Higgins, pt 3: Anacalypsis: Preface, Preliminary Observations
Higgins lived during a pre-neogrammarian age, and hence at the time, comparative linguistics had not reached the point where it could be called a science.
For a very long time, and during the writing of the greater part of my work, I abstained from the practice of many etymologists, of exchanging one letter for another, that is, the letter of one organ for another of the same organ; such, for instance, as Pada for Vada, or Beda for Veda, in order that I might not give an opportunity to captious objectors to say of me, as they have said of others, that by this means I could make out what I pleased. From a thorough conviction that this has operated as a very great obstacle to the discovery of truth, I have used it rather more freely in the latter part of the work, but by no means so much as the cause of truth required of me. The practice of confining the use of a language while in its infancy to the strict rules to which it became tied when in its maturity, is perfectly absurd, and can only tend to the secreting of truth. The practice of indiscriminately changing ad libitum a letter of one organ for another of the same organ, under the sanction of a grammatical rule, - for instance, that B and V are permutable, cannot be justified. It cannot, however, be denied that they are often so changed; but every case must stand upon its own merits. [1, preface]
At the time of his writing, historical linguistics did indeed operate a bit along these lines - although some basic idea of regular sound change had occurred to the scholars of the time. It was this kind of completely ad hoc approach to historical linguistics that lead the neo-grammarians to come up with less ad hoc reasoning.
The idea that languages go from infancy to maturity is not generally taken seriously by anyone these days. Certainly, languages change over time, and assuming that the same rules apply now as a thousand years ago in some language would be misguided.
In a somewhat better speculation on how language may have come about, he expounds:
4. After he [early mankind] had arrived at the art of speaking with a tolerable degree of ease and fluency, without being conscious that he was reasoning about it, he would probably begin to turn his thoughts to a mode of recording or perpetuating some few of the observations which he would make on surrounding objects, for the want of which he would find himself put to inconvenience. This I think was the origin of Arithmetic. He would probably very early make an attempt to count a few of the things around him, which interested him the most, perhaps his children; and his ten fingers would be his first reckoners; and thus by them he would be led to the decimal instead of the more useful octagonal calculation which he might have adopted; that is, stopping at 8 instead of 10. ... There is nothing natural in the decimal arithmetic; it is all artificial, and must have arisen from the number of the fingers; which, indeed, supply an easy solution to the whole enigma. Man would begin by taking a few little stones, at first in number five, the number of fingers on one hand. This would produce the first idea of numbers. After a little time he would increase them to ten. ... To these heaps or parcels of stones, and operations by means of them, he would give names; and I suppose that he called each of the stones a calculus, and the operation a calculation. [1, p. 1]
Indeed, it is generally agreed by all linguists today that the preponderance of the decimal system is closely related to our ten fingers - however, it is also noted that there is a preponderance of vigesimal systems (base-20), with sub-bases of 5 or 10. It is unclear whether Higgins genuinely meant that the early humans called these stones (or pebbles or fingers or whatever) and the act of counting calculation and calculus, or whether he is just giving a name to these things so as to be able to talk of them later on.
5. The ancient Etruscans have been allowed by most writers on the anitquities of nations, to have been among the oldest civilized people of whom we have any information. In my Essay on the Celtic Druids, I have shewn that their language, or that of the Latins, which was in fact their language in a later time, was the same as the Sanscrit of India. This I have proved not merely by the uncertain mode of shewing that their words are similar, but by the construction of the language. The absolute identity of the modes of comparison of the adjective, and of the verb impersonal, which in my proof I have made use of, cannot have been the effect of accident. [1, p. 2]
As it turns out, precious little is known of the Etruscan language. One entire book is extant - liber linteus zagrabiensis. Scholars have not been able to read it - despite knowing the alphabet. If it were (closely) related to Latin, it would undoubtedly be possible to read by recourse to Proto-Indo-European or somesuch. Robert Ellis' The Armenian Origin of the Etruscans listed about 200 words - other sources give about the same amount even 150 years later. Some of these words have been obtained through Greek and Latin sources. It is generally agreed that it is not an Indo-European language .
Its grammar is rather different from Indo-European languages of the time as well . It shares the rather notable feature of suffixaufnahme with a bunch of other languages, including Old Georgian, Hurrian, Urartian and Lycian - of which only Lycian is Indo-European.
Suffixaufnahme, for those who are interested, is a generalized congruence phenomenon. Normally, a noun (and maybe its adjectives and other determiners) are marked for a case - e.g. Latin meo antiquo malleo - my(dative, masculine) ancient(dative, masculine) hammer(dative, masculine). In languages with suffixaufnahme, such case markings can be stacked, obtaining things like - and this is fake Latin - artificiso antiquo malleo. "the builder(masc,genitive)(masc, dative) ancient(masc,dative) hammer(masc,dative)".
