Return to Logic: the Case for Paraconsistent Logic

Standard logic is explosive, that is, anything follows from a true contradiction. This is a semantic consequence of the fact that standard logic does not admit of true contradictions. However, if a logic admits of true contradictions and therefore does not have explosiveness as a semantic consequence, one can avoid explosiveness and have a paraconsistent logic. The question remains: Is there a true contradiction?

There is. Each person is an individual, that is, is unique, particularly in their perspective. However, the very fact that this is true for every person creates a paradox: in our uniqueness, we are all the same. This is a paradox, a contradiction, but is it true? Can two persons share a perspective? If so, then differences could only come through the constitution of the persons. Is every person internally unique? Even if two persons start out as internally exactly similar and share a perspective, is it inevitable that one of them will change, thus making them both unique?

All that aside, it remains the case that if this contradiction is true, then the justification for explosiveness fails, thus making the logic paraconsistent. This means that not anything follows from a contradiction, so some standard theorems also fail; one of those that fails is "P -> (~P -> Q)".

Meta-Ethics 2: Formulations of the Categorical Imperative

Ones intention should be to conform to the moral law, otherwise known as the categorical imperative (CI). It is the most basic principle against which all actions are judged on an ethical basis. An agent is obligated to follow the moral law, which is to say that should be rationally autonomous, which requires that it has free will; however, a person is a being which must operate under the presumption that it has free will: persons are also bound by the moral law.

The Humanity Formulation of the CI or "to treat other person as end-in-themselves, not merely as a means to your own ends" is logically equivalent to three other statements. Kant's original formulation of the CI is "Act only in accordance with that maxim through which you can at the same time consistently will that it become <i>a universal law of nature for all persons</i>" is is the first; it sees persons as potential legislators of universal laws. Laws of nature must be consistent, so in order to graduate from potential legislator to actual legislator, a person must will only what is right.

The Autonomy Formulation of the CI or "the Idea of the will of every rational being as a will that legislates universal law" obligates persons to act as though they were actual legislators of universal law. It sees persons as citizens, that is, persons with the right of franchise which is the right to vote. Voting is a fundamental right of all persons, but one should only vote for what is ethically right. To do otherwise is to vote for an exception for some person, which creates a legal privilege not an ethical right.

"To act as though one were a subject in the Kingdom of Ends" is another formulation of the categorical imperative; unlike the the Autonomy Formulation, the Kingdom of Ends Formulation focuses on persons not as citizens, but as subjects in the Kingdom of Ends. It introduces a social aspect to the CI; if a legislator makes an exception for him- or herself, then it is, by definition, a legal privilege, not an ethical right. This highlights the distinction between law and ethics; neither law nor ethics logically implies the other one, but they are deontologically related: law should enforce only ethical actions.

Meta-Ethics: Grounding Morality

Agency is rational autonomy, which is the control of the self by the intellect. Without agency, one is not responsible for ones actions, which means that one is not an ethical being. The fundamental duty of all ethical beings is to respect agency, not merely ones own agency (as that is merely respecting oneself), but the agency of all agents. This is what Kant called the categorical imperative, which means that unlike so-called hypothetical imperatives, it is not done for the sake of something else. That is, one ought to respect agency not because of any positive consequences it could have for oneself, but simply because it is the right thing to do. To respect somebody means to not use them as merely means to your own ends, but to treat them as ends-in-themselves; this is the ground of morality.

Knowledge: Internal and External

Internal knowledge is independent of any particular external experience; it uses intellectual intuition to abstract necessary relationships and patterns between possibilities. Primarily, this includes knowledge of ones own existence, but extends to all logical truths as well; the truths of the logic used in analyzing and synthesizing possibilities ought to be accepted as necessarily true, otherwise we are believing inconsistently. Knowledge of ones own existence is, as Descartes showed us, provable (at least to oneself): I think therefore I am; perhaps there are at least two levels of being, since it is also true are "I have an experience therefore I am" and "I feel therefore I am". Importantly, knowledge of ones own existence implies one has knowledge that an external world exists (although ones experiences of it might be inaccurate); that is, in order to distinguish oneself as an individual, one must draw a distinction between oneself and the external world. In other words, there is no I without a not-I.

Since external experience can be inaccurate, external knowledge must have a coherentist, fallibilistic nature; that is, what justifies a belief about an external experience is that it coheres with other external experiences with the caveat that it can be inaccurate and may be superseded by more coherent experiences that have contradictory implications. At the foundation of external knowledge lies sensuous intuition, which is our way of gathering information about the external world; sensuous intuition exists in multiple modalities: auditory, visual, tactile, olfactory, gustatory, kinesthetic, etc.. Each modality provides fallible information about the world through its medium; through apperception, we unify the various sensory modalities into an experience, upon which we base our empirical beliefs.