[Ichneumon]

For a good example of trying to "quantize a continuum", see this page on the comparison of various fossil hominid skulls. Scroll down a page or two to the table, "Creationist Classifications of Hominid Fossils". As the chart makes entirely clear, and the text explicitly points out, when the creationists try to "quantize" fossil skulls into the two disjoint categories of either "ape skull" or "human skull", they trip all over themselves (and each other) trying to decide which one goes where.

Excerpt:

As this table shows, although creationists are adamant that none of these are transitional and all are either apes or humans, they are not able to tell which are which. In fact, there are a number of creationists who have changed their opinion on some fossils. They do not even appear to be converging towards a consistent opinion. [...] Creationists, on the other hand, assert that apes and humans are separated by a wide gap. If this is true, deciding on which side of that gap individual fossils lie should be trivially easy. Clearly, that is not the case.

[highligting in original] The point is that even if one refuses to accept the evolutionary explanation for the apparently transitional skulls between ape and man, the fact remains that the skulls actually *do* map out a *continuum*, with various skulls having more/less ape and less/more human features, and it is an error which leads to immediate confusion if one attempts to "force" the skulls into artificially quantized categories of "all ape" or "all human".

The *reality* of the skulls is that they lie along a spectrum from "fully ape" on one end and "fully human" on the other, with "some of both in varying amounts" in between. Any attempt to quantize them into separate "buckets" immediately ties itself in knots and fails, as the chart makes quite clear.

[Alamo-Girl]

Thank y’all so much for your replies!!!

PatrickHenry: I think we have different understandings about what this fallacy is all about. To me, the fallacy of quantizing the continuum occurs when: (1) the subect being dealt with actually is a continuum; and (2) someone siezes upon an artifically defined segment thereof (a quantum) to declare something about that segment which is allegedly unique to it and not to that segment's boundry regions.

We agree on what the fallacy is about up to the point about the assertion of a “segment’s boundary regions”. To use Ichneumon’s rainbow – the fallacy would also say that one cannot distinguish red from blue even though they do not sit in juxtaposition – because one would have to base that determination on a quantization of red and blue. All one could say is blueness>redness in the continuum of the rainbow.

The application to biology is readily apparent. If Darwin were right, and all life is related by common descent, then it form a continuum, rather than a collection of discrete groupings we call "species." Thus, even where no intermediate forms are now alive, the theory predicts that they once did live, and perhaps will be found.

Indeed. Darwin’s theory is that the continuum exists. And certainly, the geologic record is a continuum but Darwin was speaking to the continuum of life.

Further, Darwin’s theory also asserts that there is an ancestry in the continuum leading from species to species and that is what I am saying requires a quantization of the continuum to assert. To use the rainbow metaphor again, it would be saying that because of the juxtaposition in the continuum of the rainbow, blueness descended from greenness which descended from redness (which we know is not a heritable trait in a rainbow).

So finding transitional forms confirms a prediction of the theory, and establishes the continuum.

I’m not fussing about the theory of evolution but rather the fallacy of quantizing the continuum – pitch the fallacy and we don’t have a problem. But back to your point at hand, those fossils which were found were (and are today) quantized by consensus of scientists and inserted in a particular presumptive order as you say, to establish the continuum. That doesn’t make them any less a quantization or the continuum any more “real” than the quantization itself.

Whereas insisting that each "kind" is and always was unique is an example of the fallacy.

Again, if we apply your statement to the rainbow – there is no distinction between red and blue. When applied to abiogenesis, there is no distinction between life and non-life.

That is patently absurd and why I reject the appeal to the fallacy of quantizing the continuum to argue against abiogenesis.

The blending of colors in the rainbows does not prevent us from knowing red from blue in the rainbow much less in everyday life. The blending of fossils in the geologic record does not prevent us from recognizing the difference between a horse and a man. And none of the proposed theories of abiogenesis would keep us from knowing the difference between a rock and rabbit or a live cat and a dead cat.