Considering how successful Indo-Europeanists have been with both Hittite and Tocharian, basically showing what regular sound changes and other changes needed to take place to derive those languages, the failure to do so with Etruscan - for which evidence has been available for a much longer time - indicates something about the problem.
Considering how ignorant Higgins has proven to be already about linguistics, I will not ascribe any credibility whatsoever to his claim to have shown Etruscan to be identical to Sanskrit; he seems unaware it is not even related to Latin.
7. A very careful inquiry was made by Dr. Parsons some years ago into the arithmetical systems of the different nations of America, which in these matters might be said to be yet in a state of infancy, and a result was found which confirms my theory in a very remarkable manner. It appears, from his information, that they must either have brought the system with them when they arrived in America from the Old World, or have been led to adopt it by the same natural impulse and process which I have pointed out. [1, p. 2]
Today, we know there are numeral systems of varying complexity in the Americas, with some especially simple ones in Brazil, for instance the Pirãha language. Other bases than 10 do occur - Higgins does point out 5, but he fails to point out the vigesimal systems. 
8. The ten fingers with one nation must have operated the same as with the other. They all, acccording to their several languages, give names to each unit, from one to ten, which is their determinate number, and proceed to add an unit to the ten, thus ten one, ten two, then three, &c., till they amount to two tens, to which sum they give a peculiar name, and so on to three tens, four tens and till it comes to ten times ten, or to any number of tens. This is also practised among the Malays, and indeed all over the East: but to this among the Americans there is one curious exception, and that is, the practice of the Caribbeans.
Exceptions also occur in Papua New Guinea, where various strange systems obtain in languages, even ones where it does not make great sense to talk of bases. Bases of size 4,5,6,8,10, 12, 20 (subbases 5 or 10), 24 (subbase 6), 32, 60 (subbase 10) and 80 (subbases 20, 10 and 5) are attested. Some both in the Americas and the Old World, some exclusively in the Old World, etc.
They make their determinate period at five, and add one to the name of each of these fives, till they complete ten, and they then add two fives, which bring them to twenty, beyond which they do not go. They have no words to express ten or twenty, but a periphrasis is made use of. From this account of Dr. Parsons', it seems pretty clear that these Americans cannot have brought their figure and system of notation with them from the Old World, but must have invented them; because if they had brought it, they would have all brought the decimal system, and some of them would not have stopped at the quinquennial, as it appears the Caribbees did. If they had come away after the invention of letters, they would have brought letters with them: if after the invention of figures, but before letters, they would all have had the decimal notation.
Although he is probably somewhat right about counting not having developed very far at the time the Americas first were settled, the logic here still is terrible. Certainly there could have been tribes with more advanced counting systems in parts of Eurasia at the time the first tribes had passed into America without the numbers being taken along. Ultimately, he presents a theory of convergent evolution for the numeral systems. Now, it seems today this evolution is more one of assimilation into the predominant systems of the big languages of the world - small languages in Latin America adopt it from Spanish and Portuguese, Aborigines from English, Africans from English, French and Arabic, and so on. Comrie even apparently noted that unusual numeral bases are going extinct faster than the languages that have them!
From that point on, the numbered paragraphs go on for a few pages elaborating on things about the development of astrological things, such as the zodiac and lunar mansions and so on. In paragraph 16 he claims that "the science of the Babylonians and Egyptians was but the débris of former systems, lost at that time by them, as it is known to have been in later times lost by the Hindoos" [1, p. 4]. I think this seems to be a strawman argument - he assumes they were more advanced than they were, their achievements were entirely achievable with the tools we know them to have used, and so on. At the very least in order to make the claim that they had lost some knowledge, he should provide some actual argument that shows they knew of things or had calculated things they should not be capable of with their tools.
22. A traveller of the ancients, of the name of Jambulus, who visited Palibothra, and who resided seven years in one of the oriental islands, supposed to be Sumatra, states, that thei nhabitants of it had an alphabet consisting of twenty-eight letters, divided into seven classes, each of four letters. There were seven original characters which, after undergoing four different variations each, constituted these seven classes. I think it is very difficult not to believe that the origin of the Chinese Lunar Zodiac and of these twenty-eight letters was the same, namely, the supposed length of the Lunar revolution. The island of Sumatra was, for many reasons, probably peopled from China.
Took me a while to find anything on Jambulus, since his name apparently normally is written Iambulos. His works are considered absurd and mere fiction .
