Math deals with possible worlds. (Think science fiction, or space fiction, depending on where you are from.)
Science purports to describe the real world of facts and events. This is called "semantic interpretation." (Think maps.)
Lars P. Syll’s Blog
The perils of calling your pet cat a dog …
Lars P. Syll | Professor, Malmo University
Lars P. Syll’s Blog
The perils of calling your pet cat a dog …
Lars P. Syll | Professor, Malmo University
31 comments:
Numbers deals with possible worlds.
Numbers describe the real world of facts and events.
Math deals with possible worlds.
Math describes the real world of facts and events.
Language deals with possible worlds.
Language describes the real world of facts and events.
Science makes guesses and then tests them to see if they are false.
T - Numbers deals with possible worlds.
F - Numbers describe the real world of facts and events.
T - Math deals with possible worlds.
F- Math describes the real world of facts and events.
T- Language deals with possible worlds.
T- Language describes the real world of facts and events.
Math is is comprised of signs and rules for relating them to each other — definitions, formation rules and transformation rules. Math is entirely syntactical.
Truth in math is syntactical truth that is determined by tautology, with falsity being contradiction.
Math as math is non-descriptive.
Math can be applied to the real world of objects, facts and events through quantification.
Applied math and theoretical science overlap, e.g., string theory. Applied math and theoretical science deal with idealized worlds and stylized "facts." They are concerned with models rather than testing.
Math models can be used in describing the real world of facts and events by being interpreted semantically.
Science uses math models that are interpreted semantically.
Truth in science is semantic truth — correspondence of a model to facts and events through hypotheses testing.
There is a grey area between applied math and theoretical science.
Much of the controversy in economics is in this grey area.
Those emphasizing applied math are on one side of the debate and those emphasizing theoretical science are on the other.
The chief area of contention is over the use of data and the relevance of testing wrt to the fitness of models in contrast to formal rigor.
One side argues that all long as the math is precise it doesn't matter if the model is inexact as a representation of reality.
The other side counter that this is doing applied math rather than science, and results are incorrectly claimed to be scientific.
Science makes guesses and then tests them to see if they are false.
Scientists make educated guesses about assumptions.This is called abduction. These assumptions may be tested inductively as a preliminary step.
Then a formal model (algorithm) is developed from which theorems can be derived from the assumptions as axioms through the use of functions that are presumed to correspond to causal factors.
Theorems derived from the model are then interpreted semantically and used to formulate hypotheses that are amenable to testing.
Experiments are designed to test the hypotheses as prediction. This is experimental science.
Positive results from testing are taken to be evidence for the correctness of the theoretical model and its fitness as an explanation of the facts and events.
Depends on how narrow a definition you give math. I think I disagree but I've got to think about why for a few days before I open mouth and insert foot.
Why did you mention maps?
Depends on how narrow a definition you give math. I think I disagree but I've got to think about why for a few days before I open mouth and insert foot.
Take a look at semiotics, which is comprised of syntactics, semantics, and pragmatics.
There are various views of philosophy of science and philosophy of mathematics, so it would be cavalier to present one as definitive.
The one I have presented is in terms of semiotics.
Why did you mention maps?
Good question.
A description functions like a map. One can follow a map to a destination and confirm along the way that one is on the correct route by observing landmarks indicated on the map through interpreting the legend and scale onto the actual route.
Take a simple (elementary) descriptive proposition as a statement of fact. In Wittgenstein's Tractatus terminology, an elementary descriptive proposition "pictures" a state of affairs and asserts or denies that the state of affairs is the way things stand in the world, that is, that a fact corresponds to it.
Understanding the proposition, that is, interpreting it semantically, involves being able to use it as a "map" to confirm or disconfirm it in experience.
A scientific theory that is interpreted semantically can be confirmed or disconfirmed through hypothesis testing. While the theoretical model is purportedly descriptive of the world, most scientific models are sufficiently general and conditional that they cannot be confirmed or disconfirmed as a whole.
re Ryan first post.
