my original position and support Feser's comment. Granted, we cannot really explain God, but insofar as we are discussing the principle of sufficient reason or causality, we can, and must, explain God’s role. We cannot understand causality without realizing that God must be an uncaused caused insofar as he, unlike everything else, did not come into existence. God is the necessary being if there is any such thing as being at all. Also, we cannot fully understand causality without understanding that creation itself must be caused and that God is the cause or reason for its existence. In these, and other ways, we can explain God’s role.StephenB
July 11, 2014
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Piotr @404: You still haven't answered the question that your example rests on: Is a square identical to, in other words the same thing as, a circle in non-Euclidean geometry? Yes or no?Eric Anderson
July 11, 2014
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F/N: I should add on getting the plane Z. The plane is the set of points z such that z = x1 + i*x2, where x1 and x2 are reals. z --> (x, y). Building the plane on a unit square with 2r = 1, draws out euclidean properties. KFkairosfocus
July 11, 2014
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PG, 401:
I gave you two sets of examples. The first was mathematical concepts, concerning which you missed the significance. The second was far more important. Feser failed to make any exceptions, but God clearly should be one. The Ground of All Being does not need nor does He have, an explanation. Otherwise, the “who created God” objection would apply in full force.
Q, 402:
Just as calculus is based on dividing by zero (OK, large values of zero), and Euclidean geometry is based on correct reasoning applied to incorrect figures, non-Euclidean geometries are based on correct reasoning applied to absurd definitions.
SB, 403:
Did I not say that the law of causality has nothing to do with mathematics? Did I not say that numbers cannot be a part of a causal series of events? Did I not say that the first rules of right reason are not simply assumed? Why do you allude to mathematical axioms in this case when, unlike reason’s rules, they are not necessarily based on self-evident truths? . . . . Feser should have used the words “every event” or something to that effect. Otherwise, someone might get the impression that God must be subject to explanation in order for PSR to be true.
Piotr, 404:
The definition of a regular polygon is, “a polygon that is equiangular (all angles are equal in measure) and equilateral (all sides have the same length)”. Since you can prove that in Euclidean geometry each interior angle of an n-sided convex polygon measures [(n-2)/n]×180° (= 90° for n = 4), there’s no need to specify this value in the definition. So if we use the term “square” as shorthand for “regular quadrilateral”, then of course in Euclidean geometry every square has four right angles; this, however, is a corollary of the definition, not part of it. Likewise, a regular convex pentagon has five equal angles and five equal sides. This is enough to define it, and then you can calculate the measure of each angle (108°), assuming that you’re doing geometry on a Euclidean plane. Such a parsimonious definition has the advantage of remaining meaningful in geometries that are not Euclidean. You can still have equiangular and equilateral quadrilaterals in spherical and hyperbolic geometries, but each angle will be, respectively, larger or smaller than 90°. The alternative description of a regular polygon, “a polygon with equal sides, inscribed in a circle” is equivalent to the definition above, and also remains valid in non-Euclidean geometries.
1 --> First, the principle of sufficient reason (weak or strong form) should not be divorced from the analysis of modes of being that it invites. Which will inform us that of possible beings -- in light of the issue of enabling factors -- there are contingent and necessary beings. 2 --> In that context, God is best understood philosophically, conceptually, as a maximally great and necessary being. Indeed, the reference, The Eternal One, points to necessary being status. And that is a sufficient reason . . . as opposed to a causal explanation. 3 --> Theism thus implies that one cannot build a feasible world without God as its root. Thus, it is an implicit prediction of theistic worldviews that non-theistic views will at some point run into insuperable worldview difficulties. (But such may not necessarily be obvious on merely understanding the skeletal structure of the views.) 4 --> Where, yes, Mathematical axioms today tend to stand on their own, but are shaped by a tradition and framework that historically tied mathematics to insights on reality and reasoning, such that incoherence is a major red flag, and indeed a key step in proofs by contradiction of the denial of a claim. Where of course, Mathematical axioms do not need to be self-evident, though some in fact are. 5 -> Similarly, whether by the conventional limits approach or the hyper-real numbers and their reciprocals used in non-standard analysis [which BTW is close in spirit to Newton's initial ideas, and I found that echoed in an early, mid-C19 edn of the famous Elements of the Integral and Differential Calculus textbook by Smith, later Granville, Smith and Longley], Calculus scrupulously avoids division by zero. Though, popular talk about infinitesimals might give that impression. 6 --> In fact, that is why Mathematical definitions are often as carefully composed as terms of a legal contract -- to avoid trouble. 7 --> Where, I find it very interesting to see how a key element in the ordinary definition of a square and indeed a polygon, is subtly being dropped in the way P is arguing: straightness of sides. As in a square is a rhombus [an equal-sided quadrilateral] with a vertex angle as a right angle, or a rectangle with equal sides. 8 --> Again, as Collins Dict. reports on ordinary usage . . . which prevails without clear stipulation of special usage in a new context:
polygon n 1. (Mathematics) a closed plane figure bounded by three or more straight sides that meet in pairs in the same number of vertices, and do not intersect other than at these vertices. The sum of the interior angles is (n-2) × 180° for n sides; the sum of the exterior angles is 360°. A regular polygon has all its sides and angles equal. Specific polygons are named according to the number of sides, such as triangle, pentagon, etc
