A sure sign of a worthless piece of science or a lousy web page is too great a concern with terminology. Conversely, terminology within science and philosophy of science, especially as popularized, varies enormously and is grounds for considerable confusion that can be avoided by some internal consistency. Below I extract some definitions from the on-line (at University of Washington) Oxford English Dictionary (preceded by parenthetical numbers and letters) and offer some comments where my usage departs from convention.
Theory -- (4a) A scheme or system of ideas or statements held as an explanation or account of a group of facts or phenomena; a hypothesis that has been confirmed or established by observation or experiment, and is propounded or accepted as accounting for the known facts; a statement of what are held to be the general laws, principles, or causes of something known or observed.
Hypothesis -- (1) A subordinate particular thesis involved in a general thesis; a particular case of a general proposition. (2) A proposition or principle put forth or stated (without any reference to its correspondence with fact) merely as a basis for reasoning or argument, or as a premiss from which to draw a conclusion; a supposition. (3) A supposition or conjecture put forth to account for known facts; esp. in the sciences, a provisional supposition from which to draw conclusions that shall be in accordance with known facts, and which serves as a starting-point for further investigation by which it may be proved or disproved [sic.] and the true theory arrived at.
I suggest that one not get too concerned about the fuzzy boundary between theory and hypothesis. Note that hypotheses can arise from theory as deductions or may predate theory as untested conjectures. The idea is important, however, that small ideas (hypotheses) within science fit hierarchically within bigger ones (theories or theses). Beware that in legal jargon "hypothesis" implies lack of "proof" or conclusive evidence and is thus used pejoratively. It carries no negative connotation in science.
Model -- (1) Representation of structure. (2b) Something that accurately resembles something else; a person or thing that is the likeness or `image' of another; esp. in little model, a thing that represents on a small scale the structure or qualities of something greater. (2e) A simplified or idealized description or conception of a particular system, situation, or process (often in mathematical terms: so mathematical model) that is put forward as a basis for calculations, predictions, or further investigation.
It is difficult to overstate the idea that a model, whether it be in the form of an equation or the form of a flume to simulate a bottom boundary layer, is not intended to simulate nature exactly. If one wanted all that complication, one would not bother with the model. "A model is a purposeful and often radical abstraction. It should contain only those elements of reality that are needed to solve the problem. The least necessary model is the best possible model for the purpose." -- Judson (1980)
Parameter -- (2a) gen. A quantity which is constant (as distinct from the ordinary variables) in a particular case considered, but which varies in different cases; esp. a constant occurring in the equation of a curve or surface, by the variation of which the equation is made to represent a family of such curves or surfaces; also in Computing. (2d) Math. An independent variable in terms of which each co-ordinate of a point is expressed, independently of the other co-ordinates. (2f) Statistics. A numerical characteristic of a population (as distinguished from a `statistic', which relates to a sample). (3) In extended use: any distinguishing or defining characteristic or feature, esp. one that may be measured or quantified; an element or aspect of anything; loosely, a boundary or limit.
Variable -- (1Ba) Math. and Phys. A quantity or force which, throughout a mathematical calculation or investigation, is assumed to vary or be capable of varying in value. (1Bb) Computers. A data item that can take on more than one value during or between programs and is stored in a particular designated area of memory; the area of memory itself; (also variable name) the name referring to such an item or location. (1Bc) Logic. A symbol whose exact meaning or referend is unspecified, though the range of possible meanings usually is. (3) Something which is liable to vary or change; a changeable factor, feature, or element.
Dimensionally homogeneous -- referring to equations whose sides reduce to the same fundamental dimensions [M, L, T]. Warning: Cosmetic fixes of dimensional heterogeneity are easy. One simply sticks in a coefficient that conveniently eliminates the dimensional problem; witness the many special K's of chemical kinetics. Conversely, don' t assume that dimensionally heterogeneous equations are useless; they can have considerable statistical predictive capability (of the sort that Lakatos deplored but that pragmatism and urgency force upon us all).
Interpretability of variables and parameters -- Are the parameters and variables used interpretable?
Closure -- (6) An agreeing upon terms, a coming to an arrangement with; agreement, union, unity. (8) A bringing to a conclusion; end, close. Closure in the modeling sense usually means having the number of unknowns equal the number of equations. Sometimes, closure is achieved by making assumptions (e.g., in turbulence closure that energy always cascades downward in the length-scale hierarchy).
I use "model" in the sense of abstract description, rather than in the "if-then" sense of theory or hypothesis. Beware of highly variable usage regarding variables and parameters; when the distinction is made, it often is along the lines of say, an equation predicting how fast an organism will swim. The swimming speed is a variable, whereas the gravitational parameter may enter into the equation. If we changed planets, however, this gravitational "constant" would change.
There are well established scaling principles for building some kinds of models. Among the best known are those for maintaining dynamic similitude in fluid dynamics, e.g., the Reynolds number. A problem in using microcosms or mesocosms is that similar scaling principles have not been established for ecological applications.
It is a useful exercise to try to write a model in the sense of a parsimonious, often mathematical description. It makes one think about what parts of the problem are essential. Perhaps even more importantly, it makes one articulate what the problem is. Attempting an explicit model also is an excellent means for avoiding a very common situation that virtually assures lack of scientific progress. Take as an example a term from the lexicon of environmental impact studies: "community health." No two people would define the term (a vague analogy with individual health, itself difficult to define) similarly or write the same model. Nevertheless, two people can talk for a long time before realizing that they mean something quite different. The danger of such vague terminology is that not even scientists among themselves speak the same language. Nevertheless they yield to the tempting term because it gives laypersons a feeling that they understand what is meant.
