## Beyond mathematical modelling

from** Lars Syll**

Mathematical modelling has now dominated the economics academy for so long that younger people that emerge from economic studies who are dissatisfied with what they are taught, cannot think beyond the modelling. They have been immersed in it so long that it is a kind of common sense to them. The idea that modelling is bound to be almost always irrelevant just does not compute for many. Yet they recognize that modern academic economics mostly does

notprovide any insights. So, they assume that the fault lies in the sorts of topics covered, or conclusions drawn etc. with the solution to be found by way of doing the modelling differently. It is all quite dire …The only diversity the mainstream advocate is that which remains consistent with the mathematical modelling emphasis. So, it is more or less all irrelevant, because it all carries an unrealistic ontology. Different accounts or ways of modelling of isolated atoms … The result is that academic economics has been and remains a big failure in terms of providing anything of relevance … The modelling project in economics, as it turns out, has in fact not produced a single insight into the real world – as opposed, of course, to occasionally tagging on insights determined independently of modelling. If that assessment were wrong, it would be so easy to provide a counterexample. Yet so far none has ever been seriously suggested in defence of the methods …

I love mathematics. But everything has a context of relevance. Mathematical modelling methods are just irrelevant to the analysis of most social situations; I suspect you have as much chance of cutting the grass with your armchair as generating insight by way of addressing human behaviour using the methods in question … The problem is not mathematical methods in themselves but their employment in conditions where doing so is simply not appropriate.

Using known to be false assumptions, mainstream modellers can derive whatever conclusions they want. Wanting to show that ‘all economists consider austerity to be the right policy,’ just e.g. assume ‘all economists are from Chicago’ and ‘all economists from Chicago consider austerity to be the right policy.’ The conclusions follow by deduction — but is of course factually wrong. Models and theories building on that kind of reasoning is nothing but, as argued by Lawson, a pointless waste of time and resources.

Mainstream economics today is mainly an approach in which you think the goal is to be able to write down a set of empirically untested assumptions and then deductively infer conclusions from them. When applying this deductivist thinking to economics, economists usually set up ‘as if’ models based on a set of tight axiomatic assumptions from which consistent and precise inferences are made. The beauty of this procedure is of course that if the axiomatic premises are true, the conclusions necessarily follow. The snag is that if the models are to be relevant, we also have to argue that their precision and rigour still holds when they are applied to real-world situations. They often don’t do for the simple reason that empty theoretical exercises of this kind do not tell us anything about the world. When addressing real economies, the idealizations necessary for the deductivist machinery to work, simply don’t hold.

From a methodological point of view one can, of course, also wonder, how we are supposed to evaluate tests of theories and models building on known to be false assumptions. What is the point of such tests? What can those tests possibly teach us?

From falsehoods *anything* logically follows. Modern expected utility theory is a good example of this. Leaving the specification of preferences without almost any restrictions whatsoever, every imaginable evidence is safely made compatible with the all-embracing ‘theory’ — and a theory without informational content never risks being empirically tested and found falsified. Used in mainstream economics ‘thought experimental’ activities, it may of course be very ‘handy’, but totally void of any empirical value.

So how should we evaluate the search for ever-greater precision and the concomitant arsenal of mathematical and formalist models? To a large extent, the answer hinges on what we want our models to perform and how we basically understand the world.

The world as we know it has limited scope for certainty and perfect knowledge. Its intrinsic and almost unlimited complexity and the interrelatedness of its parts prevent the possibility of treating it as constituted by atoms with discretely distinct, separable and stable causal relations. Our knowledge accordingly has to be of a rather fallible kind. To search for deductive precision and rigour in such a world is self-defeating. The only way to defend such an endeavour is to restrict oneself to prove things in closed model-worlds. Why we should care about these and not ask questions of relevance is hard to see.

“Using known to be false assumptions, mainstream modellers can derive whatever conclusions they want.”

Yes, all of neoclassical economics is based upon false assumptions shrouded in mathemagics.

The neoclassical model can be reduced to the following:

1. Consumers always pursue psychological ends, except when they don’t … but we won’t discuss when they don’t because that would require the ‘consumer’ to be a life form which must, like firms through their economic activity, support and maintain themselves from the remuneration they get for their ‘sales’.

