The relationship between logic and truth

26 Apr, 2020 at 14:20 | Posted in Theory of Science & Methodology | 13 Comments


To be ‘analytical’ and ‘logical’ is something most people find recommendable. These words have a positive connotation. Scientists think deeper than most other people because they use ‘logical’ and ‘analytical’ methods. In dictionaries, logic is often defined as “reasoning conducted or assessed according to strict principles of validity” and ‘analysis’ as having to do with “breaking something down.”

anBut that’s not the whole picture. As used in science, analysis usually means something more specific. It means to separate a problem into its constituent elements so to reduce complex — and often complicated — wholes into smaller (simpler) and more manageable parts. You take the whole and break it down (decompose) into its separate parts. Looking at the parts separately one at a time you are supposed to gain a better understanding of how these parts operate and work. Built on that more or less ‘atomistic’ knowledge you are then supposed to be able to predict and explain the behaviour of the complex and complicated whole.

In economics, that means you take the economic system and divide it into its separate parts, analyse these parts one at a time, and then after analysing the parts separately, you put the pieces together.

The ‘analytical’ approach is typically used in economic modelling, where you start with a simple model with few isolated and idealized variables. By ‘successive approximations,’ you then add more and more variables and finally get a ‘true’ model of the whole.

This may sound like a convincing and good scientific approach.

But there is a snag!

The procedure only really works when you have a machine-like whole/system/economy where the parts appear in fixed and stable configurations. And if there is anything we know about reality, it is that it is not a machine! The world we live in is not a ‘closed’ system. On the contrary. It is an essentially ‘open’ system. Things are uncertain, relational, interdependent, complex, and ever-changing.

Without assuming that the underlying structure of the economy that you try to analyze remains stable/invariant/constant, there is no chance the equations of the model remain constant. That’s the very rationale why economists use (often only implicitly) the assumption of ceteris paribus. But — nota bene — this can only be a hypothesis. You have to argue the case. If you cannot supply any sustainable justifications or warrants for the adequacy of making that assumption, then the whole analytical economic project becomes pointless non-informative nonsense. Not only have we to assume that we can shield off variables from each other analytically (external closure). We also have to assume that each and every variable themselves are amenable to be understood as stable and regularity producing machines (internal closure). Which, of course, we know is as a rule not possible. Some things, relations, and structures are not analytically graspable. Trying to analyse parenthood, marriage, employment, etc, piece by piece doesn’t make sense. To be a chieftain, a capital-owner, or a slave is not an individual property of an individual. It can come about only when individuals are integral parts of certain social structures and positions. Social relations and contexts cannot be reduced to individual phenomena. A cheque presupposes a banking system and being a tribe-member presupposes a tribe.  Not taking account of this in their ‘analytical’ approach, economic ‘analysis’ becomes uninformative nonsense.

Using ‘logical’ and ‘analytical’ methods in social sciences means that economists succumb to the fallacy of composition — the belief that the whole is nothing but the sum of its parts.  In society and in the economy this is arguably not the case. An adequate analysis of society and economy a fortiori cannot proceed by just adding up the acts and decisions of individuals. The whole is more than a sum of parts.

Mainstream economics is built on using the ‘analytical’ method. The models built with this method presuppose that social reality is ‘closed.’ Since social reality is known to be fundamentally ‘open,’ it is difficult to see how models of that kind can explain anything about what happens in such a universe. Postulating closed conditions to make models operational and then impute these closed conditions to society’s real structure is an unwarranted procedure that does not take necessary ontological considerations seriously.

In face of the kind of methodological individualism and rational choice theory that dominate mainstream economics we have to admit that even if knowing the aspirations and intentions of individuals are necessary prerequisites for giving explanations of social events, they are far from sufficient. Even the most elementary ‘rational’ actions in society presuppose the existence of social forms that it is not possible to reduce to the intentions of individuals. Here, the ‘analytical’ method fails again.

The overarching flaw with the ‘analytical’ economic approach using methodological individualism and rational choice theory is basically that they reduce social explanations to purportedly individual characteristics. But many of the characteristics and actions of the individual originate in and are made possible only through society and its relations. Society is not a Wittgensteinian ‘Tractatus-world’ characterized by atomistic states of affairs. Society is not reducible to individuals, since the social characteristics, forces, and actions of the individual are determined by pre-existing social structures and positions. Even though society is not a volitional individual, and the individual is not an entity given outside of society, the individual (actor) and the society (structure) have to be kept analytically distinct. They are tied together through the individual’s reproduction and transformation of already given social structures.

Since at least the marginal revolution in economics in the 1870s it has been an essential feature of economics to ‘analytically’ treat individuals as essentially independent and separate entities of action and decision. But, really, in such a complex, organic and evolutionary system as an economy, that kind of independence is a deeply unrealistic assumption to make. To simply assume that there is strict independence between the variables we try to analyze doesn’t help us the least if that hypothesis turns out to be unwarranted.

