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The principles of contradiction and identity, as we will see, are also the foundation of demonstrations. But these principles are true because all contradictions are impossible. That is, there is no possible world in which a contradictory proposition is true. 9 An identity (whose form ‘A = A’) is also said to be true since no further reason, other than non-contradiction, can be given for its truth. 10 Therefore, a proposition is said to be necessarily true when an analysis of its terms terminates in an identical proposition or is shown to be not contradictory. This is also what it means to demonstrate a proposition in a mathematical or geometrical sense. Below, we will see an example of mathematical demonstration (2 + 2 = 4). As just stated, the principles of necessary truths are contradiction and identity. But the principle of contingent truths is the principle of sufficient reason. Stated another way, propositions whose analysis of terms does not terminate but proceeds to infinity are called contingent truths. The containment of terms never results in an identity, and thus contingent propositions cannot be demonstrated in the strict sense of necessity. Epistemologically, this means that we finite knowers can never have absolute certainty of the reason for the connection between subject and predicate (or the containment of predicate in the subject); although, through experience we can be more certain. The connection is nonetheless metaphysically guaranteed, since it is known by God, who “grasps” the connection “in one intuition” (see quotations below). For example, the proposition, “Caesar crossed the Rubicon” is true if the concept ‘crossing the Rubicon’ is contained in the concept of ‘Caesar’. This proposition is in fact true, but it is not a necessary truth because its contrary ‘Caesar did not cross the Rubicon’ is not a logical contradiction. The latter proposition is therefore logically possible, i.e., logically contingent. A most important point, however, is that not only does God see the connection, but God determines the connection. That is, the fact of Caesar having crossed the Rubicon is a truth determined by God, who nevertheless, as Leibniz insists, freely chose this predicate to be included in the concept of Caesar. These distinctions are of enormous consequence for Leibniz’s philosophy, especially for his argument for divine and human freedom, issues about which there is much debate. 11 But here we need be concerned only with clarifying the use he makes of nor false” (NE 362). 9 To be precise, Leibniz nowhere talks of “possible worlds” in reference to necessary truths. He only says that necessary truths are those whose contraries are impossible. This implies that there is no possible world in which they are true—although Leibniz does not say this. Nor does Leibniz say ‘necessary truths are true in all possible worlds’ although this is true. Here is an example of what he does say, in Corresondence with Clarke, 5 th letter sec. 10 p. 57: “Absolute and metaphysical necessity depend upon the other great principle of our reasonings, that of essences; that is, the principle of identity or contradiction: for, what is absolutely necessary, is the only possible way, and its contrary implies a contradiction.” See Margaret Wilson for the claim that Leibniz does not speak of possible worlds in reference to necessary truths. 10 This is to say that the principles of identity and contradiction are indemonstrable, as I will explain below. 11 For example, it may be thought that the distinction between necessary and contingent truths does not really work, since supposedly contingent propositions, such as “Caesar crossed the Rubicon,” really turn out to be necessary. According to the “complete concept” of a subject, if a subject lacks any one of his or her predicates, then that subject would be a different subject altogether; thus all predicates are essential (i.e., necessary) to the concept of the subject. But there is debate about whether Leibniz must be committed to the “complete concept” theory, whether it really does commit him to spinizistic necessity. Another point of controversy involves the criterion for God’s choice of the best possible world and whether the criterion 142
these distinctions in demonstrations. To this end, we should note the following passage from, “Specimen Inventorum de Admirandis Naturae Generalis Arcanis” (c. 1698). There is an essential distinction between necessary or eternal truths, and truths of fact or contingent truths; they differ from one another very much in the way that rational numbers and surds differ. For necessary truths can be reduced to identical truths, just as commensurable quantities can be reduced to a common measure; but in the case of contingent truths, as in the case of surds, the reduction proceeds to infinity and is never terminated. So the certitude and perfect reason of contingent truths is known only to God, who grasps the infinite with one intuition. (PM 75) 12 What this passage shows is that the distinction between necessary and contingent truths depends on termination of analysis. The analysis of necessary truths terminates in an identity, while the analysis of contingent truths does not terminate. However, a couple of problems with this account should be noted. It seems difficult to understand how a proposition whose reduction is never terminated could be grasped as a whole by any knower, including God. Leibniz thinks we can understand this by analogy with mathematical surds, such as pi. The ratio of the circumference to the diameter is fixed by the size of the circle. So, while the ratio is determinable with certainty, the numerical expression of this ratio never terminates. Still, we must suppose that, if there is a sufficient reason for the contingent truth, the analysis must terminate somehow. 13 Another problem is that the distinction appears to rest on degrees of knowledge; that is, necessary truths are those of which we can be certain, while contingent truths are those of entails the necessitation of God’s “choice.” Supposedly, God chooses according to some criteria of compossibility; for example, the greatest variety of things compatible with the greatest order (Monadology sec. 58); or, according to the laws of minima and maxima (De rerum originatione radicali GP VII 303). However it is that God determines the choice, it is said to be the best choice within certain required parameters. It were possible that Caesar crossed the Rubicon; but God made this possibility an actuality by making it a fact in the existent world. But God’s decision is said to depend on reasons which incline but do not necessitate (Theodicy, in passim). That is, God’s decision is always determined by a reason, but not determined by logical necessity. It would be a moral imperfection to choose otherwise, but not a logical contradiction. Therefore, contingent truths depend on God’s choice, whereas necessary truths do not depend on God’s choice. According to Leibniz, God could have made the world otherwise—although commentators dispute whether Leibniz can consistently make this claim. However, a claim which is not disputed by commentators is that God could not have made necessary truths otherwise. 