Statements link two or more concepts. They take a logical form. The simplest is association, income (is associated with, related to, is linked with) intelligence. The form of the statement is revealed by its language, most often the verb. For instance,
Concept 1 Concept 2 for example cause effect x causes y independent dependent x influences y predictor predicted x predicts y input output x leads to y explaining explained x explains y antecedent consequence x leads to y
Statement forms as suggested by Zetterberg: reversible if x, then y; if y, then x. irreversible if x, then y; but if Y, then no conclusion about x. deterministic if x, then always y. stochastic if x, then probably y. sequential if x, then later y. coextentensive if x, then also y. sufficient if x then y regardless of anything else. contingent if x then y, but only if z. necessary if x and only if x, then y. substitutable if x, then y, but if z, then also y.
The kind of logic you use in creating statements reflects your implicit assumptions about how the world is ordered and operates. If a causal statement is made, one assumes: if x occurs, then y is going to occur; x and y always have to be present; x always has to be present for y to occur in each and every instance; y can never occur without the presence of x; and other possible causes has been ruled out as explaining change in y.
If you are a neo-positivist what you are do is trying to reproduce in your language how the world out there is ordered.
The logic of science is one of control. Rules of inclusion for things with certain properties in categories effect control over what is considered relevant and irrelevant. The rules for operalization of a concept limit observation to that slice of reality and bypass other possible slices. The perspective implied in the language of statements limits consideration to a particular domain of explanation and omits all other domains.
Propositions are statements which link two or more concepts whose properties are variates.
Statements that pose a relationship to be studied are hypotheses. Hypotheses may be confirmed or falsified with observation.
Hypotheses may be derived from induction or deduction. (See prior lecture section on induction.) In deduction the hypothetical logical deductive model is used. One assumes that the language you are using is comprised of concepts everyone takes for granted and the concepts are properly operationalized. One assumes that all statements in the argument are logically proper (follow syntax rules), the argument linking the statements is logically proper (same content domain and follow rules for manipulating statements), and the rules for deriving additional statements from the argument are followed (material implication or calculus network rules). Any statement which is derived and subjected to confirmation or falsification is a hypothesis. Empirical generalization, laws. Empirical generalizations, laws, or theoretical sketches explain how things work across different times and setting. Universal or nomothetic statements. Permit prediction. Statements limited to a given time and setting are called idiographic, particularistic, singular statements.
Theory is never directly tested. Instead of the (original, actual, real) hypothesis that is deduced from an argument being subjected to confirmation or falsification directly, one uses a null hypothesis. A null hypothesis takes the form "there is no relationship between x and y." If the researcher examines the data and finds support for the null hypothesis, then he or she does not end up rejecting the original hypothesis and thereby challenge the validity of the theory. To be a bit glib, it is a way of hedging your bets. It is also tied to Type I and Type II errors in statistics.
Some researchers stress induction in concept formation and theory building -- grounded theory. Others stress deduction. These are ideal approaches in the science of what science should do. Normatively researchers loop back and forth between their data and concepts/theory. This process is called retroduction or abduction. Historian call it versimilitude; with each successive looping you obtain finer and finer approximation to how things work.
Discussion of paradigms, normal science, paradigmatic revolution. See Greg Seals and Donald W. Hastings. A revolution is pool-side paradigms. Sportwissenschaft 18,3 (Sept. 1988): 284-295.