I guess the reason for the probable Chinese origin of the Sumatran population has to do with both the Chinese and the Sumatrans being Asian? Now, the source he quotes to support this entire thing - Asiatick Researches vol X, says:
The two alphabets of the Sumatrans consist only, one of twenty-three, and the other of nineteen letters: but it is probably that there were two sorts of them formerly, as in India, and which were originally the same. One was used by the more civilized and learned classes, and at court, the other was current among the lower classes, whose poor and barren dialect had fewer sounds to express.
Speculation instead of fact. What makes this even less easy to figure out is that on Sumatra, over 50 languages are spoken, none of which goes by the name Sumatran. At this point, it is basically unfalsifiable - sure, some group might very well entirely by accident have had 28 letters. Until I know which one, it is impossible to check the reason - maybe they just so happened to distinguish 28 sounds.
One interesting thing regarding "fewer sounds" and so on, is how until fairly recently - and even to this day in some pseudo-scientific circles - Sanskritists and Hindu nationalists were so certain about the perfection of the Sanskrit language, that they denied the existence of speech sounds that were not distinguished in Sanskrit. Thus, if a language derived from Sanskrit had increased the amount of sounds it distinguished, this was denied - the new sounds were really just versions of the same sound, since it was inconceivable that sounds unavailable in Sanskrit even existed. Therefore, many of the orthographies of the languages of India mark fewer distinctions than the spoken languages do, in this charade to make Sanskrit seem superior.
Generally, though, languages' alphabets do not tend to have a specific number of letters due to doctrine or dogma, but due to either tradition (which changes over time, of course), or due to functional concerns: these are the sound-units we need to distinguish, let us make up letters to distinguish them.
29. About the time this was going on [dividing of time into smaller units, development of astrology], it would be found that the Moon made thirteen lunations in a year, of twenty-eight days each, instead of twelve only of thirty: from this they would get their Lunar year much nearer the truth than their Solar one. They would have thirteen months of four weeks each. They would also soon discover that the planetary bodies were seven; and after they had become versed in the science of astrology, they allotted one to each of the days of the week; a practice which we know prevailed over the whole of the Old World.
Except we know it did not. Weeks of every conceivable length are attested, and the spread of seven-day weeks is ultimately rather recent - starting out at about 2000 years ago.
After arguing that the wide spread of "X" as a symbol for ten - and ad hoc explanations as to why it is absent as such in some places (not even honestly mentioning multiple places where X was not used to denote ten, which is the majority of places). This goes on to
32. General Vallancey observes, That from the X all nations began a new reckoning, because it is the number of fingers on both hands, which were the original instruments of numbering: hence יד (id) iod in Hebrew means both the hand and the number ten. [1, p. 7]
Except this is not the case! יד adds up to 14, although י itself does signify ten, and has for its name iod. However, the name of the number is עֶשֶׂר , 'eser.
He further claims to have proven that the alphabet of the Hebrews, Samaritans, Phœnicians, Greeks and so on all had sixteen letters. This sounds like so much bull, but the actual argument is in The Celtic Druids and I will not read that book just yet.
84. There have been authors who have wasted their time in inquiries into the modei n which the inventor of the alphabet proceeded to divide the letters into dentals, labials and palatines. There surely never was any such proceeding. The invention was the effect of unforeseen circumstance - what we call accident; and when I consider the proofs, so numerous and clear, of the existence of the oldest people of whom we have any records, the Indian Buddhists in Ireland, and that in that country their oldest alphabet has the names of trees, I cannot be shaken in my opinion that the trees first gave names to letters, and that the theory I have pointed out is the most probable. [1, p. 15]
The bolded part is not bolded in the book. I think the bolded part needs no actual further debunking, it quite sufficiently debunks itself. There are no such records. We have no earlier attestation of the Ogham alphabet than a few hundred years CE. There is some internal evidence that requires the Ogham alphabet to be maybe a couple hundred years older than the earliest attestation.
Generally, Higgins seldom provides sources for his claims. His writing is dense, boring and so full of misconceived notions that pointing out any starting point where he first went wrong is near impossible. It seems the lack of quality research of his time, a wild imagination, and even further lack of any kind of requisite education on how to understand linguistic evidence conspired to create some very wild claims. I have only reached paragraph #100 at this point, and I know there's a few between #84 and #100 I should explain why they are wrong; I have omitted quite a few earlier ones as well, since they repeat previous assertions or hinge upon ones I have noted already. The times he gives sources, the reference is often not to a particular page in a book, but to the book in its entirety.
This must be among the most frustrating stuff I have ever read.
 Higgins, Anacalypsis, vol 1 1.
 http://quod.lib.umich.edu/cgi/t/text/text-idx?c=moa;idno=ACL3129.0002.001, more precisely http://quod.lib.umich.edu/m/moa/ACL3129.0002.001/560?rgn=full+text;view=image. What is known of his works to this day can be found in English translation here.