12 G.7.309: “Essentiale est discrimen inter Veritates necessarias sive aeternas, et veritates facti sive contingentes, differuntque inter se propemodum ut numeri rationales et surdi. Nam veritates necessariae resolvi possunt in identicas, ut quantitates commensurabiles in communem mensuram, sed in veritatibus contingentibus, ut in numeris surdis, resolutio procedit in infinitum, nec unquam terminatur; itaque certitudo et perfecta ratio veritatum contingentium soli DEO nota est, qui infinitum uno intuitu complectitur.” 13 Leibniz also thinks that in this way he avoids both necessity and arbitrariness regarding God’s “decision” to create this world: for any contingent proposition there are reasons which incline God, in the way that a surd inclines to its resolution, without necessitating God to make a contingent proposition true. But neither is the reason arbitrary, since a reason can always be given for the decision. However, this argument by analogy with surds arguably does not prevent God’s choice from being logically necessitated. As Kenneth Seeskin claims, at some point a decision must be made; and deferring the reason endlessly would mean that the decision has no sufficient reason. Therefore, the “infinite analysis” argument for God’s freedom is faulty. See “Moral Necessity” in Leibniz: Critical Assessments. 143
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Stony Brook University The official
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Copyright by Christopher Lowell Joh
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Abstract of the Dissertation The Sc
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The more power he has, the less lic
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Section 1: Introduction............
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show, however, that pleasure and lo
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CHAPTER ONE: SUBJECTIVE RIGHT AND T
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By a plan for studies we mean a cer
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that for Leibniz the science of jur
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of these sources. In (1) the ground
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etween “fact” on one hand and
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however ‘public utility’ is def
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Grotius’ two significations of
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obligatio. That is, conceptually sp
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one’s own body; furthermore, give
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words, the sense in which God is su
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ight of war and punishment to the S
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qualities are the ground of public
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what conforms to the best or perfec
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Beginning with jus strictum or what
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proportion to contribution, this is
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of equity. 117 Nevertheless, it app
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agrees with the distinction between
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eward or fear of punishment, nor si
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eflecting God’s perfection as muc
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second degrees. As a precept of pie
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of a set of prudential instructions
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In Drafts 5 and 6 Leibniz then appl
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egulated. As we will eventually see
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advantage connected with the disadv
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To see how this passage implies pru
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establishes three important positio
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Justice must (and will always) invo
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y making the “deduction” that t
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Leibniz also seems to think that th
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[determine] the truth of propositio
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Prudence, furthermore, cannot be se
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Once again, as was to be shown, dut
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own and other good. The first defin
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of the matter. The main considerati
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of any other good, even if pleasure
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failing to recognize that pleasure
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another. Leibniz’s “epagogic”
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of right. Since right is the moral
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critical diligence to his definitio
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constant, I say, not that it may no
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mode of right have different truth
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the four types of statements of the
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accommodates this principle in the
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overcome the heart, as the Germans
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(1). “A Person is one who (2) lov
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Page 105 and 106: the Meditation Leibniz says that th
Page 107 and 108: will be tacitly understood. Because
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Page 113 and 114: However, it ought to be recognized
Page 115 and 116: CHAPTER THREE: THE MIDDLE PERIOD: I
Page 117 and 118: deductive system of natural right.
