A theory is a set of statements that are arrived through a process of continuing abstractions. A theory is aimed at a generalized statement aimed at explaining a phenomenon. as opposed to traditional or conventionalists views (which also share a shared view with platonic philosophy which aimed at elemental truths) that are detached from the mundane physical state of nature more recent (Popperian View) says that theories are falsifiable through experimentation.

A model is a purposeful representation of reality[1]. In general when people refer to modeling, they refer to mathematical modeling which is a mathematical construct that is an approximation that is used to study a specific phenomena.

As you can see, both share common elements in their definitions. What differs one from the other (in my opinion) is that one is aimed at generalized statements(theory) while the other is aimed as a helpful tool to understand specific phenomena(modeling). The second difference is also the abstract nature of the theory as opposed to more 'realistic' nature of mathematical modeling. A third difference is that in mathematical modeling the approximation is usually based on experimentation while theory does not necessarily need experimental support for its postulation.

Hope this helps

[1] A course in mathematical modeling by Douglas Mooney and Randall Swift

Within the act of scientific modeling, the theory (sometimes called "the governing theory") is responsible for the formal derivations whose results will be interpreted back in the terms of the modeled (physical) system. In this scheme, the model is the entire ensamble of both the formal systems used and the correspondences of these formal systems and structures with the structures of the idealized investigated (physical system). In this procedural view, the theory (actually a part of it, namely that part we use) is part of the model. Within model theory, the two conceps are defined fomally such that there is no inclusion between them, therefore equivalence neither.

A theory is a set of statements that are arrived through a process of continuing abstractions. A theory is aimed at a generalized statement aimed at explaining a phenomenon. as opposed to traditional or conventionalists views (which also share a shared view with platonic philosophy which aimed at elemental truths) that are detached from the mundane physical state of nature more recent (Popperian View) says that theories are falsifiable through experimentation.

A model is a purposeful representation of reality[1]. In general when people refer to modeling, they refer to mathematical modeling which is a mathematical construct that is an approximation that is used to study a specific phenomena.

As you can see, both share common elements in their definitions. What differs one from the other (in my opinion) is that one is aimed at generalized statements(theory) while the other is aimed as a helpful tool to understand specific phenomena(modeling). The second difference is also the abstract nature of the theory as opposed to more 'realistic' nature of mathematical modeling. A third difference is that in mathematical modeling the approximation is usually based on experimentation while theory does not necessarily need experimental support for its postulation.

Hope this helps

[1] A course in mathematical modeling by Douglas Mooney and Randall Swift

Thanks a lot to all for comprehensive answers.

There is a readable and entertaining book that explores the utility of models and the self-deception that may occur when those who use them mistake them for reality itself.

Emanuel Derman (2011). Models behaving badly; Why confusing illusion with reality can lead to disaster, on Wall Street and in life.  NY: Free Press.

Charlotte,

Very interesting reference and I think that the authors message is very important to be understood by every scientist. Mistaking models as universal truths is a pitfall that must be avoided.

This is an important debate. It might be useful to check out some of the work on epistemology of modelling and simulation by people like Andreas Tolk at Virginia Modeling Analysis and Simulation Center. Others, such as Bryson, suggest that models are theories presented computationally, and as such as can take the output of the model as a prediction in its own right.

Largely, I think the answer depends on the field. Generally though, one would have to demonstrate that the theory presented in English (or any other human language) was somehow different from its implementation in Java or C (or any computational or logical language). Generally, I disagree that the "intent" of a theory or model is that differentiates it. This seems problematic from an epistemological point of view.

Thanks, Justin: I will be interested to follow up Andreas Tolk' work. But so far nobody in this thread has mentioned the idea of "Models as Mediators" put forward by Margaret Morrison and Mary Morgan. Morrison in particular talks of models as "Autonomous Agents" - which I struggle with, as I see people as the only true agents involved in science. Of course a simulation model is a computer program so it *can* be an agent-based model (in the metaphorical sense of "agent" used in computing and AI) - but then these agents seem to lack most of the capacities that we would value in a human agent with whom we wanted to collaborate - basically nobody, including the "agents" themselves, understands the algorithms that they generate.

Morrison writes: "It is precisely because models are partially independent of both theories and the world that they have this autonomous component and so can be used as instruments of exploration in both domains."

In my perception, a model is some sort of theoretical construction - so it is not really independent of the world since it is made by human agents who exist in the world. A computer simulation model is doubly dependent on the world - via the capacities and intentions of the modellers who create it, and via the technical constraints of computer technology. Any model abstracts from many details of reality - constructing the model involves idealizations; but that is true of any theory. By convention, nowadays, a theoretical representation with rather specific or restricted scope tends to be called a model, whereas a theoretical representation with broader scope tends to be called a theory. But I tend to doubt whether this difference of scope reflects some essential difference between theories and models. Fundamentally they are all cultural artefacts that reflect human interests in the world in which we exist, and are judged accordingly.

Further to above, I note that the abstract of one of Andreas Tolk's co-authored papers begins: "This chapter makes the case that theory can be captured as a model, which can be implemented as a simulation."

Reference:

Diallo, S. Y., Padilla, J. J., Bozkurt, I., & Tolk, A. (2013). Modeling and simulation as a theory building paradigm. In Ontology, Epistemology, and Teleology for Modeling and Simulation (pp. 193-206). Springer, Berlin, Heidelberg.

