Substance and Individuation in Leibniz

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In addition to the historical influences of Aristotelianism are broadly theoretical constraints on the problem of individuation, variously implicit and explicit in medieval accounts of individuation. We note here three sorts of consideration that may constrain the search for a blueprint. First, in approaching an account of individuation, one may already be convinced of certain facts about the metaphysical structure of substances for reasons connected with other metaphysical or theological Here we set aside the possibility of construing substance as a mass noun: the issue will be discussed briefly in the environment of chapter.

Here using principle principium in the scholastic sense of origin or foundation or source, as inherited largely from Aristotles arche in the Metaphysics cf. Having announced early in Disputatio that he intends in that work to treat of the principle of the individual G , : MLI , Leibniz goes on to note that principle has been understood in several ways Principii quoque vox notat tum cognescendi principium, tum essendi. Essendi internum et externum opting himself in the Disputatio to avoid any epistemological or external glosses on a principle of individuation.

That accidents are individuated by their substances was a common view of the middle scholastics cf. Avicenna, Metaphysica v, c. Thomas , arguably the last of the major scholastics, who follows Aquinas in individuating accidents by the subjects in which they inhere S. Thomae certissimum est individuationem acidentium sumi a subjecto, in quo sunt, seu in ordina ad illud: Cursus philosophicus.

Reiser, p. Gracia and Kronin, John of St. Thomas, p. This view was denied by some nominalists, Suarez later among them. A scholastic philosopher may, for example, have already convinced himself of the need to distinguish the matter of a substance from the substance itself, given a need to account for substantial change a substances coming-to-be or going-out-of existence, as opposed to mere alteration. Yet, more obviously, a scholastic may well insist on distinguishing the proper accidents of a thing from other constituents of persisting individuals, as a means of explaining the diachronic identity of a substance through change alteration.

Further, that philosopher may already be convinced of the need to distinguish the essence of a created thing which would exist whether or not God chose to bring the thing into being and the existence of the thing, providing the differentia between the states of affairs of Gods actualizing, and Gods not actualizing, the essence in question. In such ways, the results of an inquiry into generation, corruption, creation, annihilation, diachronic change, and still other topics may already set our scholastic philosopher on the way toward a particular account of the metaphysical structure of substances.

A distinct if related constraint would consist of various putative conceptual truths about substances as individuals of what may be regarded as the intension of individual substances. Consider the notion of individuality itselfthe notion of what it is to be an individual as opposed to being something else. Most of the intensional elements in terms of which that notion was variously analyzed by scholastic writers survive in some form or other to this day: Impredicability on which condition an individual substance is not said of does not inhere in Similarly, the modern philosopher may be convinced of a real distinction between, say, a statue and the hunk of matter that makes it up on account of the fact that the hunk of matter existed prior to the statue.

Setting artifacts aside, the distinction itself here at issue was subject to various qualifications.

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The broad scholastic agreement with Aristotle on genuine substantial change was tempered by a theology of ex nihilo creation: where Aristotle had claimed that coming into being and ceasing to be in the absence of some persisting substratum was unintelligible, medievals viewed the Aristotelian requirement as at best correct for the realm of creaturely causes only. Leibniz follows the medievals here, though in the context of explaining how the mechanistic view of alteration via motion is consistent with Aristotelianism, the early Leibniz is cautious to remind us that numerically the same change may be the generation of one being and the alteration of another G ,: L citing among others the case of rusting iron from Hookes Micrographia.

Or, more carefully, the intension of individual simpliciter, as this terminology has been introduced and deployed by J. Gracia in his Introduction, pp.

Substance and Individuation in Leibniz

Gracia, Individuation in Scholasticism. The intension of individual comes closest to what, in our reading of of the Disputatio, Leibniz isolates as the sense of individual applied in conceptu or formaliter: his announced purpose is to investigate that real principle of individuals here applied in re or fundamentaliter which would serve as the foundation for the formal notion in the mind of individual. G ,: MLI. Whether deployed singly or in some combination, the role of such notions in a broadly conceptual analysis of what it is to be an individual will constrain the search for a blueprint for individual substance s.

A third constraint will be ones sense of the paradigm cases of an individual substance, as well as ones sense of the paradigm cases of non-substance. Here the question concerns the extension of individual substance. Alongside the well-worked distinction between substance and accident, of equal importance to medieval thought on our topic was a distinction between substances that exist at the metaphysical groundfloor, so to speak, and so-called enduring things that are metaphysically second rate. This idea too will not be altogether foreign to contemporary readers: each of us will have at least an initial temptation to think of a particular cat as enjoying a place in the metaphysical scheme of things that is of a rather different order to that enjoyed by Tabix, where Tabix is the aggregate of Tabby and Felix.

With any such distinction in place between what the medievals would reckon substances per se and substances per accidens ones search for a blueprint becomes more focused, here owing to a need to account for the sort of real unity enjoyed by first-rate substances but lacked by second-rate heaps.


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In contemporary philosophy, paradigm examples of individual substances are typically offered up as just now from within our folk, workaday, conceptual scheme. Needless to say, scholastic philosophy preceding Leibniz looked as much to theology as to the scheme encoded The provenance of the distinction itself, traceable in large measure to Aristotles familiar doubts about whether heaps, parts of organisms, the elements, and so on are genuine substances e. Metaphysics , , should not be too closely wedded to its taxonomic cousin in Metaphysics , and , about what is accidentally one versus what is one by its own nature.