Math is a formalization of a closed and unambiguous (but incomplete) language; natural languages are open (but can be as complete as you want, but ambiguous) languages. Both can be used to describe abstract or real worlds.
Maths and language are essentially the same thing (both are languages, in the proper sense). Think about numbers as some sort of lexeme, a minimal object which can have some meaning semantically, or a "monad".
Numbers can be "reified" to equate with something real as they can be used to describe quantities, which are a meaningful properties of physical phenomena, Most (all really) science deal with 'accounting' and quantification, that's why math as a language is useful to describe reality.
Off course this is only useful regarding science as long as the "reification" is real, and has a meaningful real counter party. This goes along with previous long Tom post, dealing with numbers by itself does not necessarily result in something that can be equated with reality, hence the criticism about doing 'applied math', not doing 'science', which are related but not necessarily the same thing.
After doing the math you have to actually test that the 'reification' of assumptions into math is actually real.
"A description functions like a map. One can follow a map to a destination and confirm along the way that one is on the correct route by observing landmarks indicated on the map"
A map has no function it just sits there...
Tom that is navigating by waypoints there is also dead reckoning....
https://en.wikipedia.org/wiki/Waypoint
https://en.wikipedia.org/wiki/Dead_reckoning
this is how you get the typical argument where the female is saying 'we're lost' (waypoints) while the male says 'no we're not' (dead reckoning)
Darwin people say this is because the male cavemen ventured further from the cave than females typically...
They are two different ways of navigating... similar to the two different ways of learning of 'rote' vs. 'active learning'...
We are not created equal....
Look at the title.. if somebody calls the cat a dog, a rote learner will only be able to know that it is a dog... they have no ability to get out of the falsehood...
Its like when Mike was in the video arguing with Stuart Varney, Varney says "you print money, then you're Weimar Germany!"... ie rote... he has no ability to get out of this falsehood...
Tom change out the waypoints and the traveler using the waypoints will get lost... or at least they will not reach the intended destination meanwhile they will proclaim they are not lost...
imo you get out of it via math somehow ... but dont ask me to explain how this works yet...
Tom what I like about Lars blog is he keeps it short and then it stimulates a lot of thought...
Its like not much reading but then a lot of thinking... while others are a lot of reading but then not much thinking...
"change out the waypoints and the traveler using the waypoints will get lost."
And then some will argue that those lost waypoint ones are conducting an "unknown location conspiracy!"....
A paper map just sits there, static. But with a vector or raster based map, you can perform other functions.
An elementary descriptive proposition is static. It points to "coordinates" in the world specific enough to confirm or disconfirm the assertion or denial of fact at the time.
An elementary descriptive proposition is true if and only if the state of affairs that is asserts (or denies) is the case (or not the case). That's a matter of checking at the specific coordinates.
If you can check those "co-ordinates" at different "scales" (resolutions), might an assertion be confirmed at one level and denied at another?
Well someone would say a cat is a dog and then bring both in to show you and you would compare them and determine they represented an inequality (ie inequality is a math principle) and call BS...
You have to use math to overcome a rote taught falsehood...
How to do this is a learned cognitive ability ideally trained from a very young age:
https://youtu.be/gCxrkl2igGY
If you can check those "co-ordinates" at different "scales" (resolutions), might an assertion be confirmed at one level and denied at another?
Different propositions can be framed around the same set of circumstances, just as different routes can lead to the same destination.
A two-valued (binary) system of propositional logic is assumed unless otherwise stipulated, just as the decimal system of numbers is assumed unless otherwise specified, Euclidian geometry in ordinary contexts. (Other systems can be founded on different rules.)
This goes back to ancient Greece in the West. See Law of thought.
These are the basic rules of logic.
The rule of identity states that p = p (equivalence).
