An Extended Comment on Knowledge, Science, and Why 2+2=4 Is, Indeed, an Indisputable Fact. Also, a Mango.

I had a comment to write in response to something. It ended up being 2500 words (whoopsie!), so I am putting it up as a post. Here’s the post with the comment I’m responding to, which I actually largely agree with: https://theprose.com/post/338381/conversation.

I did my best to make this engaging, but if you don’t like armchair philosophy, read elsewhere. In conclusion, writing this was fun.

I. Language is an arbitrary system.

We are able to communicate, @PolarBear228, because we use an agreed-upon language with an agreed-upon set of rules. Things have words for them that someone once chose to represent them. These words are composed of letters, which represent sounds, and we agree that a particular set of sounds represents a particular thing, or action, or idea. Thus, when you refer to “math,” I know you refer to a system of calculations to determine quantity.

There is no real reason why an M, a short A, and the soft TH consonant digraph should represent this series of calculations. These sounds could just have easily been chosen to represent a fruit, like a mango. But “math” means math, and “mango” means mango, because we need these things to be true if we are to communicate.

It is a fact that there is a mango on my desk right now (they were on sale – just $1!) The fact is indisputable. If a student walks in and points to my mango, and says, “You bought a math!” the student is not disputing a fact; the student is, rather defying a commonly agreed upon system, and to no good end. Arbitrary though language might be in its origin, it serves a vital function and enables us to communicate both about the physical world and our own subjective experiences.

In short, a mango is a “mango” because we say so, and the French “mangue” means the same thing because we say so, but its origin in human thought does not make the nomenclature disputable. It is a fact. To insist on something different is to reject our system of verbal and written communication, which a person could hypothetically do, but at the cost of meaningful interaction with society.

II. Currency as an arbitrary system.

The story is the same with money. The American dollar is fiat currency; it has value because we and the government say so; no physical asset like gold backs the dollar any longer. It is entirely arbitrary to declare a piece of paper with George Washington’s face on it to have the value of one small candy bar and a piece of paper with Ulysses S. Grant’s face on it to be worth a pair of shoes; we do it anyway. (I mean, if presidents had baseball cards, Washington would be perennial MVP candidate Mike Trout, and Grant would be whoever bats seventh for the Marlins.) The world agrees to accept the American dollar as having value because it eases commerce.

You can point out, should you wish, that the dollar has no inherent value. But it would be factually incorrect to say “the dollar has no value.” It does; it is another standard we agree upon in order to make interactions possible. You could declare, “I refuse to use dollars; I will only give or receive paperclips in exchange for goods and services.” (Less farcically, but also less entertainingly, you could use gold.) You could also, if you wish, insist on a strict barter system and avoid currency entirely because currency is a construct originating in the human mind. But there will be a very high opportunity cost to do so.

Just as with language, you cannot dispute the fact of the dollar holding value; it is a fact because it is defined as holding value. Its value changes over time, and you could argue that holding real estate or gold is wiser than holding cash. But if you reject all currency and say, “This is only paper,” you are limiting your ability to engage with the world.

It is entirely true that fixating on money can obscure the value of other things. There’s a very pretty view outside my window right now that I cannot sell to anyone, and I value it quite a bit. Thankfully, I can recognize the value of beauty while simultaneously accepting the fact that the $10 in my wallet will get me lunch. Aesthetics and currency might both be arbitrary means of evaluating value, but that is not to say they are in conflict. They’re designed, studied, and used for different purposes.

III. Math is an arbitrary system.

And so we come to math. You wrote, “…in abandoning common beliefs on what is factual, I’m also abandoning bias, which would be just that considering that we created facts, we created science and all of the principles and rules that fall within it. So, in abandoning bias, 2+2=4 is perfectly disputable.”

Indeed, humans created mathematics. Brilliant minds did so in order to better describe the physical world. Aristotle defined mathematics as “the science of quantity.” French Philosopher Auguste Comte defined mathematics as “the science of indirect measurement.” Math enables me to describe that if I eat 2/3 of that mango (it’s looking pretty good about now), I will have 1/3 left. We accept what those numbers represent so we can better communicate quantity.

