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Contraposition and Falsifiability in Scientific Inquiry and Empirical Knowledge

Posted on December 12, 2021 — 6 Minutes Read

Most problematic, and at the same time most enlightening, of all philosophical assertions are those that are in distinct opposition with the intuition that many find most at heart. These peculiar assertions, by virtue of reductio ad absurdum, call for a reexamination of the premises and with them the culprits are often found. Whether it was the groundless presupposition that there was only one sense in which a being can be, that Parmenides postulated when inquiring into the ultimate reality in Ancient Greece, which dismissed, among others, the predicative sense in which a negation might be prescribed to a non-existent being without rendering it a reality; or the false dualism that advanced the notion of selfhood residing in the psyche or consciousness of the inner immaterial realm of immanence as a causa sui (self-causing), free-willing and meaning-bestowing eternal subject for the other casually-determinate and perishing objects in the outer empirical world of transcendence, that Aristotle, Rene Descartes and Edmond Husserl subsequently conceived, when inquiring into the notion of the self, with one influencing the next, in the time past; the questions themselves were found to be the most questionable.

Should the premises be unveiled and verified, and the argument that progresses from the premises to the assertions be valid, which together with the trueness of the premises renders the argument sound; it suggests then a problem with the common understanding. Case in point is the seeming peculiarity with one basic tenet of propositional logic i.e. If p then q, that is by contraposition, if not-q then not-p. It is true in the sense that if p is the sufficient condition for the occurrence of q, then it stands to reason that the absence of q, for it being by transposition a necessary condition for p, implies beyond doubt the non-occurrence of p. For if philosophising leads in all and every case to time passed, then not a moment has passed implies no philosophising has taken place; or that if writing leads to pleasure, then the absence of which means not a word has been written. Notwithstanding that it does not require that q i.e. time passed or pleasure are to be resulted solely by p i.e. philosophising or writing, for there are countless activities that takes time or that leads to pleasure e.g. walking or reading etc.; it requires only that philosophising and writing must take time and must lead to pleasure, that is in philosophical terms, philosophising and writing are sufficient conditions for time passed and pleasure. While all of these seem to be perfectly in line with intuition, peculiarity emerges when this is applied to scientific inquiry and empirical knowledge.

If for example one believes that all swans are white, then in the construct of propositional logic, it is translated as if it is a swan then it is white i.e. if p then q. By contraposition then it follows that if it is not white then it is not a swan i.e. if not-q then not-p. Now if one is set to prove this statement by empirical observation, one may inquire into all swans one by one to verify that they are indeed white until one exhausts all empirically observable swans, with which common understanding agrees despite overtaxing as a valid way of inquiry and each one of these white swan observed is deemed as a valid evidence for the proposition. By however virtue of contraposition, the statement of interest is logically the same as if it is not white then it is not a swan, which means the proof for all swans are white can alternatively be proceeded by inquiring into non-white objects and verifying that they are indeed not swan, which is strange at best, and is nonsense at worst if one is to consider that each non-white and not-swan object observed e.g. a red snapper as evidence for the proposition that all swans are white.

Peculiar this may seem, and notwithstanding that the natural response for most may be to reject such assertion on a suspected problem with contraposition or even with propositional logic in part or in whole for it leads to absurdum, the issue in this case lies nonetheless in the everyday language for describing and understanding scientific inquiry and empirical knowledge. Provided again that the accepted way of inquiry and the valid evidence for the hypothesis that all swans are white, even if one has inspected all empirically observable swans to exhaustion, there exists still a possibility that there will be born a black swan at a future time that defeats the hypothesis, not to mention that physically inspecting all observable swans is improbable if not impossible. Rather than a way of proving a hypothesis as a candidate for empirical knowledge, a more proper way of denoting this way of inquiry would be a failed attempt to disprove the hypothesis, that is, of all the swans observed, none has emerged to be non-white and has thus yet to render the hypothesis false. Each observed instance of white swan would then be, rather than a proof for the trueness of the hypothesis, an occurrence that did not call for its rejection. In this light, it makes perfect sense in contraposition that a non-white and not-swan object e.g. a red snapper contributes to the inquiry, for it fails to render the hypothesis false to the same degree as an instance of a white swan. This renewed understanding of empirical knowledge and scientific inquiry is precisely the ground for the notion of falsifiability that distinguishes science from pseudoscience, suggested by Karl Popper, one of the greatest philosophers of science of the 20th century, in the Logic of Scientific Discovery, that rests any scientific claim on the brink of rejection should a counter observation emerge, for otherwise as one could imagine there is nothing that demarcates science from the rest of the other beliefs.

Notwithstanding that the universal validity of falsifiability on all empirical sciences is still in debate for otherwise an assertion without dispute is not of philosophical worth, it illustrates one of the many instances in which the everyday language and the common understanding could be the cause of confusion and could stand in the way of knowledge. If by reductio ad absurdum that the question is not of question, then it is the everyday answer that needs to be questioned.