SCIENTIFIC TRUTH: METAPHYSICAL OR PROGRAMMATIC?

The claim for the viability of scientific truth could also be traced to mathematical Platonism. This aspect of Platonism is a metaphysical view that there are mathematical objects and they are independent of intelligent agents and their language, thought, and practices. It suggests that the natural world is made up of mathematical objects. They exist in this manner independent of their perception by human beings. Their nature has been made in mathematical forms because the ´Supreme Intellect´ who made them thinks mathematically and conceives of physical relations mathematically. This perception of physical reality defined the mathematical physics of Galileo and Kepler, which affirms that mathematical relations and quantities are really part of nature itself.

This position has also been identified as Pythagorean.³²⁷

The brain behind the formulation of this kind of Platonism as we now know it is Gottlob Frege, who in his Foundations of Arithmetic³²⁸ maintained that the language of

325H. Floris Cohen, The Scientific Revolution: A Historiographical Inquiry, p. 512

326 Ibid., p. 465

327Rupert Hall, The Revolution in Science 1500-1750, p.286

328See Frege, G. The Foundations of Arithmetic. Trans. J L Austin (Oxford: Blackwell, 1959)

mathematics purports to refer to and quantify over abstract mathematical objects.

Accordingly, a great number of mathematical theorems are true. But a sentence cannot be true unless its sub-expressions succeed in doing what they purport to do. This implies that there exist abstract mathematical objects which these expressions refer to and quantify over. Just like many other forms of Platonism it should be noted that mathematical Platonism is very distinguished from the view of the historical Plato. As we have seen from the earlier illustrations from his Timaeus Plato believed at first that mathematics would be the key to Thought. However, in his Meno³²⁹, we see a Plato who has abandoned mathematical aids and embarked on his own quest with the Ideas. Such tremendous shift suggests that Plato´s famous ¨mathematical examples¨ were illustrations rather than central to his arguments.

Although Plato revered mathematics, he did so for its alleged ability to train the mind to receive the Forms (the higher dimension of the world) rather than as a means of gaining understanding of the physical world. Perhaps, this explains the bases for the difficulty in making neither completely logical description of how the mathematical-expressed-physical-regularities depended on the belief in the mechanical causes nor a comprehensive demonstration of the ways in which the mechanical philosophy was mathematized in the period of the early modern science.

It is not surprising that there was no experiment showing how Galileo´s mathematical laws of fall could be obtained in the physical world of concrete matter. Such law only pertained to ideal bodies moving in a frictionless environment. This raises doubt on whether Galilean physics was in essence addressed to the mathematical ideal or the concretely and physically real as the mechanico-corpuscularism pretends it was.

Perhaps, it could be that the nature of the scientific truth that ensues from our knowledge of the world is a programmatic one. In that case, the Galilean mathematical theory of fall becomes true and represents an objective view of moving things if all motions only take place in a frictionless environment, which we know is not feasible.

Assuming that the mathematical picture of the universe does not answer the questions that non-mathematical philosopher asked and vice versa, how could the success of the

329 M, Jane Day, Plato´s Meno in Focus (London: Routledge, 1994); See also G. M. A, Grube, Plato Five Dialogues (USA: Hackett, 2002) pp.75-80. When asked if a given triangle can be inscribed in a given circle, the geometer chose to proceed hypothetically knowing that a rigorous mathematical proof is impossible

early modern science provide the justification for the viability of scientific truth? The above discussion already shows that physico-mathematical current does not provide demonstrable description of natural processes any better than its Aristotelian counterpart on whose defeat its success hinges.

Newtonian mathematical physics and scientific truth

Steven Shapin illustrated that Isaac Newton´s The Mathematical Principles of Natural Philosophy argued convincingly that the world-machine followed laws that were mathematical in form and that could be expressed in the language of mathematics.³³⁰ His physico-mathematical approach serve to homogenise the platonic idea of mathematical construction of reality, which inspired Galileo and Kepler, with the Democritean conception of its atomic structure, which was transformed in the hands of Gassendi and Boyle. Shapin, summarised the Newtonian programme thus,

The gravitational force that bound the universe together was, to be sure, mathematically describable. It was even offered as a model for a practice whose end was the lawful characterization of the mathematical regularities of nature—laws (as Newton said) ¨deduced¨ from the actual observed behavior of bodies.³³¹

Newton asserted an indefinitely sized universe united only by the identity of its fundamental contents and laws as against the finite universe with qualitatively differentiated regions of space the Aristotelian and ancient Greek physics suggested. In this indefinitely sized universe there is no qualitative physical distinction between heavens and earth, or any of their components, such that astronomy and physics become interdependent and united because of their common subjection to geometry. This view re-echoes the perspective of mathematical Platonism about the existences of abstract mathematical objects by illustrating that all natural processes take place on a fabric of abstract time and space. In such homogenized world, abstract bodies move in an

330Steven Shapin, The Scientific Revolution, p. 61 331Ibid., p. 62-63

abstract space. Hence, a proper knowledge of such a universe becomes itself objective.

The independent existence which the mathematical Platonism assigns to mathematical objects is meant to substantiate an analogy between mathematical objects and ordinary physical objects. Just as electrons and planets exist independently of us so do numbers and sets. And just as statements about electrons and planets are made true or false by the objects with which they are concerned and these objects' perfectly objective properties, so are statements about numbers and sets.

4.2.3 MATHEMATICAL CONCEPTUALISATION AND PHYSICAL REALITY