Archive for the ‘Philosophy’ Category

Based on several years of research/thinking/lit review, I’ve come up with some opinions on the subject of logic et cetera. Since it’s mostly been myself talking to eccentric though lovable phil profs and a lot of old dead white men, I’d like to ask you, dear reader, for any thoughts or opinions on the final paragraph of mind-altering questions (the first few paragraphs intended to provide definitions and context):

Logic is defined here as the study of valid demonstration and inference, or the principles of correct reasoning. It concerns the structure of statements and arguments, and rules of inference in both formal systems and natural language. Formal logical systems consist of:

1. a formal language, and
2. a deductive system (or deductive apparatus) which consists of a set of inference rules and/or axioms.

Formal systems derive statements from prior statements in the system. A derived statement is called a theorem, whereas axioms are statements that are assumed to be true without proof (self-evidence).

Some of the desired properties possible for logical systems are: consistency (none of the system’s theorems contradict one another), soundness (the system’s rules of proof will never allow a false inference from a true premise), and completeness (that there are no true sentences in the system that cannot be proved in the system). Not all systems achieve all three virtues (e.g. Godel’s incompleteness theorems state no useful system of arithmetic can be both consistent and complete).

There are many types of logic – first-order logic, second-order logic, informal logic, interpretability logic, intuitionistic logic, quantum logic, categorical logic, clocked logic, linear logic, college logic, combinatorial logic, affine logic, Boolean logic, ternary logic, monotic logic, non-monotic logic, multivalued logic, paraconsistent logic, non-Aristotelian logic, relevant logic, temporal logic, sequential logic, scholastic logic, term logic — the list goes on. There are local and global logics, which hold different axioms or rules of inference. Despite its long history, the nature of logic is obscured by a number of disturbing questions that have yet to be satisfactorily answered.

Is there a single true logic, or are many logics equally correct? Is it possible to have genuine disagreements about the correctness of a logical principle? What makes a logical constant? What are the proper accounts of logical concepts (e.g. logical consequence, quantification, etc)? What is the scope of logic (e.g. does it encompass mathematics)? Is logic a matter of convention? What is the nature of logical necessity? What is the relationship between the verbal rules of logic and the mental ability to reason logically? Is logic subject to empirical revision?