2. Because they pursue psychological ends, we can presume that they have ‘offer curves’ independent of their means. Thus D(p) = f(q) is a useful subjective assumption to make, contrary to all empirical evidence. Without D(p) = f(q), we could not construct a ‘demand curve’, er, our name for an ‘offer curve’. Just assume that a ‘consumer’ has a budget to spend and this difficulty goes away.

3. Because the consumer pursues psychological ends, and because we are not mind readers, we can create preference functions reflecting that pursuit. We will, of course, have to restrict those functions in many ways to get the ‘consumer’ to behave properly, for if we don’t restrict the functions we will not arrive at the theoretical conclusions we reach by setting those restrictions.

4. Again, we have no idea how the ‘consumer’ forms his or her budget because, we must point out once more that we are not mind readers. Thus, we ‘endow’ our ‘consumer’ with a budget or budget just like we endow consumers with preference functions restricted in such manners as to get those consumers to behave like we want them to behave.

5. We must naturally further restrict the consumer into being unable to change his or her budget when faced with price changes. This means, naturally, and conforming to our theory, that the consumer, having to spend all of its budget, must by more when prices fall and must buy less when prices rise. This, mathemagically, gives us the ‘law of demand’.

6. We do not ask and must never ask how the consumer comes to have a budget, for we like to talk about ‘effective demand’ but not talk about the possibility that effective demand has anything to do with remuneration or the distribution of income within economies. Thus, we create a ‘representative’ consumer out of our ‘micro-foundations’, for this allows us to ignore whether or not the distribution of income has anything to do with the paths or trajectories economies are on.

7. Since we are only concerned with ‘consumers’:–i.e. those who have effective demand in this or that market–: we ignore non-consumers in this or that market by claiming that only the ‘welfare’ of ‘consumers’ matters at all. Bringing in people who might not be ‘consumers’ in this or that ‘market’ would severely complicate our ‘analysis’, for real people cannot avoid needing to consume because they are life forms and might suffer real consequences when they cannot ‘consume’ in this or that ‘market’.

8. We insist that the circulating numeraire that is money must always have neutral effects regardless of its distribution. To show this we have invented ‘equilibrium’, especially long run ‘equilibrium’ which, of course, does not exist any more than short-run equilibrium does.

9. Given that we endow our consumers with preferences and inflexible budgets, and restricted those preferences so that consumers ‘behave’ properly, we unveil what we call ‘theory’ everywhere. And we insist that you use our theory to defeat our theory, for it you cannot, that is your failing, not ours. BTW, you must accept our optimization techniques. These will show that if px of the X-good falls, then the consumer will maximize if and only if it acts as if, once home, it has equalized its Marginal Subjective Utilities between commodities. If, however, the consumer has a Uxy function = x^aY^a, this means that the consumer is effectively able to trade the volume of any good it has bought this shopping trip for the volume of any other good its shopping cart and break even. This idea stems out of the fact that traders exchanging goods expect to trade equal values, and on noticing this, the first great neoclassical economist (William Stanley Jevons) assumed that what is true for two traders must also be true for a consumer shopping for itself. That’s balderdash of course, but the mathemagics are really NEAT, permitting us to show how consumers ‘optimize’.

There is nothing wrong with our theory, naturally, especially if you try to use it to defeat or replace it.

Thank heavens we have our neoclassical theory. We’d hate to see anything depose it.

Economic models are used to brainwash people into supporting high wages for economists.

The future is already plain to see. Mumbling mathematical models have one purpose and that is obscuring capitalist destruction of life and happiness. One who wonders why models are needed for destruction of happiness and fun is on the right track. That line of reasoning is far more fruitful than a Harvard economist planting confusion in the minds of youthful students.

Why economists propagandize for the rich and what to do with them is essential to know because the subject is accredited scholastically even though it is used for brainwashing.

Lars, Just to clarify: “The problem is not mathematical methods in themselves but their employment in conditions where doing so is simply not appropriate.”

So, one problem is ‘old mainstream’ economists employing inappropriate models. But maybe another is not using appropriate models?

For example, economies, like epidemics, would seem to involve positive feedback and self-defeating ‘expectations’. Hence the conventional mathematics of ‘rational decision theory’ does not apply.

In the UK, the proper role of mathematical modelling, econometric-like statistics and ‘the science’ generally was problematic, as it is for economics. We now seem much more accepting that the search for inappropriate precision and confidence can only come at the cost of crises in the longer-run, at least for epidemics. Maybe there will be a similar ‘opening of minds’ for economic?. If so, maybe (appropriate) mathematics could be part of the solution?