It is relatively easy to overparameterize. That is, one can stuff in enough variables to fit any result. The opposite problem is perhaps less transparent. In economics and environmental management, there is often strong, ill-conceived, political pressure to come up with one number or "index" (e.g., a diversity index for evaluating community health). The foolishness of this practice can be seen by asking how many numbers are needed to describe a normal distribution (i.e., exactly two). No political decree will decrease it to one. Measurement theory also suggests that the model should be appropriate to the measurement level of the problem -- nominal, ordinal, interval or ratio.
Constrain t-- (5a) Physics. Any special physical or molecular condition into which a body is brought by the operation of some force, and lasting during its operation, e.g., a state of tension. (5b) Dynamics. A body has in the most general case six degrees or freedom, viz. three of translation and three of rotation; if there is a hindrance to one or more of these, the motion of the body is so far constrained; hence, degrees of constraint. Thus if one point in the body is fixed, it cannot have motion of translation, but has all the degrees of rotation: if two points are fixed, its only motion can be that of rotation about an axis passing through these two points; it has thus one degree of freedom, and five degrees of constraint: a sphere moving between two parallel tangent planes has only one degree of constraint; a cube under the same conditions has three. Kinetic constraint: the condition that a body shall move subject to certain relations: e.g., that a body shall roll on a plane. principle of least constraint: the theorem enunciated by Gauss in 1829, that when there are connexions between parts of a system, the motion is such as to make the sum of the constraints a minimum. Webster's (1b) the state of being checked, restricted, or compelled to avoid or perform some action <the constraint and monotony of a monastic life--Matthew Arnold>
I use the word constraint in the looser sense of any limit on the values that a variable could otherwise attain. Well-known constraints are mass and energy conservation. Constraints need not be grand or general. For example, an animal without jaws, raptorial appendages or injectable hydrolytic agents is unable to ingest an animal larger than its oral opening, no matter what a more naive foraging theory might predict. In my experience, ecological theory involves first finding something interesting to predict and then finding enough constraints to narrow the prediction.
Ill-posed problem -- does not have enough constraints imposed to yield a single solution (e.g., yields only three equations in four unknowns).
Proof -- Resort to a dictionary does not help here. Neither proof nor disproof is considered possible in science, yet both Nature and Science use the word routinely, and they are by no means alone in this convenience. Biochemistry and cellular and molecular biology texts also use it routinely. In my opinion, it is a major disservice by scientists to use the word casually rather than attempt to explain to non-scientists that the word is philosophical anathema in the practice of science and that any scientific explanation is tentative in the face of a better one.
Much of the problem is one of degree. Absolute proof or disproof is possible and is considered the ideal in mathematical theory. Proof beyond a reasonable doubt is the usual legal meaning, which in U.S. criminal law translates into giving no reason for doubt in the minds of 12/12 peers. (A little playing with Poisson statistics then suggests that one would be 95% certain that in the population at large fewer than or equal to 25% of people would have doubts if exposed to the same evidence -- and if the jury were a random sample. The point of this excercise is to point out that what is considered sufficient legal proof is nowhere near absolute certainty.) Proof in the lexicon of popularized science can be equated very approximately with the legal definition, and it is certainly more convenient to get on with the popular science story than to explain that lawyers and scientists mean something different, but they certainly do. There is clear pragmatism and Constitutionally intended bias in favor of the innocent in the legal definition, with reasonable but not perfect safeguards of innocent parties and plenty of wiggle room for guilty parties. There is no reason to believe that this legal definition devised by one society to protect its citizens from one another has relevance to the activity of uncovering the rules that govern nature.
Take Newton's "laws" of motion. A lawyer could argue and win the case that they are proved beyond reasonable doubt. Y et one of the triumphs of 20th century physics is relativity and its corrections to these long "proven" behaviors of moving objects. It would be far better to emphasize that science always leaves open the door to a superior explanation and therefore regards no theory as proved in any absolute or even probabilistic sense.
Anthropogenic global change is a current example of inestimable import. The populace at large is left wondering because some legislators demand proof before they will act, and they (legislators and populace) become confused when opposing scientists give arguments for and against substantial anthropogenic modification of climate at present. It would be much less misleading to educate the populace at large that well trained scientists carry doubts and multiple perspectives at the same time as part of their good training. Unfortunately, those activists who have no doubts have the loudest voices and are usually heard. Fortunately, they usually occupy two or more camps. I am not at all against activism; I am firmly against confusing activism with scientific inquiry. By the way, few scientists I know (myself included) have any remaining doubts that humans have changed global climate. It would be foolhardy to pretend, for example, that there is no ozone hole or trend in temperature.
Tautology -- (1f) A compound proposition which is unconditionally true for all the truth-possibilities of its elementary propositions and by virtue of its logical form. I might define it as an "if-then" statement that is useless because the "then" is a logical inevitability following directly from the "if." It has been noted, for example, that the idea of survival of the fittest easily becomes a tautology if one recognizes the fittest only by virtue of their survival (= survival of the survivors). In a very real sense, a tautology has too many constraints.