If you ever find yourself forced to summarize the ideas of western philosophy in a single metaphor, then the concept of a “self-modifying filter” may be your safest bet. Observation and measurement, according to this idea, are acts of filtering. A filter has a built-in bias – it lets some elements pass through but not others – and the categories embodied in this bias are the source of features and constancies in a universe that ultimately bathes in undifferentiated and structureless flux.
In the philosophical literature, the filter-metaphor hides under the distinction between “a priori”/”deduction” and “a posteriori”/”induction”. The former involve facts that are definitional in nature, like mathematical proofs or how all bachelors are unmarried, while the latter refers to facts derived from experience. For an appreciation of just how central they are, consider the following intellectual heavyweights:
- René Descartes, of “cogito ergo sum” fame, is known as a “rationalist” in how he emphasized the importance of pre-formed knowledge in the acquisition of new one.
- George Berkeley, in the early 1700s, advocated a view in which external reality did not exist unless perceived, and this stimulated different versions of “idealism”, according to which we actively create our world through mind-dependent categories.
- David Hume, writing a little bit later, pondered in his Treatise of Human Nature how sense impressions are separate events in the mind, with causal relationships not directly perceived but projected upon them. His “empiricist” brand is known for rejecting a priori principles altogether.
- Immanuel Kant’s prescient “Critique of Pure Reason” from 1781 is about the mind’s a priori knowledge of space and time organizes our sensations.
- Noam Chomsky entered the academic consciousness in the 1960s with his idea that babies are born with knowledge about how to transform linguistic expressions, and that their mother tongue is merely a parameter to fine-adjust this innate grammar.
The 20th century brought us more sophisticated tools to study the learning process in detail, and upon doing this, the deduction-induction dichotomy tends to work best if we consider it as a snapshot in time of what is actually a continuous feedback-loop. From a psychological viewpoint, a priori knowledge could be said to refer to the offline mental manipulations we sometimes perform on our cognitive entities to lay bare facts latent in the way our concepts are stored. For example, if we, via environmental interactions, form the category of “Men” with the core property of being mortal, and then proceed to categorize Socrates as a man, then the mortality associated with men will also pertain to Socrates. If Socrates turns out to be immortal, it becomes a matter of either adjusting the category properties, or brushing it over.
The most natural way to think of a filter is as a passive separator, but there is nothing to prevent us from reversing figure and ground and instead conceptualize the filter as an active inquirer. If so, the bias can be thought of as a hypothesis that the filter asks the impinging dynamic to feed back a response to, indicating what category it belongs to. And importantly, a filter is limitless in what categorizations it could perform. Just like how the mesh-size of a fishing net determines the size of the fish caught, and the polarity of a cell membrane determines what particles may pass, we may divide mankind into genders or ethnicities, or maybe “people who like broccoli” and “people who don’t”, and in an infinite number of other ways.
For an inquirer, the kind of hypotheses he can ask is equally limitless. There is an indefinite number of random variables whose outcome frequencies we may keep track of, of data we couldcollect, of relationships to potentially explore, but we cannot and should not, for that would undermine its very purpose. It would be equivalent to a filter that lets everything pass through and as a result accomplishes nothing – the filtrate would not possess any more structure than the dynamic in its raw form.
Data therefore are selection effects, restricted by the finite number of hypotheses we select for our inquiries. This is a very, very important point, central to most of science, because believing our hypotheses to be exhaustive of the space of all conceivable hypotheses has historically led to fallacious conclusions, on matters than span everything from the atomic to the cosmic and theological. So, before we address the more mundane matters, like statistical procedures used at our own scale of existence, we might as well start off on a grandiose note.