Which Is Her Real Personality? All of Them

Stuart K. Hayashi



There is a hit video-game visual-novel called Slay the Princess. It’s independent, made mostly by a husband-and-wife team. What is meant by “visual novel” is that it’s a story told mostly in the form of illustrations, text, and voice-acting, but there are many areas in the story where you choose which path the characters will take, not knowing exactly where it will lead. In Japan, this genre is also called “dating simulators,” as these visual novels are mostly about romance. And Slay the Princess is very decidedly not an exception to that.

As are many others, I’m intrigued by how explicitly and unabashedly philosophical Slay the Princess is. There is even one point in the game where you can have the player character say, “Contradictions don’t exist.” Something about that line sounds familiar . . .

In the game, the titular princess can take on many forms. She has many facets, many alters. Some of them are benign. Others are very frightening. You might wonder which of these is her “real personality.” My answer is “All of them.” All of them show different-but-incomplete aspect of her. As in real-life mental health, it is important for all of these personalities ultimately to be integrated into a single whole — that is actually the root of the word integrity.

I’m going to embed some of my favorite YouTube videos that touch upon the philosophic ramifications.

 

 

 

So far, these have been my favorite YouTube “play-throughs” of it (the most famous one, not shown here, is by Markiplier).

 

Libertarians and the Myth of the Winner-Takes-All Patent Monopoly

Stuart K. Hayashi




The libertarian political movement claims to be all about free markets and privatization, and yet this is contradicted by its maligning of intellectual property rights. That is the movement’s party line, which dates at least as early as the 1970s. In that decade, Murray N. Rothbard and Roy A. Childs, Jr., began with misrepresenting the nature of patents. Samuel E. Konkin III and Wendy McElroy then added the mischaracterizations about copyrights.

According to the party-line straw man, an intellectual property right is an arrogant proclamation of a single party to be the exclusive owner of an “idea.” And this “idea,” continues the misrepresentation, is one upon which many other parties arrived on their own independently, but of which they are now deprived of implementing because that one other party has a government-enforced monopoly over it, the patent or copyright.

In the straw-man depiction provided by The Adventures of Jonathan Gullible, a lawyer gaining a patent on the axe confers upon him a seventeen-year monopoly on the general product category of “axe,” or, as Jonathan Gullible calls it, “SharpMetalOnAStick.” Further according to such an argument, were someone to have a U.S. utility patent on a “paperclip,” she would usurp a seventeen-year government-enfranchised monopoly on the production of paperclips. The same would apply to “electric can-openers” and “the mechanical pencil.”

As this narrative proclaims that only one party gets the patent, whereas all the other chronologically-parallel-inventing parties end up bereft of anything to show for their own respective research-and-development, such libertarians would have us believe that intellectual property rights are themed on “winner takes all.” And the government-decreed winner who takes all, a Rothbardian-anarchist libertarian tells us, is the one most skillful in cozying up to politicians and having pull with them. I call this the Myth of the Winner-Takes-All Race to Patent. It is also the Myth of the Winner-Takes-All Patent Monopoly.

It is time for us to look at the actual record.

Within a Span of Seventeen Years, Why Are There Multiple Patents on the Same Type of Product?
There are resources online whereby you can see actual U.S. patents, many dating all the way back to the nineteenth century. Such resources include Free Patents Online and Google Patents. Over the years I have gone through them and made tables of multiple U.S. utility patents on the same general category of product.

Here is a non-exhaustive table I compiled of various U.S. utility patents on “the paperclip” from the years 1867 to 1957 — a nine-decade duration.

Note the intervals of years between the patents: every interval is shorter than seventeen years. In effect, each U.S. utility patent on the paperclip was granted prior to the expiration of the one directly preceding it. Had it been true that a U.S. utility patent conferred a government-enforced monopoly on an industry and product category for a period of seventeen years, then how could this be? And if the first patent on a paperclip claimed ownership over the “idea” of “paperclip,” then why were there so many subsequent utility patents on the paperclip? Wouldn’t the U.S. Patent-and-Trademark Office have granted a single seventeen-year patent on “the paperclip” and thereafter been done with it?

