Posts tagged with reasoning

This is a question about argument, counterargument, convincing people of something, and why people believe the things they do.

  • Let’s say you make a claim. For example the claim that rich people are rich because they do the most good in society.
  • I want to argue that you’re wrong. There are a couple ways I could proceed.
  • Now, to me, personally, the most logical tack to take should be to ask you for evidence.
    Wikipedian Protester

    You’ve made a sweeping claim about a large number of people, using ill-defined abstractions like "good", and so on.
  • In my mind, the way I personally think, I should ask you to back that up, you won’t be able to (or will make recourse to doctors, neglecting the real issues like LBO investors or the bottom billion) and then you end as wrong or neutral.
  • But. This is not what really works in a real debate or argument. It’s mysterious to me as to why, but I think a correct answer as to why would be pure gold.
  • What’s going to work better is if I argue a separate theory.  Like "No, the rich don’t benefit society the most, they just screw people over the most. They put the terms of trade in their favour, they set up deals that screw over powerless or uninformed parties, and the game is set up in a way that benefits them.” If I’m really impassioned and present some stories backing up my viewpoint this will work even better.
  • Now to me this seems illogical. You’re saying "X" and rather than responding "Not X" I’m supposed to respond "Y". Y relates somewhat to X and kind-of negates X, but mostly Y is just a different theory of the world.
  • Another example could be that you argue for supply-side economics. Instead of me arguing against supply-side economics, pointing out the flaws or weak points in it, it’s more convincing if I argue Keynesianism, or MMT, or some other full theory, instead.

My examples are economics debates because I’m stupid. But this principle of arguing in a different direction than directly contrary to what you say works elsewhere too.

  • Look up "Gish Gallop" for example. The phrase relates to evolutionists complaining about the way a creationist, Duane Gish, argues. Gish allegedly adds more and more propositions to his argument, forcing his opponent to look up and refute stuff much slower than Gish can add new propositions.
  • Gish is not arguing this way, and his evolutionist opponents are not frustrated by the rhetorical style, because it doesn’t work. Irrespective of how much he does it, the fact that evolutionists were bothered enough to name a “fallacy" after Duane Gish indicates that audiences were swayed by the technique of adding more and more propositions.
  • Logically—to me at least—it’s harder to prove a claim made up of many propositions than to prove just one of the propositions making up the claim. So “Not only does G-d exist, but the Christian G-d exists, and was made manifest as Jesus Christ, and died on the cross to atone for the sins of mankind, and ten other points of doctrine" —- should be harder to prove than just "Any G-d exists”. But yet I’ve seen more than one “Atheism debate” where the anti-atheist person debates this very long proposition.
  • Or let’s say you’re arguing that a thesis you read in the Times is “probably right" because it’s vetted by experts. I should argue back that vetting doesn’t imply it’s right. But to be more convincing, I probably should counter the Times writer’s theory with one of my own. If I don’t have one, but just like to carry around a bucket of scepticism to pour on fires of passion? I’m SOL rhetorically.
  • Why wouldn’t you just defend the easiest argument—the one that Pareto-dominates the long argument?
  • The fact that people don’t agree with what I’m calling simple logic means I’m missing something. In fact I don’t think anyone has a theory of why people are convinced by things, which captures the appeal of these run-on arguments. Of course I would be happy to be told I’m wrong about that; please tell me if I am.
  • Do people prefer more information-dense statements? Does making a more specific claim imply, in some wider "ecological" sense, that the speaker is “more likely to be” well-informed? Do people prefer whole frameworks to piecemeal facts? If so, why?
  • I could go on with more questions and half-baked theories of what might be happening, but I’ll spare you.

So, why do people think this way? Is it a lack of sfumato? And what does the fact that people think this way tell us about other important stuff, like rationality, love relationships, parenting, reasoning, good decisionmaking, "facts", habits, authority, marketing, judgement, court convictions, investing/retirement planning, political voting, how people come to their beliefs, and what it takes to change someone’s beliefs?

