A proposition is an assertion, a statement; but more broadly, it is any intentional connection. While a statement asserts a fact, the concept of proposition (here proposed) more generally includes assertions which are non-verbal-- for instance, acts of cognition. Thus "sugar tastes good" is a proposition whether we mean a statement in language, a thought, or the pre-verbal neuro-chemical response to certain soluble crystalline carbohydrates. A proposition is digital because it asserts a judgment or decision-- which is essentially binary (being either true or false)-- if only to assign something to a category.
Propositions are intentional because they are always proposed by an agent with purposes of its own. Propositions about structure, for instance, may reflect the interests and mentation of the agent proposing the parts involved.
The function of dualistic or digital thinking is to facilitate decisive judgment, to promote a clear-cut unification behind action. Its disadvantage is that it leads to an artificial simplicity unable to model the complexity of the real world. A proposition not only proposes the fact which it asserts, but also disposes of the alternative facts it ignores. This, of course, is its job. But there are situations in which it might be desirable to keep access to discarded information. There is always a complement or shadow cast by what has been defined into being. There is an antithesis to every thesis. Each proposition leaves out something which could nevertheless have a real and perilous influence over us.
Digitalness is a basic quality of the mental-- that is, of intentionally defined constructs: something either exists or does not, either falls into a given category or does not, is either true or false. The physical, however, is basically analog (at least on the macroscopic scale) in the sense that nothing is truly either/or, but always in between. A proposition maximizes certainty if we believe it can only be true or false. However, like the digital clock, thinking can create uncertainty if we believe the situation can be perceived more finely or be qualified by other relevant information.
Intentional constructs are indeterminate, in the sense that it is pointless to ask how many times Juliet sneezed in the year before she met Romeo, because such details are not included in Shakespeare's script. Juliet, being an intentional creation rather than a real person, is sparsely defined. If she ever sneezes at all, it is only at the times indicated in the play. If she seems to come to life for us as more than a cardboard character or a mere outline, it is because her author, and the skilled actresses who render her part, have sensitively exploited the ways in which the audience fills in her silhouette with their own feelings and imagination.
Explanation plays a similar interpretive role in science. A mathematical theory is a script for the behavior of matter. It does not of itself promise to make the "characters" come to life as comprehensible in terms of everyday experience. It must be filled in with images and metaphors borrowed from the conceptual repertory of the lay audience-- for example, the model of the atom as a miniature solar system.
A cognitive system has its own properties as a self-contained system of propositions. It rides on the analog world in the way that a drama, with its own sort of reality, rides on the primary reality of material stage, actors and props. This metaphor ultimately fails, however, because within life there is no closing of the fiction with a return to a primary reality-- only in death. In the theatre, the fiction is interpreted in terms of the real experience of actors and audience jointly. In cognition, it is the other way around-- reality is interpreted through the fictions of the mind. Prisoners within the play of life are obliged to project the world of their script into the unknown reality offstage.
Thought, and cognition in general, are partial-- in the dual sense of the word: mind can never grasp the totality of a situation, and what it does grasp by nature expresses its biases. Reality, on the other hand, appears in principle unfathomable, inexhaustible by mind, uncontainable by any formalism. Formal knowledge is a game played according to certain rules, with defined payoffs. The game may serve as a metaphor of reality, but it is not reality itself. The models of science bear a similar relationship to reality as do perceptual models. Like perception, there is always something which thought ignores. The mind has a tendency to deal with the residue that does not fit into its representational matrix as King Procrustes accommodated guests who were too long for his standard bed. Thought likes to derive everything from some basic source of axioms-- be it the Bible, the profit motive, or a scientific paradigm. Justifications then grow elaborate and spurious in the measure that more effort is required to force reality into the preconceived mold. But the remainder that does not fit returns to haunt its creators sooner or later in the ongoing confrontation with reality. It might be personal crisis, or political action by those the established regime has oppressed, or resistance from Nature to technological control.