I’m sorry Dave, but based on a thorough ontological reflection, I very much doubt that mathematics will ever be an important part of that solution. Just like you and Tony, yours truly loves mathematics. But, analysing an inherently complex and uncertain open social world — such as real-world economies — with formal mathematical modelling, presupposes that you subscribe to an unsustainable methodology where you accept closed-models thinking as an acceptable ground for explaining and predicting what goes on in an essentially open target system. In my opinion that is not a viable way to move economics forward.

Okay, economic analysis like economic ‘mathematical’ modelling, presupposes some weird stuff. And, recognizing that often mathematical mathematical models cannot ‘explain and predict’, might mathematics not nevertheless provide some useful https://en.wikipedia.org/wiki/Mereology insights?

Dave, have you come across D E Littlewood’s “The Skeleton Key of Mathematics”? For me the title of this suggests mathematical models are relevant at the “framework” level of theory, not for resolving particular problems. (Particularly not for predicting particular events in the future – though computer programs in which “equals” has been replaced by “becomes equal” might well be, especially if the context is an error detecting and correcting operating system). That suggests theorising may be about detecting errors, as when (so I understand) Kenneth

Arrow showed that the hypothesis of a General Equilibrium was an impossibility. We have therefore two types of theory, which for short I will call “basic” and “applied”: the first relational, the other programmatic. If we stick to what is mathematically certain then the basic theory ends up providing reliable axioms for the applied theory.

My framework theory simplifies to the structure of an arabic (algorithmic) number. It starts off representing nothing (0) at the time of the Big Bang, but grows like an expanding universe, being able to accomodate representations of an indefinite sequence of numbers with a limited set of number symbols by “evolving” a new type of unit when the next number is bigger than the highest numeral in the previous one. This is however not 9 but 3, for truth is complex, i.e not just True or False but these with or without errors being discovered. Beginning to apply it, the terrestrial measure of time is circular, and before numerals are introduced the only definite distinction is given by the symmetry of right angles. Hence, in my model the numerals are 0 to 3 and exceeding the third represents (in the reality) the beginning of a new era. To cut a long story short, the earlier numbers continue to exist as part of the total, as do the particles, atoms, molecules, life forms etc of earlier eras in the real universe. What little this predicts can be easily verified. In the order of their evolution there are four forms of life: microbes, plants, animals and humans. The human consumers comprise all of us; we have male and female parents who being animals as well as human, need to look after their kids, and those (notably grandparents) who have become free enough to be able to help them. One of their inventions was money, which turned exchange in “farmers’ markets’ into a variable; but it also started the evolution of a distribution control system called the FIRE economy (banking, insurance, share marketing and portfolio derivatives, the latter overflowing into another era in which economic control has been overtaken by money making (i.e. Aristotle’s ‘chrematism’).

As “framework” model this simple arabic number form has therefore indisputably led to Larry’s axioms and my conclusion that capitalism has changed from being an economic control system to mere money making. But as has repeatedly been shown, today’s abstract money is worthless, being neither costly nor scarce, hence my conclusion that the whole “FIRE” economy can be dispensed with. My own “applied” theories go beyond Larry’s, arguing re government that grandparent advise rather than lay down the law; that – unless one is blind or not yet able to read and understand one’s accounts – we can use a credit cards just as variably as we do cash or debit cards), with cash withdrawn from a dispenser accounted for in advance; that when use a credit card we are asking for and receiving credit which is repaid by our doing what we needed it for, viz eating and to some extent feathering our nest. I am satisfied with the logic of this, but getting a fair hearing about what we don’t yet do is (as not just Keynes has found out) is another matter.

So, Dave, as a mathematician living in a self-destructing world, what do you think of all that?

What Ikonoclast might like to think about is how did Copernicus’s revolutionary idea get accepted? Did it become fashionable to replace sun-dials with clocks? My gut feeling for how to subvert capitalism is to fashion a policy of always referring to our capitalists and their neo-liberal economists as chrematists, so that people become able to see what they are up to.

Dave T,

In so far as your framework challenges mainstream economics notion of ‘mathematical model’ you are on to something. I incline to the view that economies evolve, and our models need to reflect that.