Einstein opined that the great philosophical breakthrough leading to the mental possibility of science was the hypothetico-deductive method.

Which is a jargony way of saying: forget whether A is true or not (measurement of the world)—let’s talk about the separate, purely logical issue, of whetherif A were true, would B necessarily be true as well, as a result of A being true? ⧝

People aren’t great with hypotheticals, though—at least not everyone or not without education.

  • I can get people to agree with my reasoning  by first telling them that  leads to a conclusion they already agree with B.
  • (This is really dastardly because once I’ve judoed someone this far I can get them to agree to even more things, in order to maintain local consistency.)
  • We judge each other on credentials (A).
  • We judge arguments on what other experts think of them.
  • Mathematics is all about the  and most people are either scared to tears by mathematics, bored to tears by mathematics, or think mathematics irrelevant, or all three.
  • People think that if I argue that their reasoning  is wrong, I’m saying their conclusion B is wrong.
  • (Symbolically it’s obvious that A↛B = A⊬B = ¬(A→B) isn’t the same as ¬B. But people regularly interpret “That does not follow” as “That’s wrong”.)

File:Catechism-Madras Presidency Village.jpg

Whatever it is people do in arriving at their beliefs, it’s not propositional calculus; it’s not Bayesian probability; it’s not “believe whatever mama says”. But it is a little like all of those.


I was riding on a train in Italy. Watching lemon trees out the window. Fantasising of tasting a lemon-based liqueur.

Lemon trees. Amalfi Coast, Campania, Italy (color)



My travel partner and I shared a vestibule with an American monk-cum-priest who introduced himself as Father John. Father John was making a pilgrimage from the Carolinas to Vatican City. I don’t know if he always evangelised but, although my partner and I tried to steer the conversation away from religion, Father John wanted to talk about his Catholic faith—specifically in a way that might score some converts.


I don’t know whether the part of me that makes me debate with strangers online was acting out in its pre-internet form, or whether Fr J’s insistence on having a conversation we clearly did not want to have put me in a pugilistic mood.

File:Jules-Alexis Muenier - La Leçon de catéchisme.jpg

For whatever reason, I started querying him on some of the more outlandish assertions of Catholic doctrine. One thing I challenged him on in particular was transubstantiation.

File:Pietro Longhi 021.jpg

Try though the alchemists might they could never transmute lead to gold—but every Sunday around the world, holy men of Christianity transmute sacramental bread and wine into literally the body and blood of Christ.


The biochemistry involved in going from wheat flour to bone marrow or from pectin to haemoglobin is not discussed in catechism, but the transition is obviously impossible by natural processes. Nonetheless, “the real presence of Christ in the Eucharist is a mystery—something so packed with meaning that we can never fully understand it.”


I really don’t have a bone to pick with “transubstantiationalists”. I find the deeper reasons he and I think as we do more interesting than what we profess. I don’t go out of my way to attack people or hurt anyone’s feelings—but I do consider it rude to evangelise someone without consent.

So I needled the man. "Come on, you really believe that? Really? It’s not just a symbol? You can’t just have your religion without this physically impossible claim? Why would you insist on invoking the supernatural when that clearly undermines the credibility of everything else you say? Not only is it impossible according to science, even to your own sensory experience it just looks like a normal wafer—not like a hand or a butt or whatever. You literally, actually believe that this wafer literally, actually turns into actual human flesh of a dead man from two millennia ago—using up more body mass than he ever had all over the world every Sunday—really? Really?”

I still remember Father John’s response (which is how I’m able to tell you this story). He said: “OK, I understand your objections. But consider this. What if it were all true? What if the Resurrection, the Virgin Birth, G-d walking among men, the sacred mysteries, all of it were true? Wouldn’t that be wonderful? Wouldn’t that change everything about the way you see the world?”

What-if indeed, Father. What if.

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Discussing the first year of life.