Page 119 and 120: It appears that the “modes of rig
Page 121 and 122: The just—or permitted, forbidden,
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Page 125 and 126: normative character they must be un
Page 127 and 128: Precepts of Right (Leibniz, Digest)
Page 129 and 130: This passage is quite important and
Page 131 and 132: and penalties” but rather are abl
Page 133 and 134: of the three degrees in the same te
Page 135 and 136: It is interesting that Leibniz defi
Page 137 and 138: And since charity is the habit of l
Page 139 and 140: has also influenced the prevailing
Page 141 and 142: What must not be overlooked is that
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Page 149 and 150: sacrifice our own happiness for the
Page 151 and 152: CHAPTER FOUR: LEIBNIZ’S DEMONSTRA
Page 153: terms used frequently throughout th
Page 157 and 158: It is important to state the distin
Page 159 and 160: Section 3. Demonstration in general
Page 161 and 162: that Leibniz has used for various p
Page 163 and 164: necessary truths, but are contingen
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Page 167 and 168: Another example of the difference i
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Page 171 and 172: possible; but this does not show th
Page 173 and 174: Leibniz’s argument is this: To ma
Page 175 and 176: notion of probability, which they h
Page 177 and 178: quasi-platonic essences (residing i
Page 179 and 180: arguments on innateness, we discove
Page 181 and 182: manifest proofs that they are not i
Page 183 and 184: in mathematics, the measures of rig
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Page 187 and 188: senses what joy and sorrow are. (NE
Page 189 and 190: follows where we left off on page 8
Page 191 and 192: As Leibniz has argued similarly in
Page 193 and 194: It is not quite clear what he means
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Page 201 and 202: Essais. These sources, as he says t
Page 203 and 204: Leibniz cites a number of instincts
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our passions and our present concer
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The ordinary use of the word ‘pro
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state, constitute [natural right];
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ecognizes how the senses can obscur
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proposition; rather, possessing a v
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CHAPTER SIX: MONITA AND MEDITATION:
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committing crimes with impunity. Ul
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In the science of [right], rather,
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i.e., that she is the author of her
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sufficient to establish the obligat
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This notion of “complaint” will
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It is agreed that whatever God will
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terminology, Leibniz holds that nat
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different matter, but if it [occurs
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need of help, and another who easil
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‘equality,’ considered as “co
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such a way that no one has a reason
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excused from showing benevolence to
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this. In any case, the real problem
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This means that the slave should be
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its efficient cause in the divine i
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a degree is it repugnant to reason
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external principle that compels God
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again at last to the Ciceronian for
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as equity; justice as love) were de
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CHAPTER SEVEN: NECESSITY, OBLIGATIO
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Thus in the Theodicy Leibniz uses m
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incapable of demonstrations. A scie
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Furthermore, we must not forget tha
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perceived to be the good. 24 Howeve
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Several points are notable here: Fi
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find the eternal rules of goodness
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Accordingly, the perfection of the
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an account of virtue. This shows, o
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H Hobbes, Thomas. 1651. Leviathan.
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Studia Leibniziana. Band 22. vol.2.
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Reiner, Hans. 1977. “Die Goldene
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