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Bundle theory, originated by the 18th century Scottish philosopher David Hume, is the ontology theory about objecthood in which an object consists only of a collection ( bundle) of properties, relations or tropes.
According to bundle theory, an object consists of its properties and nothing more; thus, there cannot be an object without properties and one cannot conceive of such an object. For example, when we think of an apple, we think of its properties: redness, roundness, being a type of fruit, etc. There is nothing above and beyond these properties; the apple is nothing more than the collection of its properties. In particular, there is no substance theory in which the properties are inherence.
Bundle theory has been contrasted with the ego theory of the self, which views the egoic self as a soul-like substance existing in the same manner as the corporeal self.Vestin, Amanda "Is there a 'You' in your brain?"
https://www.diva-portal.org/smash/get/diva2:1328584/FULLTEXT01.pdf
The inability to comprehend any aspect of the thing other than its properties implies, this argument maintains, that one cannot conceive of a bare particular (a substance without properties), an implication that directly opposes substance theory. The conceptual difficulty of bare particulars was illustrated by John Locke when he described a substance by itself, apart from its properties as "something, I know not what. ... The idea then we have, to which we give the general name substance, being nothing but the supposed, but unknown, support of those qualities we find existing, which we imagine cannot subsist sine re substante, without something to support them, we call that support substantia; which, according to the true import of the word, is, in plain English, standing under or upholding."John Locke: An essay concerning human understanding (1689), Chapter XXIII, Of our Complex Ideas of Substances
Whether a relation of an object is one of its properties may complicate such an argument. However, the argument concludes that the conceptual challenge of bare particulars leaves a bundle of properties and nothing more as the only possible conception of an object, thus justifying bundle theory.
Critics question how bundle theory accounts for the properties' (the togetherness relation between those properties) without an underlying substance. Critics also question how any two given properties are determined to be properties of the same object if there is no substance in which they both inhere. This argument is done away with if one considers spatio-temporal location to be a property as well.
Traditional bundle theory explains the compresence of properties by defining an object as a collection of properties bound together. Thus, different combinations of properties and relations produce different objects. Redness and juiciness, for example, may be found together on top of the table because they are part of a bundle of properties located on the table, one of which is the "looks like an apple" property.
By contrast, substance theory explains the compresence of properties by asserting that the properties are found together because it is the substance that has those properties. In substance theory, a substance is the thing in which properties inhere. For example, redness and juiciness are found on top of the table because redness and juiciness inhere in an apple, making the apple red and juicy.
The bundle theory of substance explains compresence. Specifically, it maintains that properties' compresence itself engenders a substance. Thus, it determines substancehood empirically by the togetherness of properties rather than by a bare particular or by any other non-empirical underlying strata. The bundle theory of substance thus rejects the substance theories of Aristotle, Descartes, Leibniz, and more recently, J. P. Moreland, Jia Hou, Joseph Bridgman, Quentin Smith, and others.
He goes on to explain what is meant by each of these seven assertions, but briefly in a subsequent commentary he explains that the conventions of the world do not exist essentially when closely analyzed, but exist only through being taken for granted, without being subject to scrutiny that searches for an essence within them.
Another view of the Buddhist theory of the self, especially in early Buddhism, is that the Buddhist theory is essentially an eliminativist theory. According to this understanding, the self can not be reduced to a bundle because there is nothing that answers to the concept of a self. Consequently, the idea of a self must be eliminated.James Giles, No Self to be Found: The Search for Personal Identity, University Press of America, 1997.
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