The answer is in the convenient conflation when libertarians say that an intellectual property right is a demand that the government enforce someone’s monopoly on an “idea.” Here, the libertarian expects you to interpret “idea” as a general idea — a general idea for a general category of product, this one being “paperclip.” From that misreading, we are to assume that if in the year 1867 the U.S. Patent-and-Trademark Office (PTO) certified Samuel B. Fay’s rightful patent over his paperclip, that would preclude the U.S. PTO from certifying ten years later Erlman Wright’s patent on his own paperclip.

Actually a patent does not claim ownership over a general idea for a whole product category such as “paperclip,” and it does not grant to its owner a government-enforced monopoly on any industry — not for seventeen years or any other duration.

Rather, patents — this applies both to utility patents and design patents — are the State’s acknowledgment of a party’s already-existing rightful ownership over a specific original design, delineation, or configuration. The reason why there have historically been so many different U.S. utility patents on the paperclip for almost a century is that there have been differences in design in terms of the object’s exact shape and size and the material with which it is comprised.

In effect, a utility patent on a paperclip is not a utility patent on the paperclip. That applies even to the first-ever paperclip to be patented.

I have previously written another blog post that discusses other aspects of the fallacy of libertarian conflation about “ideas” — about their false insinuation that the patent arrogates to a single party some governmental control over just about any vague, hazy, broadly-defined and unrefined “idea” into which just about anyone can passively and serendipitously fall in. To stigmatize intellectual property rights as a government-enforced monopoly on an industry, it is important to libertarians that they mislead people into believing that patents are defined and enforced much more broadly than they truly are.

Both Utility Patents and Design Patents Are for Specific Original Designs
Yet another misconception must be cleared up with respect to the word design. There are occasionally some people who think of themselves as free-marketers — many of whom do not share in the Rothbardians’ vehemence against patents — who nonetheless misunderstand the distinction between “design patent” and “utility patent.” According to their misunderstanding, it is only design patents that protect a specific original design, whereas a utility patent’s enforceability is much broader and, unlike a design patent, does confer a government-enforced monopoly on an entire industry.

That misconception is belied by the fact that all of the U.S. patents listed in my “paperclip” table are utility patents, not design patents. A U.S. design patent is designated by its patent number beginning with the letter D.

Both utility patents and design patents are to protect only specific original designs. The actual distinction is this. A utility patent protects a specific design with respect to the aspects pertaining to its practical functionality. Conversely, a design patent protects a specific design with respect to the aspects pertaining to its aesthetic qualities.

When Frédéric-Auguste Bartholdi drew up his plans for the Statue of Liberty, for it he earned U.S. Design Patent D110,23S. This was on account of how Bartholdi raised funding for Liberty by selling handheld replicas of her. He therefore did not want imitators to snatch the aesthetic of his work and produce their own statues in the exact likeness of a woman in Greco-Roman garb, adorned with a Mediterranean “radiate crown” and holding up a torch. Likewise, celebrated filmmaker George Lucas earned U.S. Design Patent D264,109S for his “Boba Fett action figure.” Lucas did not want other toymakers producing their own toys, absent of his authorization, that were in the exact likeness of his own Star Wars character Boba Fett. Ralph Lauren had U.S. Design Patent D319,932S on a bed of a particular shape and U.S. Design Patent D259,098S on the fancy appearance of a cologne bottle.

I hope that it is now clear that design patents are about artistic features, whereas utility patents are about operational features, and both types are on specific original designs — what, for further distinction, we might also call specific original configurations, delineations, or plans. In short, a design patent is on how a specific design looks, and a utility patent is on how a specific design operates. For another blog post of mine about the line of demarcation between utility patents and design patents, and how both pertain to discrete aspects of the design, you can go here.