The rule of non-contradiction states that p ≠ not-p, that is, not both p and not-p.
The rule of the excluded middle states that p or not-p is true, but not both.
The rule of inference is if p, then q.
The rule of transitivity states that if p then q, and if q then r, then if p, then r.
The propositional calculus is built on these stipulations as rules.
Other systems can be founded on different rules, but they are not in general use.
I'd need to look at some real world examples involving maps.
One can think of description in terms of topology — the way signal topology corresponds to physical topology, for instance.
A schematic of an electronic circuit does not correspond to the circuit's physical layout, only to its network topology. A schematic is not a map.
A map of geographic features corresponds to their physical layout. A map drawn on a scale of 1:1 would be as large as the area it describes. Smaller scales come at the cost of feature generalization. 2D maps of 3D spaces require projection which results in distortion, but this factor is taken into account.
What this has to do with anything in the OP, I do not know.
What this has to do with anything in the OP, I do not know.
The logic of depiction. How humans use symbols to orient wrt to the world.
Ryan, Tom is presenting one view of the philosophy of mathematics, rooted in 20th century philosophy, most schools of which, especially the dominant, "mainstream" ones, were quite opposed to the philosophies and traditions of the previous centuries and millennia. James Franklin's book, An Aristotelian Philosophy of Mathematics, which there was a even post about here at MNE a couple years ago may be more congenial.
I think there are some problems with Lars Syll's posts - and other similar ones at Real World Economic Review. They go beyond the popular sport of making fun of modern mainstream economics, to attacking a presumed mathematically rigorous modern mainstream econ, to attacking mathematical ideas and patterns of thought in economics.
(a) It presumes modern mainstream econ is mathematically rigorous, is something congenial to the working mathematician in the street. (Or behind closed doors) Hah hah hah!
(b) It even goes to the point of belittling and deriding mathematical rigor a la classical Euclidean geometry, because of guilt by association with MME I guess, while "Heterodox" econ supposedly goes by the "scientific method", whatever that is. This is nuts.
In the real world, as in physics, people use "unrigorous" math they don't understand all the time. They approach confusing physical, experimental phenomena & unpleasant results often enough ignored or dismissed. Too much of either can be bad- especially in combination, using math you don't understand to approach science you don't understand or can't do good experiments & measurements.
But the problem of MME isn't so complicated. The dominant group tendency, irrespective of the good will of the members of the group, simply isn't interested in economics at all.
This is shown by rejection of heterodox work which is superior both logically and empirically. As is shown by the fall of the postwar "Keynesian" econ, which for all its faults was superior both logically and empirically to today's MME. This is shown above all by the theory of money of MME, which overall, nobody has ever or could ever understand and has no empirical use.
But there are truth-seekers and seeking in the vast decaying empire of MME, there are valid insights and methods which should not be discarded. There are worse economists than the MMEers (e.g. UBIers)). The point is to absorb MME, rewrite it in more philosophical, scientific, logical and empirically valid terms, more strongly tied to neighboring disciplines, like math, like philosophy - not to constantly kvetch about MME, even the good parts. Keynes had it just right when he called his book a General Theory.
BTW Matt Franko is quite right when he mentions mathematical maturity in connection with MMT. The MMT guys & gals are good mathematicians, think mathematically, especially when they are doing stuff with words, when they might not think they are doing/think mathishly. This isn't unknown. Faraday was self-educated and always bemoaned his ignorance and inability at math. An admittedly better, or at least purer, or surely more knowledgeable and educated mathematician, Maxwell, knew better and said that Faraday's work was math, even if he didn't know it.
We should always be challenging the mainstream's qualifications in this regard...
They are not qualified ... They do not possess the requisite cognitive abilities to be working in material systems...
Good points, Calgacus.
Lars is upfront about being an advocate for Critical Realism, which is a sort of neo-Aristotelianism. I have critiqued it in comments on other blogs.I am fond of Aristotle myself, but the issues he was dealing with were different from the critical realists and it doesn't seem to be that they have come to grips with the traditional issue around terms like "causal powers., which I find cringeworthy.
