The case for canonical realism.
I am a big fan of mental arithmetic.
There is one, admittedly morbid, trick I perform for people as a joke; I ask them for their age and respond with how many weeks they likely have left to live. The “trick” works as follows:
I tell them I am assuming they will live up to “around 85”.
Since 1 year≈52.17 weeks on average, I use the fact that I know many multiples of 52 by heart
2*52=104
3*52=156
4*52=208
5*52=260
6*52=312
7*52=364
8*52=416
9*52=468
etc.
This is simply converting years to weeks before adding a small correction, so I calculate 85-their_age and convert it.
If I need to convert a number of years whose multiple of 52 I do not already know, I piece it together; say the person is 38 years old.
Since 85–38=47, the number of weeks in 47 years (before adjustment) is 47*52=(4*52)*10+(7*52)=2080+364=2444, where “4*52” and “7*52” are recalled directly from memory (in this case, I also know that “15*52=780” so I could have chosen instead 47*52=(45*52)+(2*52)=3*(15*52)+104=3*780+104=2340+104=2444, just a matter of what pops into my head first).
I then* use the fact that 0.17=1.7/10 to add a small correction; every 10 years we get an extra 1.7 weeks, so in our example above, since 10 goes into 47 four times, we need to add 4*1.7=6.8, giving us 2444+6.8=2450.8, which I then round up to 2451 (this is very close to the real answer and as accurate as WolframAlpha).
If they insist I should assume they will live longer than 85, I redo the calculation using their preferred maximal age.
*- In practice, most people cannot appreciate this extra step anyhow and since it is only meant to be an approximation, I often just omit it and make sure to mention that “the answer is a bit more than X”, where X is my estimation.
I once accompanied two colleagues on the way back from a work event and performed card tricks for them as we were walking. They have known me for a while now and have seen ample demonstrations of me mentally squaring, dividing, extracting roots, telling them the day of the week for a given date and performing other odd “tricks” like the morbid one, so what followed was not out of the blue for them. We stopped for a short chitchat before going our separate ways and I jokingly commented at some point (was relevant in the conversation’s context) that I have “merely X weeks left to live” and “from here, it’s only downhill”.
One of them responded with “but how do you know this?”, so I explained the entire method, as I did above.
They then retorted, “you can’t know, you might live to 104”, to which I replied, “I might, but it’s statistically unlikely”.
It is true, the average probability of reaching the age of 100 seems to be 5.1% for women and 1.8% for men. Being even older than that is even less likely because of the Gompertz–Makeham law.
People have a very hard time conceptualizing uncertainty.
For many, it is as if the mere possibility of having doubts outweighs the things that can be known.
When I say “I have carrots in my fridge”, I do not mean that I have absolute, godlike certainty that if I open my fridge, I will see carrots.
Instead, I mean:
1. I have reasons to anticipate seeing carrots when I open the fridge
(I remember buying them, I remember seeing them earlier, I do not remember eating them, etc.).
2. I feel confident in those reasons.
3. I am going to operate under the assumption that, indeed, I have carrots in my fridge.
The same applies to something’s negation; when I say I “know” something is not the case, I mean that I lack reasons to believe it and do not intend to change my behavior to accommodate this possibility.
The crucial part is that of “confidence”.
When we actually look at how people use words such as “believe”, “think”, “opine”, “know”, etc. we see gradation and context sensitivity:
• Low confidence in one’s reasons is associated with the utterances
“I believe”, “I think”, “it seems to me”, etc.
• “I believe”, “I think”, “I feel” and other linguistic softeners like “personally” and “in my opinion” signal politeness
• “She opined”, “he maintains”, etc. are more literary and are used to signal sophisticated language usage and/or distance
• “I know” is normally reserved for information we are highly confident is true
and so on.
This hints at a very realistic, non-platonic conceptualization of knowledge:
(★) What makes a piece of information “knowledge” is our attitudes toward it.
Generally speaking, if we behave as if some statement is true, it means we are confident enough to treat it as if we “know” it and, vice versa, if we truly believe we “know” something, we will behave as if it is true. Note:
1. The criterion is concrete (with respect to the individual) and requires us merely to be confident enough for the belief to be reflected in our behavior. “Knowledge” is then not a “platonic”, abstract thing, rather, it is something we do. How much is “enough” in “confident enough” is a quasi-empirical question which nonetheless will inevitably have a subjective, idiosyncratic element (i.e. humans, even though they differ from one another, probably do share similar intuitions, and those intuitions can be studied).
