XA. Logic; Elements of Argument

1. Premise: A statement that (it is argued) can in combination with other premises generate a conclusion.

a. Assumption. A type of premise that is deliberately hypothetical. Implicit assumptions can be designated synthetically; otherwise explicit is the default.

e. Evidence: A type of premise that is grounded in empirical observation.

2. Conclusion: A statement that follows from certain premises. Note that conclusions can be either right or wrong.

p. Proof: A conclusion that can only be true, given the premises it is derived from.

3. Inference: The pattern of reasoning that leads from premises to conclusion. Can distinguish deductive (results must follow from premises absolutely) or inductive (can make a probabilistic argument). [Could use ‘result’ to denote conclusion from inductive analysis?]

4. Claim: An assertion that is not justified by premises. [Note that we eschew the term ‘Argument,’ as this is sometimes used synonymously with inference, and sometimes with ‘claim.’ Philosophers also use ‘argument’ to denote a set of at least two propositions that are used to achieve a conclusion.]

5. Definition.

6. Algorithms: [Not part of logical argument, but of argument more generally.]

These can be classified in terms of their internal nature or paradigm:

d. Dividing a problem into manageable pieces

e. Exhaustive: try every possible method

r. Randomizing some elements

t. Translating to a similar problem with known solution.

u. Using graphs to identify strategies for different possibilities

Other approaches to classifying algorithms can be addressed synthetically. Algorithms may be associated with logic, determinism, iteration, certain mathematical techniques, use approximations, or operate in series versus sequence. Algorithms can also be identified in terms of their field of application, their purpose, and their speed and complexity. It may prove desirable to identify certain common algorithms, perhaps with Cutter numbers.

Though we generally try to avoid subdividing any class in multiple ways, this may prove the best place to put:

s. Steps, Stages: Discrete elements of any algorithm, or indeed any well-defined process. [Note that the term ‘phase’ is avoided as this has a host of specific meanings across diverse sciences.]

7. Citation: Reference to an inference or premise from another author.

8. Other types of statement

b. Belief

h. Hypothesis

i. Implications: For public policy, individual behavior, business practice, and so on.

m. Motivation

q. Question (Guiding) [Answer is here the same as conclusion]

Note that ‘Issue,’ any topic/subject over which people disagree, is captured under PO.

A note on the term ‘Axiom’: There appear to be several key axioms for each of several fields in mathematics. The word in philosophy means a proposition that appears self-evident, where in math it often just means an assumption from which interesting results can be derived. In the latter usage it is the same as a premise. We could perhaps capture the first meaning through combining the term premise with some terminology for “self-evident.”