Bill Mitchell and Steve Keen have both either stated or implied that they are better mathematicians that the econometricians that pride themselves on rigor over relevance.
The issue over what constitutes scientific explanation. Must scientific explanation be based on causality or instrumentality. Both are concerned with correct prediction but the former view holds that there must be some casual transmission set forth in the explanation, whereas instrumentalists are OK with black boxes that produce correct results even if the assumptions are unprovable or even unrealistic. Back to Aristotle v. Hume and causation v. correlation. Jason Smith has just put up a part one of a series arguing that the latter is what scientists actually do. I'll post links to the series when all the parts are up.
All rigorous thought is based on a logical structure that is implicit, but which rigorous thinkers are aware of, check as they go, and critique before publishing. This is true when math is part of the logic. Debate is about both logical-mathematical rigor and evidence for claims.
Alfred Marshall:
Balliol Croft, Cambridge
27. ii. 06
My dear Bowley …
I know I had a growing feeling in the later years of my work at the subject that a good mathematical theorem dealing with economic hypotheses was very unlikely to be good economics: and I went more and more on the rules — (1) Use mathematics as a short-hand language, rather than as an engine of inquiry. (2) Keep to them till you have done. (3) Translate into English. (4) Then illustrate by examples that are important in real life. (5) Burn the mathematics. (6) If you can’t succeed in 4, burn 3. This last I did often …
Your emptyhandedly,
Alfred Marshall
https://larspsyll.wordpress.com/2016/10/06/economics-departments-need-to-install-smoke-detectors/
Many hold that the objective of science is not merely to predict outcomes regularly but to explain the regularity, holding that without such explanation, confidence in the regularity is a matter of assumption rather than reason and could be due to luck or chance. The justification for this argument is that this is the reason for doing science. Humans are regularly fooled by their assumptions, and the scientific method was designed to reduce the potential for that. Causal inference in statistics is a big issue in medicine, where lives are directly dependent on it. It is not so much of an issue in econometrics even though many lives are indirectly dependent on it.
Now the emphasis is on the math — "Where's your model." Data is in the background. Many economists don't even publish the data sets they develop because they are proprietary. Referees just look at the model and assume the data. Reinhart and Rogoff got caught up in controversy with a grad student that had requested the data and was provided it showed mistakes. Bill Mitchell added that the data proved his contention that they did not take different monetary systems in place over the series, which was key to the outcomes. This was a huge embarrassment not only for R&R but also the whole economics profession, given the policy implications of the model as an argument for austerity instead of "debt-financed" stimulus.
continued
continuation
Economists begin by admitting the their models are simplifications that are based on "stylized facts" and even untrue assumptions, along with cite. par. They say this is justified, since they are abstracting from the "buzzing' bloomin' confusion" of the world to isolate factors that are useful in thinking about the issues. Then they go on to assume illogically that these "useful" insights are real influences relevant to policy formulation. When outcomes don't support the models, they fall back on the no true Scotsman fallacy/ involving circular reasoning, or the bring in the ad hoc rescue fallacy to "tweak" the model.
A lot of what's wrong with economics can be shown by using only logical fallacies and revealing cognitive biases, often related to ideology. But there are also actual issues that are at stake, too, not only wrt economics but also philosophy of science, epistemology, psychology, sociology, action theory, evolutionary theory, ethics, systems theory, and consilience.
I don't want to suggest or pretend that the enduring questions and contentious areas around these debate are anywhere near settled. They are still raging with many involved in them unaware of the history and therefore they repeat mistakes that where previously exposed. Or they claim to "discover" or "invent" what had already been brought to light previously.