Other Examples of How, Within Seventeen Years, There Can Be Multiple Utility Patents Within the Same General Type of Product
These principles are not confined to the market for paperclips. They also apply to a more-complex machine. Here I present a table I made on various U.S. utility patents on the electric can-opener from 1948 to 1990. Including all of 1948, that would be forty-three years. Mind you that this table does not even include patents on more-traditional manually-cranked can-openers. Even when it comes to the more-specific category of electric can-openers, there is this much variation.

Once again, when each U.S. utility patent to certify the already-existing moral right to one’s specific configuration is codified, it is prior to the expiration of the other patent on the electric can-opener that directly precedes it. Once again, there are differences in design with respect to the moving parts that turn the blade; there are differences in the location of the motor and on whether or not the electric can-opener needs to be held by hand as the motor turns the blade.

In January 2026 I decided to look into another invention, the mechanical pencil. You may have seen my drawings on my blog, and their first drafts begin with what I have done on paper using a mechanical pencil. The earliest-known patent on a mechanical pencil is said to be with silversmith Sampson Mordan and engineer John Isaac Hawkins in England in 1822. Similar patents followed in the USA some years later. Not all of these are recoverable, as a fire in Washington, D.C., destroyed many important federal government records, including many patent documents from the early nineteenth century. 

Still, from 1836 onward and going strong for a century, we see the same pattern as before: each patent was awarded while the preceding one from the same general product category was still active and enforceable. These early versions do not exactly match what we think of today when we say “mechanical pencil.” The earliest-known one that can be called a modern mechanical pencil — it has refillable pieces of pencil lead, with a mechanism inside the pencil that propels the lead out the cylinder’s tip — is from 1915 with Charles Keeran.

There were so many U.S. utility patents alone on the mechanical pencil, that I was able to make five tables. And even these are far from exhaustive. The tables range from the years 1836 to 2024 — a span exceeding 185 years. All the while, each new utility patent on the mechanical pencil arrived even as the one directly preceding it remained in effect.

There is great variety in the exact shapes of the parts of the mechanism that propels the pencil lead through the cannister; they come in pieces varying in number and material. In the final table you can see the brand that I use: Pentel of Japan.

Someone prolific in the list of inventors was “Lucifer J. Most.” Another one was “Christ Andonov.” Among the respective inventors of the mechanical pencil are Lucifer and Christ.

How Competitive Was the Market for Incandescent Lightbulbs in the Timespan When Thomas Edison’s Patent Was Most Strongly Upheld and Enforced?
Someone else who looked into these matters was associate professor John Howells of Aarhus University in Denmark. He and Ron Katznelson have busted four myths (1, 2–4 )that are routinely presented as case studies in how patents have supposed slowed down technological innovation. One such myth is that Thomas Edison’s U.S. Utility Patent No. 223,898A — on the incandescent lightbulb with a high-resistance carbon filament — awarded in the year 1880, slowed down improvements in this industry. The U.S. Supreme Court definitively upheld this patent in the year 1892 and it was set to expire in 1897. Were the “monopoly” narrative accurate, this five-year period would be one where Edison did the most to exercise his monopoly powers, such as in hiking prices.

John Howells shows that, in fact, it was in this five-year duration that incandescent lightbulbs had their steepest drop in real price. 

The reason is that patent law allows for the principle of “design-around.” In “design-around,” a party’s engineers examine the specific task a patented or likely-to-be-patented configuration performs, and then seek to produce their own configuration that performs that same task through an alternative route or method. With respect to incandescent lightbulbs, Edison’s competitors came up with their own unique configurations — on which they received their own respective U.S. utility patents — that performed the same tasks as Edison’s.

