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The Leibniz Review:
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32
Filippo Costantini
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This paper deals with the metaphysics of the notion of quantity in the philosophy of Leibniz, and its aim is to defend the following bi-conditional: for any object x, x has a certain quantity if and only if x has a (metaphysical) limit or a bound. The direction from left to right is justified in §3, while in §4 I develop an argument to justify the direction from right to left. Since the bi-conditional links the metaphysical notion of limit to the mathematical notion of quantity (and in this way it links Leibniz’s metaphysics with his conception of Mathesis Universalis), it allows the use of metaphysics to clarify the features of the mathematical notion of quantity. This task is accomplished in §5 and §6. Finally, §7 discusses a possible objection.
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The Leibniz Review:
Volume >
32
Richard T. W. Arthur
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In these remarks on Ohad Nachtomy’s account of Leibniz’s philosophy of the infinite in his recent book, Living Mirrors, I focus on his suggestion that living creatures be interpreted as exemplifying the second of the three degrees of infinity that Leibniz articulates in 1676, as things which are infinite in their own kind. For the infinity characterizing created substances cannot be the highest degree, which is reserved by Leibniz for the divine substance, while Nachtomy sees the lowest degree as applicable only to “entia rationis such as numbers and relations”. Against this, I argue that the lowest or syncategorematic infinite applies to any multiplicity or magnitude that is greater than any assignable, so that something further can always be added; whereas the second degree applies to the divine attributes or perfections, which are maximal in that nothing further of that kind can be added.
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The Leibniz Review:
Volume >
32
Ohad Nachtomy
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4.
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The Leibniz Review:
Volume >
32
Osvaldo Ottaviani
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5.
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The Leibniz Review:
Volume >
32
Donald Rutherford
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6.
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The Leibniz Review:
Volume >
32
Donald Rutherford
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The Leibniz Review:
Volume >
32
Christian Leduc
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8.
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The Leibniz Review:
Volume >
32
Lucia Oliveri
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9.
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The Leibniz Review:
Volume >
32
Vincenzo De Risi
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10.
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The Leibniz Review:
Volume >
32
Richard T. W. Arthur
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11.
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The Leibniz Review:
Volume >
32
Ohad Nachtomy
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12.
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The Leibniz Review:
Volume >
32
Laura E. Herrera Castillo
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13.
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The Leibniz Review:
Volume >
32
Juan Garcia
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14.
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The Leibniz Review:
Volume >
32
Ursula Goldenbaum
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15.
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The Leibniz Review:
Volume >
32
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16.
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The Leibniz Review:
Volume >
32
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17.
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The Leibniz Review:
Volume >
32
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18.
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The Leibniz Review:
Volume >
31
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19.
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The Leibniz Review:
Volume >
31
Daniel Garber
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20.
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The Leibniz Review:
Volume >
31
Donald Rutherford
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Leibniz denies that the actual world possesses the per se unity of a substance. Instead, he seems to hold, the world is limited to the mind-dependent unity of an aggregate. Against this answer, criticized by Kant in his Inaugural Dissertation, I argue that for Leibniz the unity of the actual world is not grounded simply in God’s perception of relations among created substances but in the common dependence of those substances on a unitary cause. First, the actual world is one because every created substance is continuously dependent on God for its perfection. Without being the soul of the world, God is an emanative cause through which the created world is unified. Second, every substance is a unique “concentration” of an ideal world that is God’s model for creation. Consequently, while extensionally many, created substances are versions of the same one world chosen by God for creation.
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