When I say “I know there’s no elephant in my house”, I am describing my attitude toward the proposition “there’s an elephant in my house”;
saying I “know” it to be false means nothing more than declaring that I fail to recognize reasons for it being the case and that I have no intention of behaving as if it were true.
2. You do not need to be able to recognize or verbalize that you think you “know” something for it to be the case. It is clear that you think that you know one cannot just fall through the floor, even if you are unaware of what the normal force is or have never heard of Newton’s third law.
We embody the things we think we know in our behavior.
3. This explains why not all opinions are equal; different individuals will feel confident in their behavior based on different standards of evidence.
From the inside, everyone feels justified. However, sometimes someone has to be wrong because people feel justified even when they all hold beliefs that contradict each other.
Our minds are not infinitely plastic.
Consider humans’ color perception. Even though our visual systems are able to capture and represent millions of unique shades, languages use only a handful of verbal labels to name and describe colors in our day-to-day lives.
It means that whatever raw data (in this example, visual) is being picked up by our eyes then undergoes some kind of “rounding” operation to a “nearest” canonical example (“red”, “orange”, “yellow”, “green”, etc.) upon which we then can act (either verbally or otherwise). Said “rounding operation” is probably unique to some degree (no two brains are exactly alike), but still shares enough similarities between individuals for communication to be possible and is likely affected by things like prior exposure and culture.
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The same goes for all our other beliefs.
We cannot “update” our confidence and/or skepticism to arbitrary levels of precision. At some point, your confidence in the veracity (or falsehood) of a proposition is “rounded” to some archetypal attitude you can work with.
This means that the brain guesses reality in some sense; we are bombarded with information from the environment, which the brain then must compress and make sense of using different degrees of confidence.
Nevertheless, not all guesses are equal.
Imagine I sent you a text, but alas, the text got partially corrupted and instead of my original message you received:
“c_ts and d_gs”
Can you guess what I intended?
I am willing to bet that, even when given 0 additional context, a majority of people reading this would guess “cats and dogs”, a minority would guess “cuts and digs” and an even smaller minority would guess something else entirely (“cots and dugs”).
You later learn that my intended message was indeed “cats and dogs”.
How did the ones who guessed correctly “know”?
Did the message not have some ambiguity to it?
Now imagine a different scenario: I sent you a message, unfortunately, it was corrupted again. This time you received:
“xhvoiptdjrzpc”
Given 0 additional context, could you guess what the intended message was?
Obviously not, right? You later learn that my original message was “I’m on my way”.
How come, even though technically both of these had ambiguity to them (uncertainty that allowed multiple completions), the first one was still recoverable, whereas the other one was not?
Simple, it is because of how much ambiguity was in each.
The first one still contained enough structure to constrain the space of possible guesses to such a degree that if your brain operates under the assumption (so-called “prior”) that the phrase “cats and dogs” is much more common in everyday English than, say, “cuts and digs”, you will get it right.
This assumption is indeed factually correct, meaning, having this “prior” (even if you are not aware that you have it and cannot verbalize the fact that you follow it) is, factually, a more accurate representation of reality, at least in this specific case. Using additional information (like the context surrounding the message) might have made one inference over the other even more convincing.
The second statement, however (again, without extra contextual information), could represent any other string* (technically, even assuming it must represent other 13-symbol-long strings is an exogenous assumption) so, in this specific case, all guesses are technically as valid as one another, but in a completely vacuous sense: no guess would be any more justifiable than any other because there is nothing to justify guesses with.
*- As a matter of fact, I generated this string using random.org.
Since you now know my two original messages, we have a canonical, verifiable way to compare which people guessed correctly:
1. In the first case, people who guessed “cats and dogs” were objectively correct and, more importantly, they could very reasonably justify their guess (“the phrase ‘cats and dogs’ appears more frequently in English than the alternatives”).
This remains true even if they are only able to say something along the lines of “it is obvious”; they do not need to have the extra declarative knowledge that the phrase is more common in order for it to affect their choices. People act out their beliefs/values whether they are aware of it or not; they do not need to also be able to honestly report their own beliefs/values.