As for actual economic models, the best one can do as a mathematician is to critique some pre-existing conception, as in physics. One does need practical some insight to start with. Where to start?

My own view is that there is much that economists could take from game theory and cybernetics, but for some reason, as Lars says, the seem to presuppose a lot of weird stuff, and so misinterpret or misapply whatever they have. So if one is going to offer something it helps to have some appreciation of their weird ways. Which I don’t, really. But we can but try.

Maybe we should describe the real world and the real economy, and then build a model on this reality? Then mathematics will also receive a worthy place in the economic model.

In another thread I wrote the following which is slightly amended here for clarity.

How do we effect a revolutionary change? In broad terms, we need to take power away from capital. But capital IS power: (a mode of power in our political economy system as shown by CasP theory backed by its empirical analyses). It is the very existence of the large concentrations of capital (and the earnings differentials) in elite hands which we need to abolish. The clear path is to break up the big capitals (in anti-trust fashion but going further.) Equally, part of that path is to radically reduce the private ownership of big chunks of capital.

Take apart the corporations and divest the billionaires (start with the billionaires). Reduce permission to personal ownership of capital down to a mandated level. If the 68-95-99.7 distribution rule holds for wealth (capital) then set the mandated rule at the current 2nd standard deviation. That is to say the top 5% should be broken back to the current 2nd standard deviation point.

Somehow the 95% have to overrule the 5% and break up their wealth. The people have to break up the private corporations and the elites and oligarchs from the billionaires down to the decamillionairs. It’s a simple and as hard as that. How to do it? Well, it will only happen by revolution. The world is in such a parlous state that revolutions will start spontaneously. They are already starting, all over the world. The difficulty will be guiding them and making them as positive and peaceful as possible.

But Ike, WHO is going to take corporations apart etc, and WHY? I’ve suggested ridiculing your 5% by all of us “speaking truth to power”, so that politicians who want to get re-elected will become aware of the easy way out. Merely by governments authorising interest free credit cards we become able to create our own money as and when needed, so the whole FIRE economy and the accumulations of the wealthy become redundant.

This will preferably be internationally, becoming an addition to the UN Charter of Human Rights. But even nationally, authorising the issue of local cards by local government is no different in principle from permitting private companies to issue “store cards”. As I argued with Jonathan, capitalists don’t really have power: they are pulling the strings in a remote control system, so we give them our own power if, when they tell us to jump, we do so.

However, Britain’s General Strike of 1926 and Thatcher’s demolition of our miners showed that just striking is not the answer. One must first undermine the credibility of the string pullers, not just their minions in the economic profession or their political figureheads, as we tend to do here. Strategically, it may come down to our local governments striking against our national governments: issuing local free credit cards and accepting payments in voluntary work rather than rates. Local officials are easier to get at than those of central government.

Of course this is not “me telling you”, as black and white thinkers might object. I am offering you a proposal worthy of discussion. As Keynes said in his General Theory, “It is for others to determine whether either of these [it being trivial or nothing new] or the third alternative is right”.

Hi Lars,

thanks for the contribution. I’m not quite sure how Lawson’s critique needs to be strengthened with regard to econometrics etc. But I agree with you.

The main point for me, though, is that many of the heterodox economists are themselves subject to this deductivism. Lawson “Beyond Deductivism” (2018) has summed this up well with regard to post-Keynesianism. There are also heterodox economists who flirt with complexity economics and whose textbooks also look very mathematical (something along the lines of: more and more complicated mathematics).

Now one could give a good example and show alternatives. They really do exist. But hardly anyone knows them well and in the end everything leads back to post-Keynesianism, evolutionary economics or complexity economics. Quite apart from that, it seems to me that other (more non-formal) ‘schools of thought’ are also marginalised by heterodox economists who work predominantly mathematically. So how to deal with this?

There is a second problem: in order to approach ‘the mainstream’, I often experience that students from Plural Economics first give in and say “Yes, mathematics has its place and should be on an equal basis with other methods.” But this is an attitude that in practice leads those who actually work differently (non-formally) or want to work differently into a reactive and defensive situation: They still have to justify themselves for doing something differently. Here, too, the question is: How to deal with this?

