Language

The Cave

entirelyuseless Logic , , , ,

Book VII of Plato’s Republic begins with this conversation between Socrates and Glaucon:

And now, I said, let me show in a figure how far our nature is enlightened or unenlightened: –Behold! human beings living in a underground den, which has a mouth open towards the light and reaching all along the den; here they have been from their childhood, and have their legs and necks chained so that they cannot move, and can only see before them, being prevented by the chains from turning round their heads. Above and behind them a fire is blazing at a distance, and between the fire and the prisoners there is a raised way; and you will see, if you look, a low wall built along the way, like the screen which marionette players have in front of them, over which they show the puppets.

I see.
And do you see, I said, men passing along the wall carrying all sorts of vessels, and statues and figures of animals made of wood and stone and various materials, which appear over the wall? Some of them are talking, others silent.

You have shown me a strange image, and they are strange prisoners.
Like ourselves, I replied; and they see only their own shadows, or the shadows of one another, which the fire throws on the opposite wall of the cave?

True, he said; how could they see anything but the shadows if they were never allowed to move their heads?

And of the objects which are being carried in like manner they would only see the shadows?

Yes, he said.
And if they were able to converse with one another, would they not suppose that they were naming what was actually before them?

Very true.
And suppose further that the prison had an echo which came from the other side, would they not be sure to fancy when one of the passers-by spoke that the voice which they heard came from the passing shadow?

No question, he replied.
To them, I said, the truth would be literally nothing but the shadows of the images.

That is certain.

The human situation with respect to truth is somewhat like Plato’s cave dwellers. I argued in the previous post that all human knowledge is imperfect and vague. A more precise argument to the same effect would be the following.

There are two basic ways that we can learn the meaning of words. In one way, by having the meaning of the word explained to us. This requires the knowledge of other words. In another way, by learning the contexts in which the word is used. This does not necessarily require the previous knowledge of other words. Thus for example we learn the meaning of the word “red” by seeing it used in reference to red things, without a necessity of explaining the idea of red using other words. Third, we might learn the meaning of some words by a combination of the above methods.

Defining a word by other words cannot lead to an absolutely precise meaning unless the other words that are used have an absolutely precise meaning, so such a definition cannot be a source of absolute precision. And unless one points to all possible cases in which a word might be used, which is a physical impossibility, experiencing the contexts in which a word is used will also never lead to an absolutely precise meaning. It is consequently unlikely that you can arrive at an absolutely precise meaning by any combination of these methods, and consequently unlikely that you can arrive at such absolute precision in any way.

Language and thought are very closely connected. There are perhaps not many real cases of feral children, but the experience we do have of such situations suggests that someone who does not learn a language is basically unable to think. This is perhaps not true absolutely, but it is surely true that such a child cannot think clearly. Clear thinking requires language. This at least suggests that perfectly clear thinking would require perfectly clear language. But this is impossible, by the above argument. Consequently perfectly clear thinking is impossible for human beings.

This argument does not refute itself. It it of course impossible to have a proof that there are no proofs. Likewise, if absolute subjective certainty is impossible, as I have suggested, then it is impossible to have such certainty about this very fact. There is no inconsistency here. Likewise, if all thoughts and all arguments are vague, then these very thoughts and this very argument is vague. There is no inconsistency here.

Origin of Species

entirelyuseless Science , , , , , , ,

As we noted previously, Philip Gosse published his book attempting to reconcile geology and Scripture just a few years before Charles Darwin published his book On the Origin of Species.

In that previous post, I quoted Gosse’s summary of the state of geology. It would be useful to look again at several particular statements taken from that summary:

6. A series of organic beings appears, lives, generates, dies; lives, generates, dies; for thousands and thousands of successive generations. Tiny polypes gradually build up gigantic masses of coral,—mountains and reefs—microscopic foraminifera accumulate strata of calcareous sand; still more minute infusoria—forty millions to the inch—make slates, many yards thick, of their shells alone.

7. The species at length die out—a process which we have no data to measure, though we may reasonably conclude it very long. Sometimes the whole existing fauna seems to have come to a sudden violent end; at others, the species die out one by one. In the former case suddenly, in the latter progressively, new creatures supply the place of the old. Not only do species change; the very genera change, and change again. Forms of beings, strange beings, beings of uncouth shape, of mighty ferocity and power, of gigantic dimensions, come in, run their specific race, propagate their kinds generation after generation,—and at length die out and disappear; to be replaced by other species, each approaching nearer and nearer to familiar forms.