Anticipating the 1880 approval of Edison’s carbon-filament incandescent lightbulb patent, inventor William E. Sawyer and attorney Albon Man arrived at their own version in 1878, U.S. Utility Patent No. 205,144A. Working in Great Britain, Joseph Swan had his own version receive a U.S. utility patent also in 1880 — U.S. Utility Patent No. 234,345A. The prolific Black inventor Lewis Latimer, whom Edison would hire two years later, produced his own competitive version in 1882, U.S. Utility Patent No. 252,386A. And Hiram Maxim, who today is most-remembered for his automatic machine gun, did his own design-arounds. In 1880 he was awarded U.S. Utility Patent No. 230,309A, and, in 1881, it was U.S. Utility Patent No. 237,198A and U.S. Utility Patent No. 247,380A. In 1891 Reginald Fessenden, who would later be renowned much more widely for his developments in radio, gained U.S. Utility Patent No. 452,494A. In 1893, William Emery Nickerson and Edward Egbert Cary received U.S. Utility Patent No.507,558A.

Companies in competition against Edison in the electric lighting business clamored to pay licensing fees for these other patents. George Westinghouse — Thomas Edison’s main rival in this industry — paid licensing fees on William E. Sawyer’s patent (1, 2). The Beacon Vacuum Pump and Electrical Company paid royalties to William Nickerson and Edward Cary for theirs.

As U.S. utility patents are on specific original configurations and not on the general idea, that the U.S. Supreme Court upheld Edison’s 1880 patent in 1892 was unable to withhold from the market the incandescent lightbulbs configured in the patents of William E. Sawyer and William Nickerson. And to keep up with the competition from these other versions of the incandescent lightbulb, in the period ranging from 1892 to his patent’s scheduled expiration in 1897, Edison still had to cut his own prices.

John Howells and Ron Katznelson explicate what should now be clear: “...a patent is not an economic monopoly...”

What About the Claim That Multiple Parties, All Unknown to the Others, All Arrive at the Same Invention Chronologically Parallel to Each Other?
Left to be addressed is the allegation that multiple parties, each unbeknownst to the others, all arrive at the exact same invention at the exact same time. What actually happens is that separate parties, working independently of one another, arrive at the same general idea within relatively close temporal proximity to one another. The exact specific original designs, though, are different, and it is not unusual when these parties each obtain their own specific patent. When these parties dispute one another in court, it has to do with “overlap” in terms of the aspects of their respective designs that are similar.

One such example, provided by Adam Mossoff (1, 2) is with different sewing machines patented by Elias Howe and Isaac Merritt Singer, the latter being the namesake behind Singer Sewing Machines. They eventually resolved the disputes by pooling all of their patents into a single trust — a patent pool. Such patent pools are not uncommon.

Another case study has to do with the integrated circuit that is vital to today’s personal computers. At Fairchild Semiconductor, Robert Noyce came up with one version, and, with another Fairchild cohort, he would co-found Intel with this invention as its basis. And within a short distance of time, Jack Kilby had his own version at Texas Instruments. Kilby’s patent was on the body of the device on its own, whereas Noyce’s placed more emphasis on the arrangement in which this was to be connected with other components.

With respect to where the two patents were similar, the two firms eventually arrived at something else that would become commonplace — a cross-licensing agreement. This meant that each company could use both its own patents and the other’s as far as the integrated circuit was concerned.

That is not the winner-takes-all model that the Rothbardians promulgate.

To reiterate, the Rothbardian narrative against patents, such as in The Adventures of Jonathan Gullible, is that many parties invent the same “idea” at the same time, and, with but one of these parties gaining the patent-enforced monopoly, the R-and-D of the other simultaneously-inventive firms come to nothing. And, concludes the Rothbardian misrepresentation, the one solution to this dilemma is nothing short of the abolition of intellectual property rights outright.

And as we see with the sewing machine and the integrated circuit, the reality is far different.

Let us imagine that within times relatively close to each other, seven separate firms independently arrive at the same general idea. Those seven firms each receive their own patent, but, at first, there is difficulty in terms of similarities among the patents. Here we find that it is not the case that but one of the firms receive the patent and the other six see their efforts wasted. Rather, they have a cross-licensing agreement. Note how this is solved without capitulation to the drastic demands of the patent-hating libertarians.