Generally I agree with some of the points you note. I've also struggled with the idea that anything but a human has agency in the scientific method and theory development. However, in one of our projects, we came across a situation where there were three equally plausible mechanisms for a theory of religious ritual systems and human motivation. To settle the issue, we programmed the model with all three mechanisms, and turned them on and off during calibration experiments. In this way the model acts like a sort of "genetic knock-out mouse". Here the ultimate decision in adopting one of the three stances was made by humans. However, the way in which we came to that conclusion was in many ways by using the model as a mediator with a sense of agency in the theory building process.

Sorry, I do not intend to provide answer. Thanks for the previous contribution. But my worry is that I am still struggling to differentiate between theory and a model in a sociological context. Kindly help clarify further

Sally - I can see two issues underlying your query:-

(1) It's not clear whether the conception of "theory" current in Sociology is sufficiently similar to that current in natural sciences for the same model-theory distinction to be applied in both fields;

(2) It is also not clear whether the distinction between theory and model used in natural sciences is clear enough to be helpful even within that more restricted field. As I've said in a previous post: "By convention, nowadays, a theoretical representation with rather specific or restricted scope tends to be called a model, whereas a theoretical representation with broader scope tends to be called a theory." But there does not seem to be an essential difference between theories and models - they are both a conceptual apparatus that we bring to the world.

Going back to the sociological context: different schools of thought in Sociology - e.g. Marxism, Phenomenology, etc - are often referred to as different "theories". On the other hand, in Psychology I learned to think of a theory as something that could and should be tested (therefore it could not really be a complete school of thought!) This is of course one of the main trends of Popper's philosophy - in "Conjectures and Refutations" he contrasts Marxism and Psychoanalysis on the one hand, with Einstein's theory of Relativity in Physics - all three of which were widely discussed in Vienna when he was a young man. Popper regarded it as a defect of both Marxism and Psychoanalysis that no matter what happened, their adherents were able to fit those events into their "theory", whereas Einstein's theory took the risk of being disproved - but survived the test of Eddington's observations during the solar eclipse. Experimental Psychology also tries to advance by developing testable theories (or theories from which testable hypotheses follow). A great thing about the experimental approach is that nature itself has a chance to tell you that your idea is wrong. Altough Popper's idea of decisive refutation is generally now rejected, testability of hypotheses is still recognised as crucial to experimental science.

Now, where do models stand in all this? In the social sciences we have some models (e.g. in economics) which are so dependent upon "all other things being equal" that really they amount to untestable theories. I remember being astonished on first looking into an economics textbook to find there were graphs with no numbers on the axes. We have also increasing numbers of simulation models of various social processes which may or may not have any relation to what can be observed - for example models that purport to show that segregation will take place even where people are quite willing to live in a community where the "other" ethnic group is in a majority, because they *do* want to have *some* neighbours of their own group. Whether either of the foregoing examples belong to a Sociological context, I rather doubt. Most of the interesting Sociology I have read is more inclined to draw out the complexities of real life, rather than to seek lessons from abstraction.

(Note however that Weber's notion of "Ideal Types" has something in common with modern ideas of "Idealization" in modelling, which means deliberately abstracting away from certain things that are known to be important - as Weber put it, a one-sided accentuation of certain characteristics. Well, that can help in developing terminology - but does it bring us sufficiently closer to the truth, even to *a* truth?)

I would be inclined to sum up your dilemma like this: If it is a Sociological theory it is probably *not* a theory in the scientific sense; if it is a mathematical model it may have a sociological dimension or inspiration, but will probably contribute little to sociology as such.

Julian-Thanks a lot for a more elaborated response to my query. However, the information you have provided is too complex for me to grasp in a simplest form the difference between the two concepts.

But I truly appreciate your valuable time in helping me to understand this.

Sorry if my answer was too long and unclear. That's really because I don't think there is a clear answer. Originally, I think, people used the term "theory" for any kind of hypothesis or guess about the world - that could be the physical world or the social world. Later they began to restrict the term "theory", using it to refer only to some very grand system of ideas, and introduced the term "model" for something which previously could have been called a theory, but which was restricted or focused in its coverage. Can you give an example of the use of the words "model" and "theory" in sociology which is a problem for you?

Hi, Indrajeet

Theory is a generalized thinking or conclusion of something which is a consequence of an analysis. A theory is always proven scientifically with evidence. While, model is a physical, verbal or a graphical representation of a concept or an idea. Models can be developed depending on the theoretical aspects. Models have been made in order to simplify the theoretical concepts.

Hi Esraa

Your answer is interesting, but I think you are wrong to assume that a theory is proven (or even can be proven). We could however say that a theory must be supported by evidence (if it isn't we will discard it). On the other hand because of the simplification involved in models (often referred to as 'idealization') it will never be possible for a model to gain support as being 'the truth'. This is why Elgin calls models 'Felicitous falsehoods' - they are useful simplifications but they cannot be exactly 'true'.

The concept of theory is broader in meaning than the model. theory can apply to everything and also nothing specific, whereas the model should be presented in a specific, systematized, logical, and other way.

I agree with Dariusz Prokopowicz

النظرية اكثر شمولية من النموذج النموذج شي محدد ومخصص

It is certainly true that the word theory can be used very loosely, but for scientific purposes I think that theory has to be specified in a specific, systematised and logical way just as a model must - so I don't think Dariusz's response captures the difference between a theory and a model.

I agree with Dariusz Prokopowicz regarding the 'scope' and parameters of theory and model. However, I think sciences research (including economics and management sciences) and natural & engineering researches undertake theoretical underpinnings in very different ways.

A model is a mathematical representation of those aspects of reality that are relevant in testing the theory.