…

9. Millions of forest-trees sprang up, towered to heaven, and fell, to be crushed into the coal strata which make our winter fires. Hundreds of feet measure the thickness of what were once succulent plants, but pressed together like paper-pulp, and consolidated under a weight absolutely immensurable. Yet there remain the scales of their stems, the elegant reticulated patterns of their bark, the delicate tracery of their leaf-nerves, indelibly depicted by an unpatented process of “nature-printing.” And when we examine the record,—the forms of the leaves, the structure of the tissues, we get the same result as before, that the plants belonged to a flora which had no species in common with that which adorns the modern earth. Very gradually, and only after many successions, not of individual generations, but of the cycles of species, genera, and even families, did the vegetable creation conform itself to ours.

10. At length the species both of plants and animals grew,—not by alteration of their specific characters, but by replacement of species by species—more and more like what we have now on the earth, and finally merged into our present flora and fauna, about the time when we find the first geological traces of man.

Careful analysis of the rocks reveals an order of time, and that order of time reveals a history of life on earth. In that history, life was at first very different from its present form, and approached more and more closely to its present form over time, reaching that present form more or less with the existence of man. When we consider this together with the idea of what happens when imperfect copies are made repeatedly over time, we can see that this is very good evidence for the theory of evolution, considered as a theory of the common descent of living things. Gosse in fact vaguely suggests such a theory himself, when he suggests that the relationship of various species is much like the relationship of one individual to another.

Charles Darwin begins the introduction to his work:

When on board H.M.S. Beagle, as naturalist, I was much struck with certain facts in the distribution of the organic beings inhabiting South America, and in the geological relations of the present to the past inhabitants of that continent. These facts, as will be seen in the latter chapters of this volume, seemed to throw some light on the origin of species–that mystery of mysteries, as it has been called by one of our greatest philosophers. On my return home, it occurred to me, in 1837, that something might perhaps be made out on this question by patiently accumulating and reflecting on all sorts of facts which could possibly have any bearing on it. After five years’ work I allowed myself to speculate on the subject, and drew up some short notes; these I enlarged in 1844 into a sketch of the conclusions, which then seemed to me probable: from that period to the present day I have steadily pursued the same object. I hope that I may be excused for entering on these personal details, as I give them to show that I have not been hasty in coming to a decision. My work is now (1859) nearly finished; but as it will take me many more years to complete it, and as my health is far from strong, I have been urged to publish this abstract. I have more especially been induced to do this, as Mr. Wallace, who is now studying the natural history of the Malay Archipelago, has arrived at almost exactly the same general conclusions that I have on the origin of species. In 1858 he sent me a memoir on this subject, with a request that I would forward it to Sir Charles Lyell, who sent it to the Linnean Society, and it is published in the third volume of the Journal of that Society. Sir C. Lyell and Dr. Hooker, who both knew of my work–the latter having read my sketch of 1844–honoured me by thinking it advisable to publish, with Mr. Wallace’s excellent memoir, some brief extracts from my manuscripts.

As indicated by Gosse’s summary, by this time geology had basically reached the state where the idea of evolution was a very natural understanding of the history of life on earth. Consequently Darwin was not inventing some strange and marvelous idea, but simply drawing out the implications of what was already present in the science of geology. As he indicates here, he was not alone in doing that, and he was not alone in doing it at the time.

Darwin discusses natural selection in chapter four of his book:

