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Before establishing his mature interpretation of infinitesimals as fictions, Gottfried Leibniz had advocated their existence as actually existing entities in the continuum. In this paper I trace the development of these early attempts, distinguishing three distinct phases in his interpretation of infinitesimals prior to his adopting a fictionalist interpretation: (i) (1669) the continuum consists of assignable points separated by unassignable gaps; (ii) (1670-71) the continuum is composed of an infinity of indivisible points, or parts smaller than any assignable, with no gaps between them; (iii) (1672- 75) a continuous line is composed not of points but of infinitely many infinitesimal lines, each of which is divisible and proportional to a generating motion at an instant (conatus). In 1676, finally, Leibniz ceased to regard infinitesimals as actual, opting instead for an interpretation of them as fictitious entities which may be used as compendia loquendi to abbreviate mathematical reasonings.

Toward the end of 1676 Leibniz met Spinoza a number of times. In one of those meetings Leibniz presented a proof of the possibility of God's existence. In his proof Leibniz presupposed that a proposition is necessarily true only if its truth is either demonstrable or self-evident and that the divine perfections are simple and affirmative qualities. I contend that Leibniz's presuppositions undermine, rather than establish, the necessary existence of 'a God of the kind in whom the pious believe'. My assessment is based upon a consideration of Leibniz's argument in the context of other early papers, works written before the "Discourse on Metaphysics" in 1686.

Reminiscing about his early views on the continuum problem in a dialogue penned in 1689,2 Leibniz recalled the period in his youth when he had enthusiastically subscribed to the "New Philosophy", embracing the composition of the continuum out of points and the doctrine that “a slower motion is one interrupted by small intervals of rest.”3 Speaking of himself through the character Lubinianus, he continues: And I indulged other dogmas of this kind, to which people are prone when they are willing to entertain every imagination, and do not notice the infinity lurking everywhere in things. But although when I became a geometer I relinquished these opinions, atoms and the vacuum held out for a long time, like certain relics in my mind rebelling against the idea of infinity; for even though I conceded that every continuum could be divided to infinity in thought, I still did not grasp that in reality there were parts in things exceeding every number, as a consequence of motion in a plenum. That “atoms and the vacuum held out for a long time” among Leibniz’s cherished views is readily confirmed by an examination of his manuscripts. One may find papers containing some measure of commitment to atomism intermittently throughout the period from 1666 to 1676; moreover, if his later memory is to be trusted, he first “gave himself over to” atomism as early as 1661.4 As for his reasons for rejecting atoms, Leibniz’s mature..

In this paper I attempt to trace the development of Gottfried Leibniz’s early thought on the status of the actually infinitely small in relation to the continuum. I argue that before he arrived at his mature interpretation of infinitesimals as fictions, he had advocated their existence as actually existing entities in the continuum. From among his early attempts on the continuum problem I distinguish four distinct phases in his interpretation of infinitesimals: (i) (1669) the continuum consists of assignable points separated by unassignable gaps; (ii) (1670-71) the continuum is composed of an infinity of indivisible points, or parts smaller than any assignable, with no gaps between them; (iii) (1672-75) a continuous line is composed not of points but of infinitely many infinitesimal lines, each of which is divisible and proportional to a generating motion at an instant (conatus); (iv) (1676 onward) infinitesimals are fictitious entities, which may be used as compendia loquendi to abbreviate mathematical reasonings; they are justifiable in terms of finite quantities taken as arbitrarily small, in such a way that the resulting error is smaller than any pre-assigned margin. Thus according to this analysis Leibniz arrived at his interpretation of infinitesimals as fictions already in 1676, and not in the 1700's in response to the controversy between Nieuwentijt and Varignon, as is often believed.

In this paper we argue for the robustness of Leibniz's commitment to the reality (but not substantiality) of body. We claim that a number of his most important metaphysical doctrines — among them, psychophysical parallelism, the harmony between efficient and final causes, the connection of all things, and the argument for the plurality of substances stemming from his solution to the continuum problem— make no sense if he is interpreted as giving an eliminative reduction of bodies to perceptions.