My Understanding about Science

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It was in the Inorganic Chemistry, a course for Year 1 undergraduates taught by Prof. Huang, that I first received serious lecturing and discussion on Science. So far twelve years have passed, I cannot be more thankful because the enlightenment from Prof. Huang has long been benefiting me. It grants me a peaceful, grateful, and fearless belief in life. It also provides me principles to follow, and the discernment to trust. Today I would like to write down my understanding and thinking about science, as a memorial of my humble Ph.D. life.

Science is a systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the universe (Quoted from wiki).

Science usually manifests the pattern as follows. A single proposition or multiples can comprise either presumptions or hypothesis. A hypothesis then becomes a theorem if it is accepted by reproducible tests or proofs. After which, one or several theorems plus optional presumptions can build a theory, a field, or even a subject, and finally our edifice of science. The “proposition” can be seen as the most basic component of science.

Scientific Propositions

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What is a scientific proposition? There are five necessary conditions1.

Falsifiable

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  • Condition 1: the proposition must be falsifiable, not verifiable.
    • (Falsifiable) All swans are white.
    • (Verifiable but Non-falsifiable) There exists at least one swan that is white.

For Condition 1, it reflects two ways of examining a proposition, by discovering a counterexample for rejection, or by discovering a positive example for supporting. This lead to falsificationism and positivism, respectively. The logic behind these two genres is as follows.

  • (Falsificationism) If \(P\rightarrow Q\), and not \(Q\), then not \(P\).
  • (Positivism) If \(P\rightarrow Q\), and \(Q\), then \(P\).

Positivism fails because of the logical fallacy of affirming the consequent. Here, \(P\) might not be the unique cause to \(Q\). Thus, even if \(Q\) is true, that does not necessarily mean that \(P\) is true. \(P\) is true only if \(Q\) is true and \(P\) is the only cause of \(Q\). On the other hand, the falsificationism wins because once \(P\) is the cause of \(Q\) (with or without the uniqueness) and not \(Q\), then not \(P\) can be safely claimed.

The positivism fails also because it is not operational to conclude \(Q\). Because we can claim \(Q\) only after we enumerate every example from the whole population of \(Q\) and during which the positivity holds. On the other hand, falsificationism wins because it is practical to claim not \(Q\) once we find a single counter sample.

Universal

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  • Condition 2: the proposition must be universal, not particular, nor existential and tautological.
    • (Universal) All swans are white.
    • (Particular) All swans on Lake A are white.
    • (Existential) There exists at least one swan that is white.
    • (Tautological) All swans are in the color of their own.

For Condition 2, the point is that a proposition is meaningful only if we can find a way to examine it, and, as we aforementioned, we resort to falsifiability. A universal proposition is meaningful because it is falsifiable. To falsify, we can examine the swans until we find a counterexample. It is operational.

By contrast, the existential proposition and tautology are not falsifiable. For the former, the counterexample, in this case, is not a single swan, but the entire population of swans as a whole, no matter they are dead, living, and yet to born. Only if every swan in this "infinite" counterexample is enumerated and verified to be non-white can we reject the existential proposition. Such a procedure is not operational. For the latter, it is simply essentially true and useless.

As for particular propositions, the falsifiability may be fine. However, it is hindered by another factor, the Quantities of Information (QoI). The proposition "all swans in Asia are white" has definitely more QoI than the proposition "all swans on Lake A are white", and is, therefore, more "meaningful" to be considered scientific. Note, the tautology has zero QoI.

Objective

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  • Condition 3: the proposition must be objective, not subjective.
    • (Objective) The swan is white.
    • (Subjective) The swan is beautiful.

Condition 3 requires the truth of proposition independent from individual subjectivity. The truth condition of the proposition is somehow "consistent" and "fixed", across different people with various backgrounds.

Deductive

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  • Condition 4: the proposition must be deductive, not inductive.
    • (Deductive) All swans are white because of the law of inheritance.
    • (Inductive) All swans are white because 10000 white swans are observed to be white in this area.

Condition 4 concludes the sharp difference between science and technology. Science is cultivated by solid axioms and accepted theorems, based upon which the higher-level theories are deducted. It moves from idea to observation. A theory can be 100% correct if and only if all its premises are correct. Whereas technology is developed by dealing with partial information about our world. It moves from observation to idea. If the premises are true, the conclusion can still be wrong, because it is impossible to observe every sample of the population.

Empirical

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  • Condition 5: the proposition must be empirical, not theoretical.
    • (Empirical) All swans on our planet are white.
    • (Theoretical) All swans in the 11-dimensional universe are white.

Being empirical is equivalent to being operational, observable, measurable, and testable, etc. This further limits the definition of science, i.e., a proposition must be falsifiable, meanwhile, the way to falsify must be empirical. Being falsifiable rejects subjects like Art and Literature, and being empirical can further reject subjects like a large portion of mathematics and logic! Because they may be true but are purely mind-based. Actually, being excluded from science is not a shame, instead, it can sometimes be honorable! Why? Because logic and mathematics are the father of science!

Some Conclusions

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According to the five conditions, we could attempt to draw some conclusions.

The greatness of a proposition is determined by its generality. For example, the equation

$$E=mc^2,\tag{1}$$

where \(E\), \(m\), and \(c\) denote the energy, mass, and the speed of light, can be applied to "almost" everything of our universe -- maybe also other parallel universes. For everything I mean atoms, molecules, proteins, viruses, germs, cells, animals, plants, mountains, the air, light, etc... It contains tremendous QoI, and is therefore theoretically easy to be falsified. It should be wrong if only we could find a counterexample among all of these objects it is applied to. Yet, so many years have passed and it still holds.

The modification of a proposition must increase its falsifiability, not decrease it. For example, you hypothesized that "all swans are white". Later, some black swans were spotted in Australia, so you modified your hypothesis to "all swans outside Australia are white". Yet unfortunately, black swans from other places were spotted. You felt frustrated and decided to modify again to "all swans on Lake A are white", just because you lived near Lake A so you were pretty sure about it. So now you finally make your hypothesis true and Yeah! In this whole process, the falsifiability of your hypothesis is decreasing. In the beginning, we can attempt to falsify your hypothesis by examining any swans on our planet, but later we have to pay attention to the nationality of the sampled swans so that we will not choose any from Australia, and finally, we have to travel all over the world, just for visiting Lake A outside your humble home. By contrast, great theories can "reborn" and "level up" after being falsified. For example, the Euclidean geometry fails when the space is not flat, yet it can be generalized to several non-Euclidean geometry models. As a result, it holds no matter the space is flat or not. It is worth noting that a modification towards the direction of falsifiability decrease is usually favored by many pseudo-scientific or superstitious tricks.


  1. A necessary condition is a condition that must be present for an event to occur. If \(P\rightarrow Q\), then \(Q\) is the necessary condition of \(P\). The presence of necessary condition (\(Q\)) does not guarantee the occurrence of the event (\(P\)).