These kerfuffles would not interesting if economics were not taken to be a policy science and economists to be policy scientists. But they are, and their wacky ideas and methods are driving the world toward chaos, along with the game theorists running foreign policy based on ideology rather than fact, assuming that they are the standard for rationality.
There are several issue that are foundational to conventional economics, which is basically neoclassical.
1. The first is methodological individualism. The antidote from the heterodox side is institutionalism and systems theory. There are also problem with the action theory assumed in conventional economics in that it is not consilient with findings in biology and psychology, and it ignores ethics.
2. The second is the assumption of natural laws in economics. There are no natural laws governing human behavior. There are regularities but they are not timeless or based on ergodicity. Economics is historical.
3. The third is the assumption of general equilibrium. Keynes showed why economies don't necessarily tend to equilibrium in the neoclassical sense of resource optimization as a result of free play of market forces. Barter-based models are unrealistic in comparison with monetary models. Models based on misunderstanding of money and banking are also flawed, especially when they overlook differences of monetary systems and their effects, or fail to understand the existing monetary system correctly.
4. The fourth is rational optimization. Rational optimization is limited by bounded rationality.
According to heterodox economics, these methodological assumptions are perverse and need to be discarded to put economics on a sound foundation rather than sand. These may not be the only perverse assumptions, of course. Another is the over-simplification involved in cet. par. other than for gadgets. Models based on cet. par. are ahistorical and static.
This is not to say that conventional economics should be jettisoned entirely. For example, there are regularities discernible in human behavior. The problem is weighting the significance of regularity. In psychology there are dispositions and tendencies but not laws. Those dispositions and tendencies can be the basis of regularity in behavior that is discoverable statistically.
Economic policies are deliberately designed to benefit the wealthy at the expense of everyone else. Academia is used to lend legitimacy to a self-serving political agenda by the elite. It's an appeal to authority comprised of carefully vetted 'experts'.
The time for debate is over.
"They are not qualified ... They do not possess the requisite cognitive abilities to be working in material systems..."
Hard to do in a world driven by credentialism and 'expertism', unfortunately hopelessly abandoning scientific method in favour of arguments of authority, this all propelled by stupid and ignorant corporate media platforms.
"Economic policies are deliberately designed"
NO WAY in hell....
There are ‘laws’ governing human behaviour because there are laws governing human beings; we are a part of nature. I don’t know what the psychologists are thinking or looking at?
One of the most obvious ‘law’ in a human being is ‘conscience’. Putting aside the origin of the voice of conscience for a moment, it is also obvious that if people really did follow it a little more faithfully, they wouldn’t get into any trouble at all; they would learn the ‘good’ lessons instead of the ‘bad’. Remember – this is your voice, coming from you. Conscience is a strong, tactile, stable, sentient, wise, highly illuminated guiding rope - that takes everyone back home; to safety. Back to the Self as it turns out. Now tell me - why should a human being have to listen to anyone else; or go to anyone else? The human conscience transcends culture. One of its ‘laws’ are – ’do no harm. If you want to be strong, be gentle. If you want to wise, be simple. If you want to be rich, be kind’. Conscience has many laws, all to do with clarity and compassion – life. Consciousness. These laws spring out of the nature of consciousness and condition the human personality.
If you want a rudder, compass and map – you have one. Why on earth would anyone ‘vote’ for anyone else to take charge of the affairs of a Nation, when it is obvious they have thrown their conscience, their integrity, away? They are not worthy. People learn through touching the good in themselves and they learn through touching the bad in themselves. Which learning method should we respect?
When conscience leads a person back to the Self, to You – then you realise you have a whole human personality at your disposal with which to interface with the world. You can use that personality for greed and selfishness, turn it into a demon that takes life for power; or use it for what it is meant to be used for. Conscience will guide you to exactly where you need to be. Looking down into the world of the persona is one thing. Looking above, the Ageless Wisdom has always said - the Self is focused on only one Sun, the seat of all that is both law and lawless (revised law)– Kabir laughed a lot!
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