But the numbers are, of course, made up representations. Continuing to consult Wikipedia for definitions in order to sound more knowledgeable than I am, I read that a mathematician who subscribes to formalism would even highlight the arbitrary nature of mathematics in defining the field, like this: “Mathematics is the manipulation of the meaningless symbols of a first-order language according to explicit, syntactical rules.” The whole point of math is that it is a system. Humans invented and accept it because it is useful, not only in telling me how much fruit I have, but in determining how quickly a swimming pool warms, or whether a bridge can withstand high winds, or when my aunt and I will arrive at the same location if she is in a car traveling east at 40 miles per hour and I am traveling west on my tricycle at 75 miles per hour.

If you declare that because humans devised mathematics it means nothing and that you are, instead, going to pronounce 2+2=3, you are not disputing a fact; you are rejecting reality and our ability to quantify it, to understand it. Because we want to communicate and make judgments about our physical world, we use the defined system of mathematics. Operating within this universally accepted system, as we do in order to live in and describe the world, 2+2=4 is true, a fact, and indisputable. The fact of the system’s human origin does not invalidate it or cloud it.

If you do wish to reject mathematics, I suppose you can, but any attempt at buying, selling, or bartering will probably end with you swindled, and you probably should not build bridges.

As with money, reliance on mathematics can lead to biased assumptions, favoring that which is quantifiable. Ask a math teacher whether the students learned anything in class, and you’ll probably receive data related to lesson objectives. Empathy learned through social interaction during that class might not be quantifiable, and is therefore less likely to be reported, but it’s very meaningful nonetheless.

It is true that not everything is quantifiable and also that math works; empathy is powerful, and 2+2 still equals 4. I need not undermine mathematics to put aside a bias toward the countable.

IV. Mangos are delicious.

I have now eaten my mango. Did you know mango skin is edible? It balances the sweetness, really.

V. Science is also a construct, and a necessary one.

And so, science. You wrote, “we, as humans, created what we know as ‘facts.’ If you depend on science you limit yourself to the creation of it. Science is not above itself. It is not even above everything we know in this world.” To make my terminology more concrete, I’m going to specifically discuss the scientific method and the relation of empiricism to facts.

We need to depend on science. And we can do so without limiting ourselves, any more than I am limiting myself my calling that delicious fruit a “mango” instead of a “math,” or by paying for it with one US dollar, or by using fractions to describe how much of it is left, now that I’m realizing there’s still a bit more fruit I can scrape from around the pit.

I agree that science is certainly not “above everything we know in this world,” because science exists solely to aid us in understanding that world and making determinations about it.

The great advance of the scientific method was its emphasis on falsifiable knowledge. A scientist formulates a hypothesis based on previous knowledge. Rather than assuming the truth of the hypothesis, the scientist attempts to falsify it by making observations of the physical world. If a thing is true, it will prove true over and over and over again. Experiments can go wrong, as nearly all my high school lab reports showed, but by replicating experiments, we can advance human knowledge. We test hypotheses against physical reality. We accept the natural world as real and use it to check our work.

Further study can find old errors and incorrect understandings; Newton gave way to Einstein. But always, science remains the quest for explanations of the natural world.

I do not want to bog down this writing with discussion of hypotheses, laws, theories, and the distinctions among them. I will shorthand it all by saying that through the scientific method and replication, we determine facts. We gain understanding of the physical world.

Declare science and facts “disputable” and what you’re really doing is rejecting either physical reality or our ability to understand it. The latter—rejecting the very concept of empirically-derived knowledge—is dangerous. Without the scientific method, we remain limited to our own guesswork and inferences based on individual experiences and hunches, and that’s not freedom from bias—it’s anarchy, and it’s dangerous, because dismissing the scientific method means dismissing the possibility of reaching common understanding about our world and places us all firmly in our own heads. Remove science and the most eloquent tongue and the catchiest meme will be the victor. There is very real harm in dismissing empirical study [see: antivaxxers and Andrew Wakefield’s infamously unscientific paper - https://www.historyofvaccines.org/content/articles/do-vaccines-cause-autism]

The scientific method is an agreed-upon construct to bring us to greater understanding of our agreed-upon physical reality. We check our hypotheses against the world around us. You can deny the existence of the world if you like—viewed properly, solipsism is freaking hilarious, and who doesn’t love The Matrix?—but in practice, pronouncing that things surrounding you aren’t real probably won’t do a whole lot for your quality of life.

