Sunday, May 30, 2010

Foundation 1 - Equivalence and difference.

The modern Cartesian Meditator

To consider the nature of the world requires first that the Cartesian meditator, in pursuit of rigor and foundation, consider the preconditions for thinking about anything. This accords with Quine (1969) that one should base one’s knowledge on psychology, presumably cognitive psychology, to assure us that what we think we know is at least something for which there is some mental state capable of drawing well reasoned beliefs.

Before you go further, you need to begin at the beginning.

A challenge to Descartes’ epistemology (meaning theory of knowledge) and hence Descartes’ goal of a sturdy ontology (meaning sturdy description of the world) is Hume’s assertion that all ideas come from impressions. If true, then one might ask Descartes where he gains a basis for thinking about anything from an internalist perspective, for all that one thinks of originated in impressions alone yet is simultaneously subject to doubt. Hence even the contemplation of particulars that might be doubted would leave one in a position that no distinction could be made between anything and anything else with any certainty. By this gauge, Descartes’ meditator could mistake one’s spouse for one’s hat (see Sacks 1985).

Hume said that to refute him one need only provide an idea that does not come from impressions. I will argue that the ideas of equivalence and, by extension, difference (inequivalence) are independent of impressions. These ideas must be inherent within humankind and any sentient being for any impression to become an idea. This will provide the initial step toward a Cartesian ontology, although expanding this into a rich ontology is outside the scope of this section of the blog.

Refuting Hume is of little importance. However, in showing that the Copy Principle itself is dependent on recognising equivalence and difference, and that this is innate, provides a foundation for epistemology, for these associated ideas are at the base of well-founded knowledge. Without them we are bereft of the capacity to think, and indeed bereft of any mental objects that might found a world model of any kind at all. That is, ideas of equivalence and difference are the foundations upon which all that one can know, and how one might go about knowing it, are built.

Foundations of thought

In conformity with Quine’s wishes, I begin this area of inquiry with the view of cognitive psychology, that (Kuhn 1991, p. 6):

Thinking entails the internal manipulation of symbols, and as a means of understanding thinking it is therefore essential to understand how symbolic stimuli are attended to, encoded, and operated on.

In this context, it is when this internal manipulation suggests an inconsistency or hole (incompleteness) in an argument that one’s doubts are raised. If there is no hole, such doubt is not justified, and has no place in well reasoned discourse. One hole, identified by Descartes, is that one might be dreaming, in which case the impression itself is suspect. Consequently one cannot from the internalist perspective vest judgment in impressions received from an assumed external source over the top of rationally derived ideas; for it is the thinking that informs the meditator what is or might be true. But this would not be true if Hume (1995, p. 839) is right when he says ‘all our ideas or more feeble perceptions are copies of our impressions or more lively ones,’ for if true, there is no foundation for thought outside received impressions and all our thinking is founded on it.

This contrasts with Aristotle’s belief that another form of knowledge is accessible, a knowledge that establishes the first premise, that anchors demonstrations of other pieces of knowledge as justified truth worthy of belief (Smith 2004).
This would be the view of the Cartesian meditator also, who follows foundationalism.

From a foundationalist perspective there is initially only two ideas that do not come from impressions: the ideas of equivalence and difference. The Humean might argue that it is receiving impressions from the external world that gives one the idea of there being things that are the same and things that are different. I don’t think this is true, and will present two arguments in support of my case: an argument from priority and an argument from dependence.

The priority argument

Without the prior idea of equivalence and difference it is not possible for one to make sense of impressions. Beyond hardwired responses, such as the pain response (which is not understanding in this context) a human’s first impression is essentially meaningless because it has no point of reference, no point of difference, and, insofar as thinking entails the internal manipulation of symbols (Kuhn 1991), no meaningful mental symbol that can be used as a basis for recognition. This equates at an epistemological level to an absence of understanding about the external world. Even the notion of manipulation requires difference, for the idea of manipulating a mental symbol in isolation is as sensible as the sound of one hand clapping. The mere naming of this concept of equivalence and difference comes after its existence in the human mind (this process of naming, of course, applies to received impressions as well).

The dependence argument

Without the internal idea of equivalence, no number of presentations can convey meaning. The Copy Principle (Hume 1995) itself requires that one assign an equivalence status between externally sensed objects and internal mental symbols. Otherwise the world is an internal fiction brought from who knows where and there is no copying at all, but this reverts to the earlier argument of priority.

These priority and dependence arguments gain strength in the recognition that definitions of equivalence and inequivalence first require an internal understanding of the terms.

One might argue that ideas of sameness and difference have no value without acquaintance, but even if the meditator has no sensory input, there is self awareness. Such awareness is a sense of identity, and identity is the notion of being the same as oneself. If it is any more than this, then one must admit notions of inequivalence, so the counterargument is thwarted. Descartes himself argued that one can be certain of one’s existence, so there is value in this directly. It remains only for the meditator to develop these ideas of self, equivalence and difference into a rich ontology populated by recognisable objects.

If these ideas are so important, why did Hume not notice them himself? As Heidegger (1969) notes, we encounter same and different so unquestioningly, the encounter itself goes unnoticed, and nothing compels us to notice it. Having noticed it, that these ideas echo the Laws of Thought goads one to explore this link further. But more importantly, it would seem that for the Cartesian meditator, the pursuit of all knowledge must be grounded in equivalence and difference.


For the Cartesian meditator there is a basis for thinking about an ontology or domain or discourse. Firstly, the meditator can know he/she exists within the ontology so has a place from which to consider it. Secondly, the meditator has an inherent idea of equivalence and difference by which the objects of the domain might be distinguished. Moreover, because ideas of equivalence and difference are epistemologically prior to all other ideas, it is on these ideas that all well-founded ontologies must be built.


Heidegger, M 1969, Identity and difference, Harper and Row, London.

Hume, D 1995, 'An enquiry concerning human understanding', in SM Cahn (ed.), Classics of western philosophy, 4 edn, Hackett Publishing Co., Indianapolis.

Kuhn, D 1991, The skills of argument, Cambridge University Press, Cambridge.

Quine, WV 1969, Ontological relativity and other essays, Columbia University Press, New York.

Sacks, O 1985, The man who mistook his wife for a hat, Summit.

Smith, R 2004, 'Aristotle's Logic', in EN Zalta (ed.), The Stanford Encyclopedia of Philosophy Fall 2004 edn,

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