In the patent pool, the firms that have invested their own resources into research-and-development still reap the benefits of that effort. Commensurately, the many-more firms out there that made zero contributions to that same R-and-D are not able to pilfer, through piracy, the specific original configurations resulting from that R-and-D. But, had the patent-hating libertarians gotten their way, the firms that invested no R-and-D would be able to free-ride off the seven firms that did do the R-and-D.

Clearing Up What the U.S. Constitution’s Copyright Clause Means By Exclusive Right — Hint: Pay Attention to “Their Respective Writings and Discoveries”
With this understanding, we can observe the clause in the U.S. Constitution that enshrines copyrights and patents. Pertinent here, we can ascertain how the opponents of intellectual property rights mischaracterize the meaning of the clause. U.S. Congress, says the document, is tasked “to promote the progress of science and useful arts by securing for limited times to authors and inventors the exclusive right to their respective writings and discoveries.”

The patent-haters seize on that phrase exclusive right and misrepresent that as a State-enforced monopoly. But here we should see that a party has an exclusive right to what that particular party originated. Suppose you claim a plot of wilderness and improve upon it and then live on it, with the State recognizing that homestead as your private property. That would not confer upon you a State-enforced monopoly on the entire real estate market. Likewise, points out Revolutionary Era attorney Daniel Webster, a “man’s right to his own invention ...is no more a monopoly for him to possess ...than to possess his own homestead.”

We can see that with U.S. utility patents on the mechanical pencil. Lucifer J. Most’s 1939 U.S. utility patent on his own mechanical pencil was an exclusive right on this particular configuration. Note from the table above that in the seventeen years that followed, the patent did not confer upon Mr. Most some State-enforced monopoly on mechanical pencils. 

The essential phrase in the Copyright Clause is not exclusive right but respective writings and discoveries. Let us read the clause again, this time with Lucifer J. Most’s situation in mind: “...securing for limited times to authors and inventors the exclusive right to their respective writings and discoveries” (emphasis added). Here, respective means that Lucifer Most’s U.S. utility patent covers only the specifics on what he originated. 

Mr. Most did not originate mechanical pencils in general, and the patent does not secure for him any exclusive right over the entire market for mechanical pencils. Nor was it secured for his predecessor in producing the overall modern and general version of the mechanical pencil that we use in the present, Charles R. Keeran in 1915. Lucifer J. Most did originate, though, his own specific arrangement of the inner workings of a mechanical pencil. Hence, the U.S. Constitution is securing for him the exclusive right over his respective “writings and discoveries,” meaning the specific aspects he devised himself. And, thankfully, throughout our history the U.S. courts have been remarkably consistent in respecting that distinction.

Indeed, the absurdity of the libertarian accusation that intellectual property rights are a government-enforced monopoly on an industry is even more apparent when applied to copyrights than it is with utility patents. His copyrights on his Percy Jackson series of books don’t give Rick Riordan a State-enforced monopoly on the literature market. He has a “monopoly” only on his specific Percy Jackson prose, as he should, as he is the one who composed it.

Conclusion: The Original Intellectual Property Right 

Daniel Webster is apt in identifying the connection between the right to homestead and the right to patent — the former forms the basis of the latter. And this exposes yet another self-contradiction of the Rothbardians who hate intellectual property rights so much. They denounce intellectual property rights and yet wax enthusiastically about John Locke’s discussion of how, by improving the land he has settled on, the homesteader gains proper ownership over it. Indeed, the homestead is the original intellectual property right. Karl Marx wanted to pretend that this right was all about the physical toiling. But such toiling improves the land no more than the extent to which it has been properly planned — the work of the intellect, of the mind. The homesteader has to identify the right crops suited to this environment. The homesteader has to plan properly in the irrigation.

Just as with works that are patented and copyrighted, it is through the devising of a rational plan — the proper configuration and design — that the homesteader produces, from the homestead, a net increase in economic value. And as with the patenter and copyrighter, this is a newly emergent value that had not previously existed or circulated anywhere in any society’s economy. The homesteading principle that the Rothbardians worship is the origin of the intellectual property right that these same Rothbardians try to deny.

