The Science of Prejudices

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1. Prejudices

Our inclination to give in to prejudice is at the root of many afflictions plaguing humanity. We will veer away from conventional newspaper article writing and adopt a style closer to scientific articles, and explain why most of us, by not having kept up with science and logic, have helped these prejudices survive. In particular, we explain why statements such as “I believe in X” or “X is true”(1) are inconsistent with logic and science, and should be replaced with “I assume X” or “Under the following assumptions I can derive X as true”.

The aim is not to turn people into complete skeptics but to encourage them to find the postulates and inference rules that their beliefs assume.

Every person comes equipped with two collections of prejudices, the prejudices arising from a flawed understanding of the universe (scientific prejudices) and the ones arising from fallacious inference (logical prejudices).

Our inability to reason logically is evident to anyone who has done any maths or
​programming. It seems clear that any collection of natural numbers should have a smallest element(2) or that “If it rains, then it rains“, yet these are not trivial to prove. In fact, proving that “whenever you draw a loop on a piece of paper, there will be a region inside the loop(3), and a region outside” turns out to be very hard.

The history of logic itself shows how naive we are when it comes to deduction. Until the end of the 19th century (so far over 2000 years), Aristotelian logic remained essentially unchallenged and was considered to contain all there was to know about logic, yet it was later shown to be unable to account for even elementary mathematical reasoning(4). The end of the 19th century also hosted the foundational crisis of mathematics(5): mathematicians realised maths contained many paradoxes and that even basic concepts such as “A set is a collection of objects” were flawed(6); it became unclear whether the theory of natural numbers itself(7) was self-contradictory!

To understand scientific prejudices, we need some history. During the 20th century, physicists started studying nature away from the “macroscopic, low speed, weak gravity” regime we observe in our daily lives. Since our intuition is based on our observable experiences, it is not surprising we found out nature in other regimes is counter-intuitive. For example, if you see two (falling) objects hitting the floor at the same time, they will not hit the floor at the same time for someone who is moving relative to you(8). Thus, to construct the standard model and general relativity(9), physicists relied increasingly on advanced mathematics. The consequences have been amazing for society: using these new theories and freed from their “prejudiced intuition”, scientists have made incredible advances in technology.

Sadly, schools have failed to pass on the advances in logic and science. People have not kept up with scientific progress and still rely on intuition to build beliefs that are therefore more consistent with naive/anthropocentric religions and intuitive philosophical notions (determinism, free will, ethics…) than with logic and modern science.

2. The Scientific Method

Science is not a collection of facts, it’s a method. There is no such thing as a scientist, just humans that sometimes apply the scientific method. Actually, Logic shows there are no facts or “true statements”: any truth is only valid within an axiomatic system(10). Very loosely speaking, it means that to have a “true statement P”, we must have a set of postulates (statements assumed to be true) and inference rules (rules of deduction that are assumed to be true) in order to derive that P is true(11).

For example the “fact” the earth is an oblate spheroid can only be deduced using a theory of light, which itself relies on postulates(12). Similarly, 1+1=2 is not a “fact beyond dispute” and requires Peano postulates to be proved(13).

Given any observable (say, energy or even things like “hate” if you’re interested in finding out whether X hates Y), the goal of the scientific method is roughly to
(a) Build a predictive theory, i.e. an axiomatic system containing logic, mathematics and postulates specific to the theory(14), that predicts the observable and demands that(15):
(b) Until such a model exists you remain skeptical (“What makes you think X hates Y“).
(c) Once a model exists you should do your best to break it. Then update it.

​The request that the theory belongs to an axiomatic system ensures “you know exactly what you’re saying and assuming“. The predictive character of scientific theories was mainly theorised by Popper, who realised how easy it was for any non-predictive theory to be verified by adding ad hoc modifications whenever it became inconsistent with nature. Only an unambiguous predictive theory can genuinely fail and the ability to predict is what distinguishes science from philosophy and religion. (b) ensures we do not prejudice the observable until we actually have a theory about it. Finally (c) guarantees that people using the scientific method do not respect or identify with any belief (saying “I believe in X” is unscientific(16) ) and always aim to disprove the current models, because this is what makes science progressive.

3. A Few Applications

1) J. Watson’s statement “Africans are not as clever as westerners“, breaks (b) since there is no unambiguous definition of “clever” and there can be no predictive model about it. The statement is therefore scientifically meaningless(17).

​2) Consider the following statements:
(a) “Blue lives matter” is racist
(b) “Blue people are dumb” is racist
where a racist statement is one that says “a particular race has less value or intelligence than another race”. (a) is a wrong inference since “blue lives matter” doesn’t tell us whether the lives of non-blue people matter, and therefore can’t be racist. It is derived from the fallacy (P => Q) => (not P => not Q), which for example says “if italians eat pasta, then not italian people don’t eat pasta”, which is clearly incorrect. (b) does the same fallacy and is thus also a fallacious statement.

3) The fine tuning argument says, “Even a tiny change in the value of any of the constants of physics would lead to a universe in which humans can’t live. It is too unlikely for these constants to be the result of chance and are thus evidence of design”. Saying that it is “unlikely for these constants to be set at a specific value” requires knowing the probability distribution of the values these constants can take, which can only be derived by measuring the constants in many universes.

4) Things are not the way they seem: what colour is the sun? Yellow/orange? No, our theory of light predicts the sun is white, but it is the atmosphere that makes it look yellow.

5) When religions try to give theories about observables (love, ethics, consciousness, meaning…) they become subject to science. Their texts break (a) by being ambiguous and depending on interpretation(18). The ‘problem of the existence of evil’ is usually used by atheists to show the concept of a “very nice god” is underdefined, while the “celestial teapot exists” argument is used to ridicule beliefs that break (b). Finally, note that religious people often break (c) by considering their beliefs should be respected. There is no such thing as a respectable belief/theory in science.​

1   X could be anything, from the theory of evolution to “equal rights for all people”
2   For example the set {66; 3; 5; 10^80} has smallest element 3
3   A curve that does not intersect itself and starts and ends at the same point.
4   In fact Aristotle’s logic can’t prove that “If all footballers are humans, then all shoes of footballers are shoes of humans”! It is common to hear that modern logic only began in 1931, after the publication of Godel’s theorems
5   Which really is a foundational crisis of Knowledge since all scientic/philosophical/religious theories contain theassumptions of mathematics
6   The set of all sets that are not contained in themselves leads to a contradiction (see Russell Paradox)
7   The one you learn in primary school
8   Simultaneity is relative
9   The two main theories of physics
10  Actually it is common to drop the concept of truth altogether in modern logic!
11  A typical rule of inference is that ∀xP(x) => P(t), which for example says “If it rains everyday, then it rains today”
12  Compare this with example 4 in the applications section
13  It took Russell over 300 pages to prove 1+1=2 in Principia Mathematica, which he described as an “occasionally useful theorem”
14  For example “the speed of light in vacuum has the same value in all interial frames”
15  In particular note the method is not required to belong to any philosophy (materialism, determinism…) and does not require “inductive reasoning”
16 Even if X =science
17  Note science does not presuppose racism to be unscientic: if there existed a disease that destroyed your ability to reason while changing your skin colour, say to blue, it would be possible to give an unambiguous denition of intelligence in which \blue people are dumber than non blue people” would be predictive. The fact racism is unscientific is a property of the world we live in, not an a priori assumption
18  Yet the only correct intepretation is the one of the author
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