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    The subject of underdetermination or subdetermination of science has stimulated me ever since I began reading about philosophy of science. Pierre Duhem's The Aim and Structure of Physical Theory and W. V. O. Quine's “Two Dogmas of Empiricism” are the kind of writings that never leave the mind of the philosopher alone. They continually poke the mind sparking a philosophical reflection. Unfortunately, some academics treat these philosophical works as dogmas of faith, doing a disservice to Duhem, Quine, and to philosophy in general. On the contrary, we should question these, and we should follow their example in many ways. Only by doing this, philosophy becomes a fruitful legacy; a source of intellectual richness for future discussions.

    Another big stimulus to my philosophical research has been Edmund Husserl's phenomenological doctrine, which, contrary to what is generally expected, is deeply associated with many aspects of analytic philosophy. One cannot cease to be seduced by his doctrine, which has contributed more to twentieth century philosophy than many scholars realize, and much of his legacy still endures, completely unnoticed by analytic and continental philosophers alike.

    Philosophy of science and many aspects of husserlian phenomenology deal with two of the most important universal questions that permeate philosophy: “What is?” and “How do we know?” According to Aristotle, these questions are what have made “love of wisdom” the queen of all sciences. No wonder these are the most important questions. Aristotle says in the first sentence that appears in his Metaphysics “All men by nature wish to know”. That sole statement implies that there is always a wish to know something that exists but is unknown.

    Philosophy of science tries to address one specific form of knowledge, that which comes from natural science. According to many authors, “epistemology” is defined as philosophy of science. For them, there is no difference between these disciplines.¹ The only knowledge there is for many of them is scientific knowledge.

    Husserl's and Frege's reading, as well as reflections on mathematics and logic have made me think otherwise. That conception of epistemology as philosophy of science is too narrow. It is difficult to say that mathematics and logic are just pure tautologies and that many of the most complex theorems proved in both fields are simply “nothing new”. On the contrary, historically, philosophy has always depended on both fields. Their use has made the difference between sophists and philosophers. Examples of rigor are Socrates' mayeuctic, Plato's dialectics, Aristotle's Organon, Descartes' Meditations, Kant's Critique of Pure Reason, Frege's The Foundations of Arithmetic, or Husserl's Logical Investigations. The most fascinating of Plato's works involve his thinking on mathematical entities, like his beautiful and difficult work Timaeus. We can describe Aristotle's Metaphysics as one of the greatest gems of humanity, an example of how far logical thinking can lead a man to make important rational advances.

    Most of the rejection to mathematical and logical knowledge is due to the fact that too much attention is paid to natural-scientific knowledge. Sadder still is that such a way of thinking has led most schools and universities to restrict mathematics only to applied mathematics. They never give any importance to the wisdom of knowing mathematics in its theoretical aspect, especially as a stimulus to think. Just like philosophy and science, mathematics deserves to be learned for its own sake. The more we know about it, its axioms and theorems, the better our intellect and our culture will be. The fact that some philosophers of science and epistemologists only value the useful part of logic and mathematics has even led some of them to say that we should cut all the “useless fat” of mathematics and throw it to a waste basket.² If Bolyai, Riemann, and Lobachevsky had followed that advice, most probably science would not have advanced the way it has.

    Most philosophers forget that one of the cases used by Kant to exemplify a categorical imperative is our duty to promote culture according to our talents.³ In a society like ours, it seems that only commercial culture is valued. So what can the proof of a theorem mean to someone who just wakes up in the morning, goes to work, returns home, watches TV and goes to sleep every day? Not a single opportunity arises to enrich him or herself with the legacy of the past. As Seneca put it beautifully in his On the Brevity of Life, one could prolong life in such a wonderful way. Philosophy is a way to open the doors to new possibilities and options, without losing rationality and rigorous thinking along the way. I would not be surprised if many of the ills of society were caused precisely by a lack of love for philosophy, mathematics, and logic. In other words, society could heal itself with more “love for Wisdom”, an activity done for its own sake. Formal knowledge is as enriching as natural scientific knowledge. I agree with Peter Hilton when he said that the value of mathematics does not lie in the testing of the market, nor scientific usefulness, nor its economic value. It lies solely in itself and no more.⁴

    As a daughter of philosophy, natural science enriches itself from mathematics and logic. It is not merely a tool, but a discipline with which scientists, in the long run, learn to think rigorously about the empirical world. However, unlike formal sciences, natural sciences are full of a posteriori suppositions, hypotheses, and theories. When we look at the world, our mind already has a theory on how to interpret what it perceives, and when natural sciences confront the world, they do so from an entire theoretical body. There are hypotheses that can be wrong, not exclusively because of themselves, but because of everything they suppose. At the beginning, we saw everything through the eyes of myth. Then philosophers began seeing the world a different way, developing whole theoretical bodies or paradigms throughout history.

    The fact that we have many world-paradigms and theories, means that underdetermination exists. A phenomenon or event is not enough to state categorically that a scientific theory is true. There can be rival theories that can explain the same evidence. Since, as Husserl would say, we are talking about objects formally related to each other, and these are correlated with a formal network of theoretical statements, we have the problem of how much should we revise these theories (“fictions cum fundamento in re”) in order to account for these states-of-affairs.⁵ Very important questions on this matter arise from Duhem's and Quine's works: How far does this underdetermination go? How do changes in theoretical bodies happen? How many of these theoretical principles are rejected along the way? Why do scientists accept new ones? Why do they accept old ones again? Like philosophy, science is an endless pursuit of a certain kind of truth: the truth about the physical world and the universe.

    There is a sense that the subject of underdetermination is not irrelevant, it is very important because it covers all relevant subjects in philosophy of science: the process of conjectures and refutations, paradigm shifts, religion-science debate, the problem of demarcation, scientific research programs, among others.

    This ambitious project, which is called Underdetermination of Science is divided in two parts. Part I was written to establish the importance of formal sciences (logic and mathematics) from a platonist standpoint, and see their true relationship with natural science. It will consist in mostly presenting a viable and coherent platonist doctrine based on Husserl's own philosophy of mathematics, and will refute many of the objections to platonism. Then, some challenges by Quine and Hilary Putnam will be addressed in order to see that scientific underdetermination does not reach the formal sciences.

    Part II will examine practically all aspects that have to do with underdetermination: from an examination of how the mind constitutes experience, to the way scientific paradigms and research programs are formulated, validated and accepted within the scientific enterprise and its implications to both science and philosophy.


Footnote:

¹Bunge, 1997, p. 21; Popper, 1979, p. 108.  [Return to Text]

²Kitcher, 1988, pp. 315-316.  [Return to Text]

³Kant, 1785/1999, AK 4:422-423.  [Return to Text]

⁴Gullberg, 1997, pp. xvii-xxii.  [Return to Text]

⁵LI. Vol. I. §§23,62-63.  [Return to Text]