To be able to apply the ‘analytical’ approach, economists have to basically assume that the universe consists of ‘atoms’ that exercise their own separate and invariable effects in such a way that the whole consist of nothing but an addition of these separate atoms and their changes. These simplistic assumptions of isolation, atomicity, and additivity are, however, at odds with reality. In real-world settings, we know that the ever-changing contexts make it futile to search for knowledge by making such reductionist assumptions. Real-world individuals are not reducible to contentless atoms and so not susceptible to atomistic analysis. The world is not reducible to a set of atomistic ‘individuals’ and ‘states.’ How variable X works and influence real-world economies in situation A cannot simply be assumed to be understood or explained by looking at how X works in situation B. Knowledge of X probably does not tell us much if we do not take into consideration how it depends on Y and Z. It can never be legitimate just to assume that the world is ‘atomistic.’ Assuming real-world additivity cannot be the right thing to do if the things we have around us rather than being ‘atoms’ are ‘organic’ entities.

If we want to develop new and better economics we have to give up on the single-minded insistence on using a deductivist straitjacket methodology and the ‘analytical’ method. To focus scientific endeavours on proving things in models is a gross misapprehension of the purpose of economic theory. Deductivist models and ‘analytical’ methods disconnected from reality are not relevant to predict, explain or understand real-world economies

To have ‘consistent’ models and ‘valid’ evidence is not enough. What economics needs are real-world relevant models and sound evidence. Aiming only for ‘consistency’ and ‘validity’ is setting the economics aspirations level too low for developing a realist and relevant science.

Economics is not mathematics or logic. It’s about society. The real world.

Models may help us think through problems. But we should never forget that the formalism we use in our models is not self-evidently transportable to a largely unknown and uncertain reality. The tragedy with mainstream economic theory is that it thinks that the logic and mathematics used are sufficient for dealing with our real-world problems. They are not! Model deductions based on questionable assumptions can never be anything but pure exercises in hypothetical reasoning.

The world in which we live is inherently uncertain and quantifiable probabilities are the exception rather than the rule. To every statement about it is attached a ‘weight of argument’ that makes it impossible to reduce our beliefs and expectations to a one-dimensional stochastic probability distribution. If “God does not play dice” as Einstein maintained, I would add “nor do people.” 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 organic parts prevent the possibility of treating it as constituted by ‘legal atoms’ with discretely distinct, separable and stable causal relations. Our knowledge accordingly has to be of a rather fallible kind.

If the real world is fuzzy, vague and indeterminate, then why should our models build upon a desire to describe it as precise and predictable? Even if there always has to be a trade-off between theory-internal validity and external validity, we have to ask ourselves if our models are relevant.

‘Human logic’ has to supplant the classical — formal — logic of deductivism if we want to have anything of interest to say of the real world we inhabit. Logic is a marvellous tool in mathematics and axiomatic-deductivist systems, but a poor guide for action in real-world systems, in which concepts and entities are without clear boundaries and continually interact and overlap. In this world, I would say we are better served with a methodology that takes into account that the more we know, the more we know we do not know.

Mathematics and logic cannot establish the truth value of facts. Never has. Never will.


  1. “As used in science, analysis usually means something more specific. It means to separate a problem into its constituent elements so to reduce complex — and often complicated — wholes into smaller (simpler) and more manageable parts. You take the whole and break it down (decompose) into its separate parts. Looking at the parts separately one at a time you are supposed to gain a better understanding of how these parts operate and work. Built on that more or less ‘atomistic’ knowledge you are then supposed to be able to predict and explain the behaviour of the complex and complicated whole.”
    I am sorry, but this description of “analysis” in science is so wrongheaded as to border on the dishonest — at best, it is setting up a strawman to knock down. The essence of analysis is the attempt to exhaustively identify the necessary and sufficient elements in a system. Far from examining the elements separately, the idea is to examine the relationships among those elements as they drive the behavior of the system or mechanism that they constitute together.
    A more accurate understanding of what analysis proper is, and what it must aim at, would set up a far more damning critique of mainstream economics theorizing than complaining that economics is not vague and fuzzy enough.

    • Wrong-headed or not, I’m not the inventor of that view. It is a standard definition of analysis in science. Have a look, e.g., in Michael Scriven’s classic Reasoning!

  2. Jerry B,
    It was a typo. The “=” in front of the “T” should be a “+”. I first picked up
    this equation from an early Mitchell post, which I’m unable quickly retrieve
    (he’s written so much since 2004), but you can see it in the form I gave
    on Wikipedia – – & they
    make that same error.