  • In-born aptitudes include
    • theory of other peoples’ minds (looking at where they’re looking, show surprise when they know something they “shouldn’t”) (this gives some idea of what autistic people go through—they lack a skill that one-year-olds have!)
    • animate versus inanimate things—causality, essentially

Infants do reason. They just have less knowledge than adults.

Brain hemispheres act the same at birth but begin to specialise over time. (So could there be an alien environment where human babies would specialise their brains along different lines?)

There’s no one thing that makes the human brain superior to other animals’ brains (at least not that we’ve found). It’s thought to be the interaction of various factors—as well as our long developmental period—that make us able to build rocket ships, paint potato eaters, invent radio and discuss these things on it.


(Source: BBC)

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One of the more consequential kinds of extrapolation happens in the law.

In the case of Islamic law شريعة  the Hadith and the Qu’ran contain some examples of what’s right and wrong, but obviously don’t cover every case.

This leaves it up to jurist philosophers to figure out what’s G-d’s underlying message, from a sparse sample of data. If this sounds to you like Nyquist-Shannon sampling, you and I are on the same wavelength! (ha, ha)




Of course the geometry of all moral quandaries is much more interesting than a regular lattice like the idealised sampling theorem.

Lattice of beverages
Revised lattice

imagering lattice
ring lattice


Escher's grid




Evenly-spaced samples mapping from a straight line to scalars could be figured out by these two famous geniuses, but the effort of interpreting the law has taken armies of (good to) great minds over centuries.

A_2 lattice Voronoi and Delaunay cells
PCA of British MPs in the space of rollcalls


The example from this episode of In Our Time is the prohibition on grape wine:

  • What about date wine?
  • What about other grape products?
  • What about other alcoholic beverages?
  • What about coffee?
  • What about intoxicants that are not in liquid form?

The jurists face the big p, small N problem—many features to explain, less data than desirable to draw on.




Clearly the reason why cases A, B, or D are argued to connect to the known parameter from the Hadith matters quite a lot. Just like in common-law legal figuring, and just like the basis matters in functional data analysis. (Fits nicely how the “basis for your reasoning” and “basis of a function space” coincide in the same word!) .

Think about just two famous functional bases:

  1. Polynomials (think Taylor series),


  2. Sinusoidals (think Fourier series).
    Fourier Series

Even polynomials look like a ‿or   ͡ ; odd polynomials look at wide range like a \ or / (you know how looks: a small kink in the centre ՜𝀱 but in broad distances like /), and sinusoidal functions look like ∿〜〜〜〜〜〜∿∿∿∿〰〰〰〰〰〰〰〰〰〰〰𝀨𝀨𝀨𝀨𝀨.


So imagine I have observations for a few nearby points—say three near the origin. Maybe I could fit a /, or a 𝀱, a , or a ‿.


All three might fit locally—so we could agree that

  • if grape wine is prohibited
  • and date wine is prohibited
  • and half-grape-half-date-wine is prohibited,
  • then it follows that so should be two-thirds-grape-one-third-date-wine prohibited—
  • but, we mightn’t agree whether rice wine, or beer, or qat, or all grape products, or fermented grape products that aren’t intoxicating, or grape trees, or trees that look like grape trees, and so on.

The basis-function story also matches how a seemingly unrelated datum (or argument) far away in the connected space could impinge on something close to your own concerns.

If I newly interpret some far-away datum and thereby prove that the basis functions are not  but 𝀨𝀱/, then that changes the basis function (changes the method of extrapolation) near where you are as well. Just so a change in hermeneutic reasoning or justification strategy could sweep through changes throughout the connected space of legal or moral quandaries.


This has to be one of the oldest uses of logic and consistency—a bunch of people trying to puzzle out what a sacred text means, how its lessons should be applied to new questions, and applying lots of brainpower to “small data”. Of course disputes need to have rules of order and points of view need to be internally consistent, if the situation is a lot of fallible people trying to consensually interpret infallible source data. Yet hermeneutics predates Frege by millennia—so maybe Russell was wrong to say we presently owe our logical debt to him.