How to break through mathematical modelling? Algorithmically, by introduction a bounded rationality theory that contains thinking time and limited speed, we can prove that not all information can be immediately and perfectly transformed into quantitative data (which was hinted with price mechanism under perfect rationality), and hence various kinds of data other than quantitative data, and various qualitative analyses other than quantitative analysis, are usually concomitant – although we can admit that they might still be converted, or “converge”, into quantitativeness “finally”. Next, many divergences happen, such as mental distortions, combinatorial explosions, and endogenous subjectivities, which suspend or prevent the convergences from going on, only allowing them occurring partially or temporarily, and thus the society evolves expansively, like universal Big-Bang, where both actors and theorists use various methods, other than deduction, to process various data, other than numbers; And, the ultimate doomsday will never come, and we are always during the history.

It is a shame that Lars makes this kind of logical mistake.

In a system of propositions

Sthat you assume true and if you find a propositionPthat is (1) deduced fromSand (2) false, then the systemScontains contradiction and any propositionQfollows (proof by contradiction) from such a system. However, a mathematical model if it is implementable as a computer program for example, it is internally consistent even if the model contains an assumption that is “false” (i.e. not true as a proposition of a real world). One can only get a narrow set of outputs (far from anything you want).If he repeats this kind of mistakes, neoclassical economists would think that Lars is no competent in logical arguments. Of course, everyone makes mistakes. I do very often. I hope it was a mistake and Lars corrects it..

“From falsehoods anything logically follows.” Some people not versed in formal logic — of which yours truly was a student back in the 70s — have had troubles with this sentence.

But that’s really nothing very deep or controversial. What I’m referring to — without going into the intricacies of distinguishing between ‘false,’ ‘inconsistent’ and ‘self-contradictory’ statements — is the well-known formal logical ‘principle of explosion,’ according to which if both a statement and its negation are considered true, any statement whatsoever can be inferred.

A good principle to follow is to make sure you get things right before you start lecturing people …

I learned formal logic myself. That is why I wrote

But, after the first sentence that is valid, you have claimed that

I admit that expected utility theory is wrong in the sense that it does not reflect the reality, but you cannot apply the law of deduction “From falsehoods anything logically follows” to the fictitious theory such as expected utility theory. It can be logically consistent inside of its system and it is impossible that you deduce an arbitrary proposition inside of the theory. You must remind in which formal system you are reasoning.

Please reflect slowly. It is possible that you are mislead by Tony Lawson, because he is saying similar statement in his interview.

As a mathematician, I appreciate Lars’ concern, that economics needs to go beyond mathematical modelling as it is usually practiced. My own approach would to improve the practice, not abandon it. Thus I agree with Yoshinori that there needs to be a strand of investigation that takes logic seriously, and it is unhelpful to raise important logical issues without due care to avoid giving a wrong impression. But then again, it seems to me that Lars is actually more thoughtful than many economists in his consideration of logic, so maybe his repeated (if misplaced) critique of mathematics might lead us somewhere.

As a mathematician, modelling means https://en.wikipedia.org/wiki/Model_theory, Unfortunately my experience of ‘practical affairs’ is that most domains have what Lars calls ‘axioms’ that cannot be modelled in the logical sense, and so one cannot trust the application of ‘sophisticated’ mathematics. Instead, it is ‘pragmatic’ to ‘shut up and calculate’ using approved methods. It follows from this that while mathematicians are useful tools, they can’t be trusted on ‘economics in the round’, or any other empirical subject

My own view is that it would be worth trying to develop logical variations on empirical theories, including economics. Maybe this would provide useful insights (as when Einstein reformed physics)? Why don’t we do this?

One problem is that we tend to think of subjects as if they were somehow static. For example, economies are thought of a stochastic, whereas they clearly evolve.

To come back to Lars remarks on logic: I’m no sure what he means by ‘modern expected utility theory’.

https://en.wikipedia.org/wiki/Decision-making_models#Economic_rationality_model is a good example of something that is surely not modellable in any meaningful way. But I can imagine something more limited that would be modellable in my sense, but then it still wouldn’t be anything like a real economy as I understand it. So Lars draws our attention to a good point, but not made as well as I would wish.

Keynes 1919 Treatise discusses much of this: time for a contemporary account?

Just to add. Lawson says “The modelling project in economics, as it turns out, has in fact not produced a single insight into the real world – as opposed, of course, to occasionally tagging on insights determined independently of modelling.”

I’m not in a position to disagree with Lawson, not being familiar with the history of economics. But conventional modelling (used as a tool) is a way of exploiting existing insights, e.g. to make money. If the insights are already correct then there are often no more insights to be gained, unless (as in physics) the insights present interesting conceptual challenges.

