#doxastic logic

No, this is not about philosophers behaving like unruly children (although at times, they can). Incorrigibility is a term that refers to "a property of a philosophical proposition, which implies that it is necessarily true simply by virtue of being believed. A common example of such a proposition is René Descartes' "cogito ergo sum" ("I think, therefore I am).“

Symbolic reference cannot ‘break the fourth wall’ - meaning that whatever words or gestures that we use to communicate about something can only refer to things figuratively. This sentence, for example, can’t address you the reader in a literal sense. I can write “Hey you! Yes, you! Stand still laddie!” but it is not really possible for these words to address anyone literally. The same words could come out of a random letter generator, or they could have been written by someone who died before the reader was born. The entire premise that language is meaningful depends on an audience who is able to derive meaning from interpreting messages from that language.

Doxastic logic is a type of modal logic which uses the terms ‘belief’ and ‘proposition’ to formalize, and really digitize the possible relations of belief and truth, including beliefs about beliefs, possible beliefs about possible truths, etc.

Accurate reasoner: An accurate reasoner never believes any false proposition.

Bp→p

Normal reasoner: A normal reasoner is one who, while believing p, also believes he or she believes p.

Bp→BBp

My beef with modal logic is that while it gives us an informative language to talk about mental states, it cannot access the quality of the state itself, and therefore is misguided when applied to the deeper conditions of consciousness itself. There is no modal symbol for ‘wakes up’ or ‘loses consciousness’ because those conditions affect the entire phenomenon from which reason can arise rather than a function of reasoning.

When viewed from an ontological perspective, I think that we would have to consider a proposition to be a kind of belief, even if it is a belief that is assumed to be shared by everyone or every thing. The proposition that “Fire is relatively hot” is itself only a message which is communicated through language. Before we can agree that “p = fire is relatively hot“, we must first agree that

p is literally a sensation: p is seen as a group of adjacent graphic squiggles, or heard as a phonic utterance. p is actually s(’p’), since acoustic vibrations or optical contrasts can’t literally be propositions about fire.

s(’p’) is subconsciously identified as a message (rather than, say decorative art) within our cognitive sense. We think that our sense of ‘p’ means something that we can understand. p is promoted to i(s(’p’)).

i(s(’p’)) is consciously understood as a particular message with a particular meaning. This promotion of i(s(’p’)) to the executive level of sense, where we personally evaluate and act on the contents of messages would be the third nesting of sense u(i(s(’p’))). It is not only cognitive, but articulated on the personal level of cognition.

It should be noted that deconstructing the foundation of classical logic this way is intentional. Logic begins with a philosophical assumption of semantic realism. This is ironic really, especially in doxastic logic when we are concerned with the consistency of reasoning, to being with the assumption of a reasonable universe as a given. p is simply p. A proposition is given, and in that presentation of the proposition, truth is considered (wait for it...) incorrigible. If we want to say that p is false, we would just say ‘not p’. Truth and proposition are equivalent because we are assuming an unquestionable solidity to this fundamental logical unit - a unit which represents facts as they simply are, unconditioned, present without any dependence on ontology. Logic of this sort can be used to diagram systems which remind us of physics or of thinking and communicating, but they begin with the fact of coherence and sense already in place.

By inverting this previously unexamined axiom, I hope to reveal the myth of the logical ‘given’ and replace it with the more skeptical, honest view that logic is derived from sense. Just as a child depends on developing sensorimotor skills prior to developing abstract reasoning skills, all logic derives from deeper levels of sensory experience. Even computer logic relies on the sense of a physical mechanism...the capacity for some substance to detect and project some tangible role in a tangible chain reaction. Abstract logic is always an intangible map that is projected psychologically onto such a tangibly experienced territory. It is this tangibility, this concretely participatory aesthetic spectacle which is doing the work and which can appreciate the benefits of having accomplished it.