How will the struggle for existence, briefly discussed in the last chapter, act in regard to variation? Can the principle of selection, which we have seen is so potent in the hands of man, apply under nature? I think we shall see that it can act most efficiently. Let the endless number of slight variations and individual differences occurring in our domestic productions, and, in a lesser degree, in those under nature, be borne in mind; as well as the strength of the hereditary tendency. Under domestication, it may truly be said that the whole organisation becomes in some degree plastic. But the variability, which we almost universally meet with in our domestic productions is not directly produced, as Hooker and Asa Gray have well remarked, by man; he can neither originate varieties nor prevent their occurrence; he can only preserve and accumulate such as do occur. Unintentionally he exposes organic beings to new and changing conditions of life, and variability ensues; but similar changes of conditions might and do occur under nature. Let it also be borne in mind how infinitely complex and close-fitting are the mutual relations of all organic beings to each other and to their physical conditions of life; and consequently what infinitely varied diversities of structure might be of use to each being under changing conditions of life. Can it then be thought improbable, seeing that variations useful to man have undoubtedly occurred, that other variations useful in some way to each being in the great and complex battle of life, should occur in the course of many successive generations? If such do occur, can we doubt (remembering that many more individuals are born than can possibly survive) that individuals having any advantage, however slight, over others, would have the best chance of surviving and procreating their kind? On the other hand, we may feel sure that any variation in the least degree injurious would be rigidly destroyed. This preservation of favourable individual differences and variations, and the destruction of those which are injurious, I have called Natural Selection, or the Survival of the Fittest. Variations neither useful nor injurious would not be affected by natural selection, and would be left either a fluctuating element, as perhaps we see in certain polymorphic species, or would ultimately become fixed, owing to the nature of the organism and the nature of the conditions.

This is probably the most important aspect of Darwin’s contribution to biology and geology. The fact that one species is descended from another was already becoming clear enough. But Darwin offers an explanation for why certain changes take place rather than others. We pointed out earlier that Empedocles anticipated this idea, but he did not combine it with the idea of common descent. Darwin actually mentions the passage, but mistakes it for Aristotle’s own view.

Darwin also attempts to organize the geological and biological evidence in general, and to answer objections to his theory. I will not do that here, since many others have done it elsewhere, and including a great deal of more recent evidence that could not be included by Darwin, as for example here. However, I will discuss one particular objection to his theory, as well as his solution.

In the final chapter he discusses why we do not find many more intermediate forms than we do, both living and dead:

As according to the theory of natural selection an interminable number of intermediate forms must have existed, linking together all the species in each group by gradations as fine as our existing varieties, it may be asked, Why do we not see these linking forms all around us? Why are not all organic beings blended together in an inextricable chaos? With respect to existing forms, we should remember that we have no right to expect (excepting in rare cases) to discover DIRECTLY connecting links between them, but only between each and some extinct and supplanted form. Even on a wide area, which has during a long period remained continuous, and of which the climatic and other conditions of life change insensibly in proceeding from a district occupied by one species into another district occupied by a closely allied species, we have no just right to expect often to find intermediate varieties in the intermediate zones. For we have reason to believe that only a few species of a genus ever undergo change; the other species becoming utterly extinct and leaving no modified progeny. Of the species which do change, only a few within the same country change at the same time; and all modifications are slowly effected. I have also shown that the intermediate varieties which probably at first existed in the intermediate zones, would be liable to be supplanted by the allied forms on either hand; for the latter, from existing in greater numbers, would generally be modified and improved at a quicker rate than the intermediate varieties, which existed in lesser numbers; so that the intermediate varieties would, in the long run, be supplanted and exterminated.

On this doctrine of the extermination of an infinitude of connecting links, between the living and extinct inhabitants of the world, and at each successive period between the extinct and still older species, why is not every geological formation charged with such links? Why does not every collection of fossil remains afford plain evidence of the gradation and mutation of the forms of life? Although geological research has undoubtedly revealed the former existence of many links, bringing numerous forms of life much closer together, it does not yield the infinitely many fine gradations between past and present species required on the theory, and this is the most obvious of the many objections which may be urged against it. Why, again, do whole groups of allied species appear, though this appearance is often false, to have come in suddenly on the successive geological stages? Although we now know that organic beings appeared on this globe, at a period incalculably remote, long before the lowest bed of the Cambrian system was deposited, why do we not find beneath this system great piles of strata stored with the remains of the progenitors of the Cambrian fossils? For on the theory, such strata must somewhere have been deposited at these ancient and utterly unknown epochs of the world’s history.