9 --> In short, we are back at the problem of Feynman's painter making Yellow from white and red paint, then brightening it up with a bit of yellow. 10 --> By all means, explore non-Euclidean Geometries and ask whether our space in the large is Euclidean, and whether we are seeing only an ideal based on the small scale we are used to. But, kindly appreciate that the Euclidean type space has a validity on its own, is broadly applicable in ever so much real-world work, and is the ordinary spatial sense employed. 11 --> So, when one discusses the problem of the square circle, that context is implicit. And, to get to the geometry of a spherical surface, key elements are reshaped. 12 --> That reshaping ought not to be done without announcement of a diverse context, and key differences such that a "square" as redefined loses the requisite of straight sides and right angle corners for a planar figure, should not be glided over as if they were unimportant. 13 --> Just for illustrative purposes, let me take the reals line as definable by using the development of numbers from collected sets in order from {} --> 0. {0} --> 1, {0,1} --> 2 on, with fractions and reals by use of place value notation. We define an orthogonal axis as y = i*x, i being sqrt -1. (As a bonus this sets up rotations, vectors etc.) 14 --> This defines also the plane and we may then define a circle as above, algebraically. Easy version, the locus of points p stipulated by x^2 + y^2 = r^2, with r real and x, y in the closed interval [-r, r]. Where, interior points are also part of the circle. This can be displaced from the origin by suitable adjustments (which just complicate things) so this is WLOG. 15 --> Similarly, we may define a square on being a figure bounded by the lines y = 0, x = 0, y = 2r, x = 2r, with its interior points. Again, such can be displaced so this is WLOG. 16 --> We have a Cartesian plane that indicates just how important a Euclidean space is, and part of why it is the standard, default space geometry used. 17 --> It is patently impossible for a figure to satisfy both the equation for a circle and that for a square, however displaced. (And yes, I have used conditions that will make the figures of similar size.) 18 --> I do this to show that the traditional geometry which is commonly intuitively applied, is capable of being represented in a coordinates based form, and thus of algebraic representation which brings out the sorts of problems that are connected to trying to erect a square circle. 19 --> However, this algebraic case has the problem that this is not now a "simple" picture. I have had to go back as far as setting up sets of numbers and drawing out how we arrive at a plane space, including use of complex numbers. 20 --> The much simpler case that squarishness and circularity require contradictory attributes when these are understood [implicitly] in the normal everyday sense, is something accessible to any reasonably experienced person, though real-world objects and sketches are not the ideal figures of geometry, or for that matter graphs on a textbook page are again indicative illustrations not the correct figures. (E.g. A line has no thickness and a point has no size, only location.) 21 --> But the models we use on sand, chalkboard or paper or these days on screen, are useful representations. 22 --> The bottomline remains, we must not make the error of Feynman's painter brightening up a pink mixture to make yellow. 23 --> And, there's a handy name for yet another fallacy: brightening up the pink paint with yellow. KFkairosfocus
July 11, 2014
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Paul Giem (385),
Let me distract you for a little while longer from the argument regarding universal causality.
I don’t intend to return to that discussion. So no problem.  
Logically I might not have eliminated the possibility that an unguided process can create light, and it is reasonably certain that humans with their (our) present knowledge and technology are unable to create life, so it is logically possible that your scenario would work. But that is a little like saying that it is logically (and possibly even theoretically) possible that volcanic eruptions can get a piece of parchment with writing on it from earth to the moon, and that humans in their present stage (think 1860) are not capable of doing it, and therefore we should bet on the volcanic eruptions.
No. It is like saying that just because the volcano hypothesis is not viable we cannot assume there is no unguided hypothesis. The ID position is like saying we don’t how a piece of parchment could have got to the moon but we do know people carry pieces of parchment to Paris so let’s assume that some undefined thing with a super carrying ability took it to the moon, and let’s rule out unguided processes because the volcano theory doesn’t stand up and we can’t think of one that would do the trick.  The volcanic eruptions theory would be a specific hypothesis that could easily be disproved.
I am confused as to why you refer to statistics. In order to calculate statistics correctly, one has to know the underlying odds, which are usually thought to be best calculated if one has a good handle on the underlying scientific issues. This should make you more, not less, interested, in the current science, and the trajectory of scientific opinion.
I am interested in statistics in all sorts of contexts but I don’t have the time or will  to get the scientific background to apply them to evolutionary theory.
And perhaps more importantly, you seem to be completely divorcing the issue of whether there is a designer from the science involved. That sounds like scientific know-nothingism. Briefly, the argument could be put, the difficulty of nature creating even relatively small polymers essential for life and the ease with which intelligent agents can produce much larger polymers that can be functional is not even involved in the question of whether an intelligent agent was responsible for the first life. The ultimate absurdity would be to take this reasoning to its logical conclusion: if we observe intelligent agents creating life itself, this would have no bearing on the question. To sustain this position requires some really robust philosophy!