A gazelle does not need to understand why it feels the urge to jump in the presence of a predator for jumping to be an effective strategy.
2. In the second case, even if someone just happened to guess “I’m on my way” (again, without any other contextual cues), then they are technically objectively correct, but in a very boring way; they could not give any justification because the string, in and of itself, lacks any obvious structure.
Both from exchanges in real life and from consuming content online, I have a strong impression that people constantly take uncertainty of the first kind (some ambiguity) and treat it as if it is the second (complete ambiguity to the point of no justified guesses), which is the fallacy of verisimilitude. This solipsistic, “hyper-relativistic” narrative is clearly self-defeating and could be used to trivially justify anything:
Say you disagree with everything I said so far. Does it not then mean that you think your position is more justified than mine? Does it not mean that you have used some criteria by which my position is objectively inferior in respect to your canonical framework? Is it not the result of your brain exploiting some structure either in my argument or in the facts of physical reality and demonstrating a gap in what I said? The sword of (hyper-)relativism cuts both ways:
(★) If all interpretations are always, no matter the circumstances, equally valid, then the interpretation in which you are wrong is also valid.
Why then not concede that you are wrong? Why does your position get special treatment?
Even the string of symbols “1+1=2” depends on a canonical, shared framework and is not some special, human-independent, eternal knowledge.
We noticed that taking “●” and putting it next to “●” is the same as “●●”, so, since it turned out to be useful and comes up a lot, we gave those things names that let us abstract away from actually dealing with the objects themselves and focus on their quantities instead.
Nothing is stopping you from defining “‘+’:= exponentiation” and then “1+1=1” would be true under your convention, but why would you? What is the point of a convention only you follow?
We might not literally be able to see the world through each other’s eyes, yet, we do have shared frameworks through which we can construct canonical examples and definitions, and refer back to those when needed to arbitrate between borderline cases. Yes, this “canon” needs constant revision and must remain forever “open” in a sense, but a version of it must exist for communication to be possible and, in a healthy society, this is the normal result of cordial communication with your peers.
Look, I am as much of a mereological nihilist as the next person, but we cannot pretend that just because a framework is constructed via human interactions, then “anything goes”.
“Chairs” do not literally exist, yet, it is a useful label for a pattern of matter that pops up and is being used often, which means that when we hold our sensory, linguistic, cultural, etc. framework fixed, then judgements about macroscopic objects can genuinely be said to be more or less acceptable/correct relative to said framework. There might be ambiguous cases in which different individuals can make roughly equivalent cases whether the same object is a chair or, say, a bench, but it is very unlikely someone could make a reasonable case for said object being the moon.
One might have honest reasons to think a goose is a duck, while another might have honest reasons to believe it really is a goose, but do you not think both would be closer to the truth than someone who says it is a hedgehog?
We constantly understand things in the context of a given framework (how common phrases are in a given language, the agreed-upon meaning of math symbols, road signs, how common a behavior is in response to certain stimuli, etc.), many of which are also constructed on the spot, either explicitly (like when defining something) or implicitly (like how you understand that I use “(★)” to signify statements I would like to flag as important even without me saying so), but just because facts need background assumptions it does not “flatten” all differences between a fact and a non-fact within the framework containing those assumptions*.
*- The other side of this exists as well: failing to mention a necessary framework and then assuming that facts within the framework are also facts outside of it.
Though it goes beyond the scope of this text, this is one reason (among others) why I reject the idea of “IQ tests” a priori. The sequence:
←,↑,→,..
could have any continuation (for example, ←,↑,→,↓,←,↑,→,↓,.. and ←,↑,→,←,↑,→,←,↑,..), so without spelling out the expectations of the test, nothing in “←,↑,→,..” logically entails any specific continuation, which makes the test into “guess what the test-maker intended” (in what sense is the interpretation “imagine the arrow rotating clockwise” more “intelligent” than other interpretations?). This is fine, but then the test does not represent what people usually claim it does. Without telling you that “1,2,4,8,..” is supposed to be a geometric sequence, there are infinitely many ways to continue it. Saying “choose the simplest one” does not help because there are different notions of “simplicity” that favor different continuations.
Given the framework of our shared, “canonized” human physiology, I will likely not make it to 104.
Though I do not have godlike knowledge that this will be the case, I have no reasons to think this, have no intention to behave as if it were true and plan my finite time accordingly.