Ichneumon: I agree with the first half (that it would be a fallacy to define a *particular* point in the continuum at which "life" suddenly exists where it had not at all existed a moment before), but I disagree with the second half, concerning whether this would mean that "abiogenesis is idle speculation". I don't believe that was tortoise's point at all. In fact, I think it might be the exact opposite: By trying to "see" a sharp dividing line between "life" and "nonlife", one would have trouble understanding abiogenesis, because one would be looking for a "poof" moment when life "suddenly" arose from "nonlife". But this expectation would be mistaken, since abiogenesis would be the *gradual* emergence of life-as-we-know it by the slow one-at-a-time accumulation of the *many* processes which, all together, make up the complex system that we are familiar with under the label of "life". Between a chemical "soup" and even the simplest modern single-celled organism would be many stages in the "gray area" between "nonlife" and today's "life" as we are used to seeing it. Only by understanding that there *is* (or if you prefer, "would be") a continuum of nonlife/life is one able to begin to grasp the concepts of abiogenesis in a meaningful way.

You should have kept reading the Plato thread. The geologic continuum was only one of the continuums being asserted!

There were layers of continuums of what lies underneath. We were splitting rocks and rabbits until there was no distinguishable difference – i.e. matter, subatomic particles, fields, geometry.

Frankly, it was absurd - the notion that life cannot be distinguished from non-life or death because all are made up of the same “stuff”. betty boop used the example of going to the top of the Leaning Tower of Pisa and throwing off a live albatross, a dead albatross and a 12 lb cannonball.

You also should have kept reading the Plato thread because, at that time, noone was trying to define the difference between life and non-life or death from the biochemical characterizations. That is, as you probably know, a creationist argument – and we were trying to investigate abiogenesis scientifically and objectively. The model we chose was mathematical, Shannon’s mathematical theory of communications.

Later, when we gave up on trying to discuss abiogenesis, we began looking at life v non-life or death in the here-and-now. At that time another mathematical model with biological characterizations was asserted by betty boop, the Irvin Bauer model.

But the arguments against being able to define life v. non-life or death became even more absurd. Namely, since we can envision artificial intelligence such as von Neumann’s probe therefore there is no difference between life and death/non-life. So we clarified that we were speaking to life which occurs in nature.

The assertion then was that life in nature is indistinguishable in terms of “higher” or “lower” lifeforms - amoeba is equal to man. Naturally, we found that absurd as well and pointed to a host of alternative theories for the rise of complexity in biological life – Kolmogorov, functional, self-organizing, physical, etc.

There were quite a few sidebars along the way but that is the gist of it.

The geologic continuum is the continuum of focus to Darwin. From it, he asserted a continuum of biological life, common descent. But that is only one of the continuums involved here. And the conclusions being drawn right and left by asserting continuums and decrying quantizations are patently mindless.

Everyone knows there is a difference between life and death and between life and non-life. Everyone knows there is a difference between lifeforms. If they didn’t, they’d be moving to ban antibiotics and grant equal rights to bacteria.

It is the argument itself – the fallacy of quantizing the continuum - which is absurd, a smokescreen which prevents serious investigation of important issues here on the forum.

Physicist: Sophistry. Evolution is of course quantized at the level of the individual. The fossil record is of course tied to that quantization, because fossils are necessarily the remains of individuals. To claim that that disproves evolution is a farce, because it could not have been otherwise.

Indeed. It was sophistry – an attempt to make a point, hopefully with a little humor attached.

The fallacy of quantizing the continuum – this continuum, that continuum, all the continuums – was being thrown around like smoke bombs and obfuscated the issues we were trying to discuss.

But two can play that game – so I volleyed it right back to y’all by applying the fallacy of quantizing the continuum to the theory of evolution.

In sum, it is not possible for us to describe a rose and not be able to use the names of colors because their boundaries are obscured in a rainbow. If we say that green is made up of yellow and blue – the fact that green, yellow and blue all occur in a rainbow somewhere sometime – does not make it any less clear that green is made up of yellow and blue.