Sensory Observation Does Prove the Existence of Atoms

Stuart K. Hayashi




I have heard people say, “I’ve never seen an isolated atom, and yet I know atoms exist. Therefore, you can know something exists even if its existence has never been confirmed by sensory evidence.” But the truth is that atomic theory is indeed confirmed by sensory evidence. Chemical formulae in a compound — such as how, in water, for every one atom of oxygen, there are two atoms of hydrogen — are a model to explain the principles in Nature, and, the accuracy of that model is verified in how it is used successfully to make predictions that are confirmed, accordingly, by sensory observation to be likewise accurate. The following essay is inspired by discussions of similar points in David Harriman’s book The Logical Leap.

It was through sensory observation that in the years from 1797 to 1799 the tirelessly working chemist Joseph-Louis Proust had discovered the Law of Definite Proportions. The chemical compound he used was copper carbonate — CuCO3. He found that regardless of how the copper carbonate was procured, and no matter the quantity it was in, the mass ratio of copper to carbon to oxygen will consistently be a respective 5.3 to 1 to 4. Whatever quantity of copper carbonate you have, for every 5.3 grams of copper it has, it will correspondingly have 1 gram of carbon and 4 grams of oxygen. Within any chemical compound, the separate elements only could always configure together in the same proportions to one another like that

1. if each element ultimately consisted of tiny microscopic units that could not be divisible any further at the chemical level, and
2. if the chemically-indivisible units of each element bonded with the others always in the same ratio to one another.

That is how we know that a chemical compound can be reduced to separate molecules, and that each molecule of the compound consists of two or more elements with each element coming in a whole-number of chemically-indivisible units (no fractions or decimals for each number of atoms in the molecule).

Proust was able to measure the quantity of the mass of copper, carbon, and oxygen each in his samples of copper carbonate as he knew how to trigger particular chemical reactions to break down the copper carbonate into its separate elements. He heated the copper carbonate to evaporate the water and carbon dioxide. This left him with copper oxide (the result of a bond between copper and oxygen). Then, using hydrogen but not adding it, Proust was able to remove the oxygen, leaving only the pure copper. As measurements of weight were a reliable proxy for measuring mass, Proust weighed the remaining sample at each stage of the process. First he weighed the complete copper carbonate. Then he weighed the separate copper oxide, water, and carbon dioxide. Finally he weighed the remaining sample of pure copper. You can see an English translation of his own description of the procedure over here. All this involved direct sensory inputs.

Joseph-Louis Proust could not see any isolated atoms. But he did use his senses directly in measuring the quantity of each element’s mass within the compound and observing first-hand how consistent was the ratio in the quantity of mass for each element as compared to the others.

Proust observed directly through his senses the consistency of his Law of Definite Proportions. What explained this consistent principle was that, on a microscopic level, the copper carbonate consisted of tiny uniform particles, molecules. And furthermore, within each molecule were no-further-chemically-divisible units of copper, carbon, and oxygen each coming in a whole number of units, with the whole numbers of units for each of those respective elements themselves always coming in the same ratio to one another. That no-further-divisible-at-the-chemical-level units for each of those respective elements always came in a fixed ratio to one another within the copper carbonate explained why the respective directly-observed masses of those elements always arrived in a fixed ratio to one another.

Likewise, no matter the quantity of water you have, the mass ratio of hydrogen to oxygen will always be 1 to 8. For every one gram of hydrogen, there will always be eight grams of oxygen. This only could have been true if, at the chemical level, water consisted of tiny microscopic particles (molecules) in which there was an arrangement where a particular whole-number of no-further-divisible units of hydrogen existed in a constant ratio to a whole-number of likewise-no-further-divisible units of oxygen. Remembering the ancient Greek idea of Leucippus and Democritus that all matter might ultimately consist of microscopic further-irreducible units, physicist John Dalton gave these chemically no-further-indivisible units the same name that these presocratic philosophers did: atoms.