    The income side of GDP (ie, GDI) is Y=C+S=T. The expenditure side is Y=C+I+G+(X-M). C is equal to consumption on the expenditure side. It cannot equal consumption on the income side (because consumption is an expenditure).

    This is probably clearer if you go to the GDP Primer – – page 9, & look at Account 1. On the left you see the income side of GDP in words & on the right you see the expenditure side. Note that the C variable on the income side is “Compensation of employees, paid” & on the expenditure side “Personal consumption expenditures”. (You can also find those income & expenditure equations in the BEA literature in their 500+ page Handbook).

    Robert Mitchell & Allan,
    Recognize that GDP measures flow (ie, income & expenditures, an earnings statement) – not stock (ie, assets & liabilities, a balance sheet). It can measure flow with reasonable accuracy from the monthly & annual reports businesses are required by law to submit. Compilation of that data ends up as the nominal GDP (NGDP) reported.

    It’s important to recognize that GDI=GDP, so the “earnings” derived from the GDP measurements are zero, ie, do not & cannot contribute to the economy’s “net worth”. If an economy has a net worth, it’s not coming from the GDP-measured productive economy .

    • Sorry, I can’t get paragraph separation, even with copy/paste of individual paragraphs.

  3. So in a chaotic uncertain world it seems to me that social systems are created to bring order and stability like family, relatives, tribes, klans states, communes, enterprices, banks and central banks etc. The individual relate to all these systems which makes up a network of systems. Would not systems be the relevant object of inquiry as well as the individals psychology driven by social motivation to relate or participate takinga role in different systems?

  4. Jerry,
    You’ve likely seen this before, but is what I consider to be a logical approach to reaching MMT’s conclusions (at least their essence):

    GDP is the measure of our PRODUCTIVE economy. GDP is the sum of household, business and government spending (and likewise the income of those sectors equals that spending, because ALL spending is someone else’s income). Our economy depends on household spending (2/3 of GDP). That spending is limited by household income (which comes only from those three sectors). Business provides that income to the extent demand (business opportunity) exists, and government provides the rest. All that’s important to the economy is maintaining this flow, and with a fiat currency (whose value, by definition, depends ONLY on currency-users perception), there are no limits other than that perception.

    The household spending in GDP includes EVERYTHING that people buy to consume – food, housing, healthcare, entertainment, etc. Looking at the income side of GDP, you find that neither Federal borrowing nor personal or corporate income taxes are part of that income – so they DO NOT (and never have) paid for (or “funded”) that spending.

    I’d like to know if Lars considers this “logical” & if not, what he sees missing.

    I have a bit of a problem with Prof Mitchell’s sectoral balance approach, where he represents the GDP income equaling the GDP expenditures in the form: C+S=T=Y=C+I+G+(X-M), but then says one can drop the C’s to yield S+T=I+G+(X-M)}. But one cannot drop the C’s, because they’re two different variables, the first being “Compensation of employees, paid”, the second being “Personal consumption expenditures”, the two being clearly unequal.

    • Thanks Ed Zimmer. I have always thought the ‘C’ represented private sector consumption in both equations. I will double check my assumption and get back to you on that.

      But obviously your first equation is incorrect or subject to a typo. Taxes do not equal total Income anytime in my life experience. It is not consistent with what I know that Professor Mitchell has ever posited such an equation.

      • Ed, you are just wrong here and you need to go look at what MMT actually says rather than making up equations. You can do your own research easily at Bill Mitchell’s blog.

    • I would say the “C” in both equations is consumption.

  5. So, I have wanted to ask this for a while now, but figure I will ask it now. MMT, at least as taught by Bill Mitchell seems to use a sectoral balances approach to looking at the economy. And then applies certain behavioral assumptions to arrive at estimates of what might happen.
    Is this an example of the type of model you often criticize? Is it a reasonable way to analyze the economy? Is it ever safe to make assumptions about human behavior? Where does this type of analysis tend to fail ?

    • My two cents: MMT assumes the consolidated private sector balance sheet balances to zero, but it really balances to Net Worth or about $120 trillion in the US. As we’ve seen in 2008 and again now, the Fed is prepared to expand its balance sheet as necessary to insure the private sector Net Worth. The Net Worth is created privately and far exceeds official currency volume. MMT pretends Net Worth does not exist.

      • “MMT assumes the consolidated private sector balance sheet balances to zero”

        What it says is the net financial assets (savings) of the private sector (domestic + foreign), equals the net liabilities (debt) of the public sector.

        • I’m saying the Net Worth of the private sector behaves an awful lot like a new net financial asset long before it shows up, if it ever does, as a liability of the public sector. The private sector Net Worth is an implicit claim on central bank liabilities, without needing central bank pre-approval. MMT basically denies that Net Worth exists until it is explicitly backstopped by the central bank, but Jeff Bezos’s wealth is real even if it doesn’t all exist in the form of central bank reserves.

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