There, doubts about whether musical Corsicus as opposed to rational Corsicus, say is accidentally one represent concerns about proper differentia and the unity of definition. In this latter context, a bundle of sticks and an arm are alike said by Aristotle to be one by its own nature bff ; but alongside Physics ,,a and the dominant sentiment of the Metaphysics, a bundle or an arm is one in at best a Pickwickian sense.

Thanks to Patricia Curd and Martin Curd here. Insofar as one takes the existence of God as source of all reality, or a being that is both human and divine, or the transubstantiated host, to be among the deliverances of special revelation, one will reckon such information as proper input into ones search for a metaphysic of substantial individuals. Note in particular that for the scholastics it was largely nonnegotiable that some individual substances were purely spiritual, incorporeal beings: an account of individuation that only applied to corporeal substances would be at best an account of individuation of one kind of substance.

As with all approaches to a full metaphysic of substantial individuals, the blueprint approach can proceed at different levels of generality. One may be after a schematic blueprint for substance qua substance that is to say, a blueprint abstracting away from whatever is distinctive of any given particular substance and whatever is distinctive of any given particular kind of substance.

Alternatively one might seek a portfolio of blueprints one for each fundamental kind of substance taken to exist, where now each blueprint would abstract away from those features distinctive of any given particular substance. Yet again, one may be after a metaphysical blueprint for particular individuals where the concern is not so much, say, a special fascination with what makes Socrates Socrates, but rather a concern to provide some recipe for a blueprint highlighting what it is, for any individual x, that makes x the very individual it is.

Prima facie, then, one confronts at least three levels of blueprint approach, corresponding to the questions What is it for a thing to be an individual substance? What is it for a thing to be the kind of substance that it is? And here arises a fundamental methodological issue for approaching any metaphysic of individuation namely where to begin. Does one start with the most general question and then descend in order of generality? In the case of the blueprint approach, this would amount to an initial search for the most abstract blueprint of substance qua substance, followed then by some filling-in of detail according to kinds or else by some recipe for filling in detail according to kinds followed, finally, by filling in detail or providing a recipe for doing so according to the particular individual substance in question.

Alternatively does one begin at a lower level, perhaps ascending later to one of the more general questions? Thus one might begin at the level of kind, adding individual differentia to each kind-blueprint to descend, abstracting what is com-. It may of course arise that one of these levels of questioning presents itself as less coherent or otherwise less promising than the others. One may well reject the most abstract level, for example, owing to a conviction that there is nothing very useful to say concerning the metaphysical common ground between different kinds of individual substances.

Thus it may emerge that kind A and kind B enjoy the intension of individual substance via such different metaphysical routes that there is nothing much to offer by way of a general blueprint. Here perhaps one thinks most naturally of Aquinass different accounts for compound [material] substances and angels. The modal approach Questions about the nature of individual substances quite clearly have either an explicit or a tacit modal dimension to them.

The question What is the nature of an individual substance? Accordingly, one may fairly gloss the search for principles of individuation as the search for a certain class of necessary truths; in particular one is seeking the most fundamental truths de re about substances. In this connection, note that an assumption common to most medieval and contemporary thinkers alike is that substances are essentially substances: nothing is actually a substance but possibly a non-substance.

Similarly, discussions at the level of kinds, to the extent that they are central to individuation, will concern kinds that are essential to substances. And, quite obviously, questions at the very lowest level of generality concerned with, say, what makes this individual say, Socrates the very individual it is are about de re necessities, it being assumed in such contexts that Socrates could not fail to be identical with Socrates.

A natural place to look for answers to de re modal questions relevant to our topic will be to the intension of the general terms substance and individual, to the intension of kind sortals, and to the intension of singular terms names.

17th Century Theories of Substance | Internet Encyclopedia of Philosophy

One might object here that truths associated with intension must be de dicto. But illuminating de dicto truths of say the See for example De ente et essentia. It was for example explicitly appealed to by Aquinas, notably in the discussion of divine foreknowledge in Summa contra gentiles. Nevertheless it is a mistake to suppose that the modal approach itself amounts to no more than a conceptual analysis of intensions. Prior to converting any de dicto necessities into de re truths, for example, one must form some judgment concerning which truths are de re necessary a judgment not settled by the de dicto necessities themselves.

Moreover, it is unclear why some sort of high-level theory could not in any case supplement whatever modal truths are delivered by the intensions alone. Recall, inter alia, that from Aristotle to Kripke, metaphysicians have taken seriously the idea that a scientific, a posteriori inquiry into the nature of things may reveal de re modal truths altogether foreign to our pre-theoretic understanding of things.

Putting the point now in scholastic terms: the real definition of thing or kind that places it in a taxonomic order of being may look nothing at all like the nominal definition that expresses the understanding that comes first in order of knowing. In adopting what we might call the simple modal approach as so far conceived, one views the metaphysics of individuation as part of a high-level theory whereby one supplements the de dicto modal truths delivered by the intensions of relevant terms.

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The connection between the simple modal strategy and the blueprint approach is a mixed one. Some of the modal addenda about individual substances may implicitly say something about the contribution of its structural components to its The need for such supplementation becomes particularly pressing to the extent that one doubts that a proper name or a term for a kind has much by way of an intension. Contemporary doubts urged by Kripke in, for example, Naming and Necessity arise from the recognition that many singular and natural-kind terms secure their reference by reference-fixers that are contingently true of their referents rather than by connotations that are uniquely and necessarily true of them.

One cannot, however, straightforwardly equate the project of providing a theory of individuation for things with that of providing a real definition for them.