Joseph-Louis Proust’s findings were corroborated further by the similarly-named Joseph Louis Gay-Lussac. Gay-Lussac found through his experimentation that whenever the gasified elements with which he experimented bonded with one another to form compounds, their respective volumes had to be in whole-number ratios to cause such a reaction. Through his sensory observation of his measurements, he detected that it always took two exact liters of hydrogen gas to react with an exact single liter of oxygen to produce two exact liters of gasified water — water vapor. Likewise, it was consistent that a single liter of hydrogen gas reacted with a single liter of chlorine to produce two exact liters of hydrogen chloride.

From Gay-Lussac’s experiments Amedeo Avogadro induced the theory that when two different elements in gas form are each in containers of the same volume to one another, each container contains the same number of molecules as the other. And a noble gas can consist of single-atom molecules. The two liters of hydrogen with which Gay-Lussac started the trial consisted of the same number of molecules as the two liters of water vapor at that trial’s conclusion. The findings of both Proust and Gay-Lussac were synthesized to arrive at measurements of the mass of each uniform atom of each element.

Clearly, no one can observe the mass or weight of an isolated atom. But from experiments like Proust’s, John Dalton ascertained that the mass of an atom of a particular element would consistently be greater than the mass of an atom from another type of element. For example, an atom of oxygen will always be of greater mass than an atom of hydrogen. Hence, Dalton ascertained that the discrete masses of atoms from different elements could be found by comparing them against one another, with the consistent mass of an atom from a particular element —hydrogen — being used as the consistent standard.

Through successful repetition of Gay-Lussac’s trials, scientists ascertained that in water, each molecule consists of two hydrogen atoms and a single oxygen atom. And as prior experimentations already demonstrated that in water, there are 8 grams of oxygen for every 1 gram of hydrogen, the atomic weight of oxygen could be ascertained. Using the mass of a hydrogen atom as the standard — the assigned atomic mass of hydrogen being “1” — it is the case that a single oxygen atom is of a mass sixteen times that of a hydrogen atom. Hence, the atomic mass of oxygen is 16.

This is the calculation. We are solving for the atomic mass of oxygen, y. The atomic mass of hydrogen is x. 2x/1y = 1/8. And we know x = 1. Therefore, 2/y = 1/8. And so y = 2 * 8 = 16.

Aristotle is not recorded to have conducted controlled experiments, but note that all controlled experiments rely on Aristotle’s Law of Identity. To the extent that the variables in two different samples are the same in the pertinent respect, they are of the same type. Everything in the control sample and the experimental are the same in the pertinent context except for the one variable being tested. Gay-Lussac’s experimental results were meaningful because all of the other variables (the volumes, the temperature, the pressure) were, in the pertinent context, the same. By having all variables in both the control sample and experimental sample being the same except for the one variable we are testing, we can ascertain that this one variable is what causes the differences in results between the control sample and experimental sample. Also, all equations, such as the one above, rely on the principle that if A equals B, and B equals C, then A equals C, and that itself is a rephrasing of the Law of Identity. Hence, although the man himself was doubtful that all matter ultimately consists of atoms, the application of Aristotle’s Law of Identity was crucial to the eventual validation of atomic theory.

It was through the application of the Law of Identity that Amedeo Avogadro ascertained that Gay-Lucsac’s findings could be applied to ascertaining the atomic masses of other elements. And once chemists and physicists figured out the atomic masses of copper (63.546) and carbon (12.011) respectively, they could go back to Joseph-Louis Proust’s findings about copper carbonate to ascertain that a molecule of copper carbonate consists of 1 copper atom, 1 carbon atom, and 3 oxygen atoms.

Yes, an isolated atom cannot be seen. But the model that says that all matter ultimately consists of atoms is a model that, when applied, is vindicated through its observed practical results. Sensory observations confirm the validity of atomic theory.