I think it is quite possible to divorce the question of whether current evolutionary theory can explain the creation of relatively small polymers (not nature – that does not follow) from the logic of the argument – therefore something like a souped up human being did it.  On the God of the Gaps and J Harlan Bretz.  Bretz proposed a hypothesis with lots of implications that could be tested. He didn’t just look at some pieces of evidence and say “the explanation is a supernatural force that has the power to produce this evidence”.  As I have said many, many times – if ID stepped up to the plate and said we believe life was created by this God with these powers using these methods we could then do the kind of assessment that Bretz was subject to
When I look back at what appears to me to be the main thrust of your comments, it seems to be that ID hasn’t proved its case. And I think that most ID advocates, certainly the more prominent ones, would agree that ID can never logically prove its case. That’s why the reasoning is more properly described as adductive, or the inference to the best available explanation. But you seem to be requiring more; you need philosophical/mathematical/scientific proof. You can never get scientific proof. You really don’t like it when someone tries philosophical proof. And mathematics may limit, but does not dictate, the shape of the material world (you can’t show me why the moon is in the exact position it is in, or even that there is a moon, from mathematics alone). So there will be no proof for you.
I don’t want proof so much as something to prove or disprove.
Which maths would you like to see first? We’ll see if we can present them. This could get really interesting.
I have seen the maths I have found dubious. Do you think I would find it dubious without seeing it? Here are a couple of examples.
http://www.talkreason.org/articles/likely.cfm http://www.markfrank.me.uk/home/writing/SomethoughtsaboutLCI.doc?attredirects=0&d=1  
Mark Frank
July 11, 2014
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Perhaps you can tell me your definition of square, and where you got it. That is, if you are still answering questions here.
A definition should not contain redundant elements. The definition of a regular polygon is, "a polygon that is equiangular (all angles are equal in measure) and equilateral (all sides have the same length)". Since you can prove that in Euclidean geometry each interior angle of an n-sided convex polygon measures [(n-2)/n]×180° (= 90° for n = 4), there's no need to specify this value in the definition. So if we use the term "square" as shorthand for "regular quadrilateral", then of course in Euclidean geometry every square has four right angles; this, however, is a corollary of the definition, not part of it. Likewise, a regular convex pentagon has five equal angles and five equal sides. This is enough to define it, and then you can calculate the measure of each angle (108°), assuming that you're doing geometry on a Euclidean plane. Such a parsimonious definition has the advantage of remaining meaningful in geometries that are not Euclidean. You can still have equiangular and equilateral quadrilaterals in spherical and hyperbolic geometries, but each angle will be, respectively, larger or smaller than 90°. The alternative description of a regular polygon, "a polygon with equal sides, inscribed in a circle" is equivalent to the definition above, and also remains valid in non-Euclidean geometries. I'm not making this up; it's standard stuff: http://en.wikipedia.org/wiki/Square#Non-Euclidean_geometry Of course it's a generalisation of the everyday notion of "square", but maths is all about useful generalisations. Integers are a generalisation of natural numbers, and rational, real, and complex numbers are still further extensions at greater and greater levels of abstraction. But the same operations still work for them all, and they all have important applications in physical science. I don't hear people protest that zero is not really a number because the ancient Greeks didn't regard it as such, ot that π is not a number because you can't count up from one to π or have π apples in a basket.Piotr
July 11, 2014
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Paul
I gave you two sets of examples. The first was mathematical concepts, concerning which you missed the significance.
I don't understand your response. Did I not say that the law of causality has nothing to do with mathematics? Did I not say that numbers cannot be a part of a causal series of events? Did I not say that the first rules of right reason are not simply assumed? Why do you allude to mathematical axioms in this case when, unlike reason's rules, they are not necessarily based on self-evident truths? You must have something else in mind.
Feser was not careful enough.
OK. I get your point on this one. Feser should have used the words "every event" or something to that effect. Otherwise, someone might get the impression that God must be subject to explanation in order for PSR to be true. I really don't think anyone is going to misunderstand him if they read the entire three paragraphs, but I agree he could have been more precise in this case.StephenB
July 10, 2014
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Paul,
So, unless you are trying to form a complete mockery of the definition, a figure cannot be a square and a circle at the same time.
Just as calculus is based on dividing by zero (OK, large values of zero), and Euclidean geometry is based on correct reasoning applied to incorrect figures, non-Euclidean geometries are based on correct reasoning applied to absurd definitions. It's mildly annoying that this actually works. If you draw the largest square possible on the surface of a spherically curved universe, you will get a circle. If you want to have more fun, you can prove to yourself that if space is spherically curved in 4D, the minimum value of Pi is exactly 2, depending on the size of the circle in relation to the size of the universe. Oh hey, my previous post hit 400 exactly!!! Do I get three wishes? ;-) -QQuerius
July 10, 2014
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