The potential value of applying mathematics is in demonstrating that the existing insights are lacking, somehow, as Keynes showed for the economics of his day, some of which strange beliefs survive.

For example, ‘economic rationality’ requires that probabilities are never mysterious. Yet in economics, they are (at least to me). Does anyone really believe in ‘the law of large numbers’, reversion to the mean or that stocks and shares are literally just like a lottery? Alternatively, consider game theory (which applies more generally than to homo economicus): it leads us to expect convergence to an equilibrium when coalitions are stable. But why should we think that coalitions are stable? Or take cybernetics, and the law of requisite variety: what provides such variety? Surely not conventional econometrics!

More generally, if economies include positive feed-back and ‘noise’, why are they not prone to critical instabilities? Or maybe they are?

And then again, the ‘mathematics’ favoured by economists only make sense to me if one presupposes some basic assumptions that can’t be challenged within the paradigm (and hardly at all), thus limiting the ability to put forward a ‘credible’ alternatives to the broad status quo. Why is this? (I have some ideas … )

It seems to me that mathematical modelling, in the mathematical sense, can raise lost of ‘insightful’ questions. But the challenge is to answer them. All mathematics can do is to critique potential answers. But it seems to me that this would be a useful addition to mainstream practice. Or am I missing something?

Insight is a first step. You suddenly see a connection: X has something to do with Y. But that doesn’t get you very far if you want to do anything about it. If moving X moves Y, can we understand why? How large or small is the effect and how stable; what other factors influence it and how quickly? Pursuing the insight to answer those questions leads to a model, preferably one you can test. If it doesn’t you remain in the realm of literature and commentary – like Lawson. Honourable occupations to be sure but so is the effort to develop insight into something practical.

If you cut someone’s tax they’ll have more money and spend more. Yes, but which somone, which tax, and how much more? Policy to improve things requires specifics.

As the proof of pudding is in its eating, the “

proof” of a methodology must lie in whether it has produced a good theory or helped finding evidence or insight that would not not be found without the methodological hints. I want to know whether Lawson’s critical realism and ontology has ever produced any such positive results in economics. If somebody know one or two, please teach me. I want to read one or two of them.Lawson’s Interview by Jamie Morgan was published in Journal of Critical Realism. The following citations are from a recent article from the same journal, i.e. in the Abstract and the Introduction from Dennis J. Frederiksen and Louise B. Kringelum’s Five potentials of critical realism in management and organization studies,

Journal of Critical Realism, 2020 (Open Access):Frederiksen and Kringelum partly confirm my doubt on the productivity of the critical realism at least in the domain of economics.

According to

https://en.wikipedia.org/wiki/Critical_realism_(philosophy_of_the_social_sciences)

positivism is “rejected due to the observation that it is highly plausible that a mechanism will exist but either a) go unactivated, b) be activated, but not perceived, or c) be activated, but counteracted by other mechanisms, which results in its having unpredictable effects”.

This criticism applies to scientific models base on some form

of Occam’s razor, but doesn’t apply to mathematical model theory. Moreover CR denies morphostasis, which is an assumption of typical stochastic models, but not of mathematical mathematical models. The other main concern seems to be ontology, which is essential to any sensible application of model theory (unlike an economists’ ‘mathematical modelling’).

So what I don’t get is why Lars et al are so opposed to seemingly sympathetic and appropriate mathematics, as distinct from the kind that the mainstream regards as ‘pragmatic’ but which others regard as dismal. Why not take Keynes’ 1919 Treatise seriously?

Thank you, Dave, for indicating wikipedia article

Critical realism (philosophy of the social sciences). It was an article of high quality (much higher than I have expected) and I learned much about critical realism.This is the paragraph that precedes Dave Marsay’s citation:

What is claimed here is important (the last sentence in particular). I have an impression that a number of contributors to this blog still have rather a

naivephilosophy of science (referred to asempiricismandpositivism) and believe that simple accumulation of “facts” or “description” is sufficient to build a science. See for example the reply by Herbert on February 17, 2021 at 5:19 pm posted as a comment to Lars Syll’s article: Beyond mathematical modelling. (this page)On the contrary,

science is “an ongoing process in which scientists improve the concepts they use to understand the mechanisms that they study.”