In the law I could replace the mathematician’s “Let” or “Suppose” or “Consider”, with various legalistic reasons for taking the law at face value. Either it is Scripture and therefore infallible, or it has been agreed by some other process such as parliamentary, and isn’t to be questioned during this phase of the discussion. To me this sounds exactly like the hypothetico-deductive method that’s usually attributed to scientific logic. According to Einstein, the hypothetico-deductive method was Euclid’s “killer app” that opened the door to eventual mathematical and technological progress. If jurisprudence shares this feature and the two are analogous like I am suggesting, that’s another blow against the popular science/religion divide, wherein the former earns all of the logic, technology, and progress, and the latter gets superstition and Dark Ages.

(Source: BBC)

If you buy a loaf of bread from the supermarket both you and the supermarket (its shareholders, its employees, its bread suppliers) are made to some degree better off. How do I know? Because the supermarket offered the bread voluntarily and you accepted the offer voluntarily. Both of you must have been made better off, a little or a lot—or else you two wouldn’t have done the deal.

Economists have long been in love with this simple argument. They have since the eighteenth century taken the argument a crucial and dramatic step further: that is, they have deduced something from it, namely, Free trade is neat.

If each deal between you & the supermarket, and the supermarket & Smith, and Smith & Jones, and so forth is betterment-producing (a little or a lot: we’re not talking quantities here), then (note the “then”: we’re talking deduction here) free trade between the entire body of French people and the entire body of English people is betterment-producing. Therefore (note the “therefore”) free trade between any two groups is neat.

The economist notes that if all trades are voluntary they all have some gain. So free trade in all its forms is neat. For example, a law restricting who can get into the pharmacy business is a bad idea, not neat at all, because free trade is good, so non-free trade is bad. Protection of French workers is bad, because free trade is good. And so forth, to literally thousands of policy conclusions.

Deirdre McCloskey, Secret Sins of Economics

A wonderful essay. I’ll just add what I think are some common answers to common objections:

The category of categories as a model for the Platonic World of Forms by David A Edwards & Marilyn L Edwards

  • Thales (7th cent. BC) made the first universal statement (proof w/o regard to the gods or mythology, just from pure reason)
  • pre-Greek mathematics was essentially engineering maths.
  • I owe ya a post on the illiterates in chapter 2 of James Gleick’s The Information. He tells the story of some illiterates in outer Soviet Union. According to the tale, they basically do not abstract at all. No abstract reasoning, no properties ascribed to members of a class, and so on.

    It sounds kind of idyllic in the way of NYT tales of the Pirahã or Jill Bolte Taylor’s story of losing the logical half of her brain. I’m not sure if Thales set us on the path to Hell or Heaven.
  • Plato set for himself the [goal] of extending geometry [beyond] triangles and circles and such, to all of human thought. He failed, but his vision has come to pass.
  • Why did Lawvere succeed where Plato and Whitehead failed?
  • He had Descartes’ already-abstract notion of a function, along with
  • Eilenberg & Mac Lane’s notions of category and functor.
  • The definition of function for infinite sets is already implicit in the choice of “which set theory”.
  • Category theory, unlike earlier formalisations (think Peano arithmetic and Goedel’s proof), is stable to the “meta” step: you do 2-categories, you do n-categories … the abstraction is ultimately a k → k+1 kind of deal rather than a “And this is the ultimate finality!” kind of deal.

the Good People and the misguided

HT @jaredwoodard (supervenes)

the Good People and the misguided


HT @jaredwoodard (supervenes)


1. Use mathematics as a shorthand language rather than as an engine of inquiry
2. Keep to them [your models/problems] till you have them done
3. Translate to english
4. Illustrate with examples important to real life
5. Burn the mathematics
6. If you can’t succeed in 4, burn 3

Opportunity is fleeting. Experience is fallacious. Judgment is difficult.