VI. Science has one purpose, and religion has another.

You brought up religion. Is there something that exists aside from the physical world? Quite possibly. I can contemplate that possibility without dismissing the scientific method. The goal of science is to explain the natural world, not things that exist outside that realm. It’s that old quote attributed to Galileo: “The Bible shows us how to go to Heaven, not how the heavens go.” The conflict between religion and science is the canard. They serve to answer fundamentally different questions, like currency and aesthetics are designed to value different things. Personally, I think too many people worry about trying to negate one or the other rather than drawing wisdom from both. The Catholic Church used its power against Galileo, trying to deny the scientific method and assert one possible interpretation of the Bible despite physical reality… how did that work out? With the hindsight of centuries, it’s quite clear that the Church embarrassed itself.

Pitting religion and science against one another means misapplying one of them, putting a fish on land and asking it to sing instead of letting it be a splendid fish. I like to re-imagine the Sermon on the Mount:

JESUS

Blessed are the meek, for they shall inherit the Earth.

SHOUTING MAN IN BACK

Yeah, but is that Earth 6,000 years old, or is it not?

(JESUS facepalms)

And at the same time, the scientific method enables us to describe natural mechanisms (the Higgs Boson and the Big Bang and so forth), but to definitively prove those is not to disprove God.

I would add that religious experience cannot effectively replace science as a means of reaching common understanding about physical reality. We cannot say, “X or Y religious text provides all the answers about our world,” because as far as I know, none of the world’s sacred texts discuss microbes in Lake Baikal. Nor can we say, “All knowledge of the world must come to us through divine revelation,” because experiences with the divine are highly individualized (compare how Marjory Kempe and Julian of Norwich write about their mystical experiences, for instance, and that’s to say nothing of Buddha or Mohammed or John of Patmos). As individual, largely unobserved and often internal experiences, divine revelations are neither verifiable nor falsifiable; they are matters of faith.

Conclusion

In the final accounting, @PolarBear228, I think we’re more on the same page than we aren’t. Supposedly immutable givens of our life experiences originated within the human mind and exist because someone declared them to be so: language, currency, mathematics, science. [Time, if you listen to Einstein and some others, and God, if you listen to Richard Dawkins and some others, but Imma leave those last two alone.)

These human-created, human-defined constructs provide ways of navigating our world, and so they are valuable. They are true because we define them as true: in using language, the American dollar, and math we implicitly accept the end-user agreement that they have meaning. You cannot, therefore, “dispute” them or redefine their terms, because they are true by definition and fiat. You can only reject them. To use them is to accept their terms as valid; declare that the emperor has no clothes and you rob them of their utility, at great cost to yourself.

I believe you and I both think it is worthwhile to acknowledge the human origin and ultimately arbitrary nature of these systems as a reminder for ourselves. They come with biases, because when working within a system, it is natural to notice and value things that fall within that system. Language perhaps biases us against non-verbal communication and the ineffable. Currency perhaps biases us against things not easily assigned monetary value. Math perhaps biases us against things that cannot be quantified.

But this is not to say that we are “limited” by any of them; on the contrary, they expand our capabilities extraordinarily. Especially science. Science gets “disputed” by objectors more often than the other constructs I’ve focused on, as they sometimes hear of empirical conclusions that call their understandings into question, and so they resolve the cognitive dissonance by denying science. Again, the scientific method requires replication and refinement, and new knowledge emerges that exposes the errors of the old. But most commonly, in arguing against science, people are not turning to other scientific knowledge; they turn to pseudoscience that cannot be falsified, or they simply say “I don’t believe in that.” But the scientific method, the approach of checking hypotheses against reality, is the exploration of reality itself, and is an agreed-upon heuristic that lets us have knowledge. To discount an empirical finding because “that’s not what I believe” is to deny the scientific method itself and to give up on understanding our world, and to give up on the notions of common ground, fact, and truth.

Language, the US dollar, mathematics, and the scientific method are all constructs that humans thought up and defined. But “of human origin” is not “meaningless,” is not “disputable,” is not “false.”

I’m just going to finish enjoying what’s left of my one mango, purchased with a greenback and grown through scientifically optimized methods, but if you really wish to live your life rejecting all these human constructs as meaningless and invalid, I suppose you could. You could go to the grocery store with a sole piece of tropical fruit in your hand and tell the person at the register, “I will give you this undefined quantity of paperclips in exchange for this 37 maths because it will cure my cold and also grant me the power of flight.”

…actually, for real, you should do that. If you have a friend who can video you, please send along the TikTok :)