I can answer these questions and objections only on the supposition that the geological record is far more imperfect than most geologists believe. The number of specimens in all our museums is absolutely as nothing compared with the countless generations of countless species which have certainly existed. The parent form of any two or more species would not be in all its characters directly intermediate between its modified offspring, any more than the rock-pigeon is directly intermediate in crop and tail between its descendants, the pouter and fantail pigeons. We should not be able to recognise a species as the parent of another and modified species, if we were to examine the two ever so closely, unless we possessed most of the intermediate links; and owing to the imperfection of the geological record, we have no just right to expect to find so many links. If two or three, or even more linking forms were discovered, they would simply be ranked by many naturalists as so many new species, more especially if found in different geological substages, let their differences be ever so slight. Numerous existing doubtful forms could be named which are probably varieties; but who will pretend that in future ages so many fossil links will be discovered, that naturalists will be able to decide whether or not these doubtful forms ought to be called varieties? Only a small portion of the world has been geologically explored. Only organic beings of certain classes can be preserved in a fossil condition, at least in any great number. Many species when once formed never undergo any further change but become extinct without leaving modified descendants; and the periods during which species have undergone modification, though long as measured by years, have probably been short in comparison with the periods during which they retained the same form. It is the dominant and widely ranging species which vary most frequently and vary most, and varieties are often at first local–both causes rendering the discovery of intermediate links in any one formation less likely. Local varieties will not spread into other and distant regions until they are considerably modified and improved; and when they have spread, and are discovered in a geological formation, they appear as if suddenly created there, and will be simply classed as new species.Most formations have been intermittent in their accumulation; and their duration has probably been shorter than the average duration of specific forms. Successive formations are in most cases separated from each other by blank intervals of time of great length, for fossiliferous formations thick enough to resist future degradation can, as a general rule, be accumulated only where much sediment is deposited on the subsiding bed of the sea. During the alternate periods of elevation and of stationary level the record will generally be blank. During these latter periods there will probably be more variability in the forms of life; during periods of subsidence, more extinction.

With respect to the absence of strata rich in fossils beneath the Cambrian formation, I can recur only to the hypothesis given in the tenth chapter; namely, that though our continents and oceans have endured for an enormous period in nearly their present relative positions, we have no reason to assume that this has always been the case; consequently formations much older than any now known may lie buried beneath the great oceans. With respect to the lapse of time not having been sufficient since our planet was consolidated for the assumed amount of organic change, and this objection, as urged by Sir William Thompson, is probably one of the gravest as yet advanced, I can only say, firstly, that we do not know at what rate species change, as measured by years, and secondly, that many philosophers are not as yet willing to admit that we know enough of the constitution of the universe and of the interior of our globe to speculate with safety on its past duration.

That the geological record is imperfect all will admit; but that it is imperfect to the degree required by our theory, few will be inclined to admit. If we look to long enough intervals of time, geology plainly declares that species have all changed; and they have changed in the manner required by the theory, for they have changed slowly and in a graduated manner. We clearly see this in the fossil remains from consecutive formations invariably being much more closely related to each other than are the fossils from widely separated formations.

Darwin makes a number of good points here, as for example that intermediate forms, when they are found, are likely simply to be interpreted as new species. However, it seems likely that his explanation is insufficient. The geological record is surely very imperfect, but it is not clear at all that the record as he presents it match what we would naturally expect from an imperfect record with random sampling.

But let us consider another case, one where it is an undoubted fact that our record was produced by a process of historical descent with modification. There can be no reasonable doubt that the Romance languages have descended from Latin, and by a process of gradual diversification much like the process of evolution. This was surely a nearly continuous process, with children always speaking a language nearly identical to the language of the parent. So there were a nearly indefinite number of forms of languages descended from Latin, with an indefinite number of linking forms. “Why do we not see these linking forms all around us? Why are not all [Latin languages] blended together in an inextricable chaos?”

They are not blended in this way, even if there is a fairly large number of dialects, just as there is a large number of animal species of similar forms.

“On this doctrine of the extermination of an infinitude of connecting links, between the living and extinct [Latin languages] of the world, and at each successive period between the extinct and still older [forms], why is not every [historical period] charged with such links? Why does not every collection of [medieval and ancient writings] afford plain evidence of the gradation and mutation of the forms of [the Latin language]?”

We can find older forms of the Latin languages preserved in writing. But we do not find anything like a continuous series of such forms, despite the fact that it is perfectly clear that such a continuous series must have existed.

The answer is likely the same both in the case of these languages, and in the case of the evolution of living beings, and likely has to do with the mathematics governing these kinds of changes. It is related to the imperfection of the records, but not completely explained by this. If you had perfect records, you would indeed be able to find a continuous series of linguistic forms, and you would indeed be able to find a continuous series of living beings. But basically in both cases you have periods of relative stability followed by periods of relatively rapid change, rather than one extremely long period of slow change, and consequently random sampling discovers relatively few of the total number of forms.