Why there is no relationship between truth and logic

5 Aug, 2021 at 11:58 | Posted in Theory of Science & Methodology | 7 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.”

But 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.

Logic yields validity, not truth. - Post by Ziya on BoldomaticIn 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. This argument loses me with the strawman definition of analysis:

    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.

    That is a wholly inaccurate account of conceptual or logical analysis. Far from “isolating” elements, analysis is concerned with the relation of elements in a system. The objective of logical analysis is to derive the identification of the necessary and sufficient elements for a system to function together in relation of each component to the others, and from that to gain insight into what is essential and what extraneous to the phenomena of actual systems.
    Your argument would demolish itself if it took up a few examples of successful, powerful analyses. Queuing theory might serve: the four Little theorems provide great insight into a ubiquitous “social” phenomenon. It is true they do not speak to various attendant cultural customs associated with standing in line, but that ability to separate out function from “meaning” is a feature not a bug, if the goal is to figure what intervention to make in a hospital emergency room where people are dying, unseen.
    Very little of your strawman account of analysis would make sense applied to the example of queuing theory.

    • When you operationalize actual systems, don’t you have to include safety margins of 100%, or more? Bridge builders build for twice the load spec? Can you tell a lot of different stories about statics that make predictions within the 100% confidence intervals of the current arbitrary, fickle social bridge-building consensus?
      And isn’t triage ultimately political, too?

      • An anthropologist might be usefully employed in observing and analyzing the social processes of an emergency room, including triage, without invoking, I imagine, an analysis of the queues. What’s your point?
        A designer and builder of bridges must consider a variety of constant, variable and ephemeral forces that may act on and stress the bridges, as well as consider the implications of the materials used in construction aging and corroding. “It’s complicated” and “there’s a lot we do not understand or do not anticipate” are basically unhelpful truisms, in my view. Again, what’s your point?

      • “to gain insight into what is essential and what extraneous to the phenomena of actual systems”
        Isn’t the insight simply a story that becomes popular for any old reason? Data is (unconsciously) cherry-picked (and error margins are ignored) to support whatever current narrative is most highly valued by the political economy of every discipline including physics?

      • “A designer and builder of bridges must consider a variety of constant, variable and ephemeral forces that may act on and stress the bridges, as well as consider the implications of the materials used in construction aging and corroding. “It’s complicated” and “there’s a lot we do not understand or do not anticipate” are basically unhelpful truisms, in my view.”
        Isn’t my point that even after you’ve done all your complicared calculations for stress and aging, you still add a 100% safety factor? Aren’t you admitting “my bridge-building model could be 100% wrong”? Isn’t that added after-the-fact, politically-determined safety margin helpful to an otherwise potentially quite weak theory?

        • I think headlining a “100% safety factor” is fundamentally political, a response to those who will never consider the design on its own, analytic merits and therefore cannot be engaged in terms of whether the design is strong or weak in its reliance on theory. On a deep level and especially at its best, politics delegates decisions that can be reliably made by genuine experts to experts, and reserves to itself practical hedging against uncertainty. So, no, not saying “my model could be 100% wrong” and “nobody knows nuthin’ in this business”, but acknowledging no one knows everything, or even the extent of one’s practical ignorance.
          Roebling, in designing the Brooklyn Bridge, famously designed key elements to be six to eight times what was necessary to carry the load. He did not know that a politically connected supplier would profit by supplying sub-spec steel that would reduce his effective margin to four times, but it was politically helpful in the event to offer that reassurance alongside other measures to make good the deficiency. No one in 1883 understood the aerodynamics of bridges; it was good luck in a way that the open truss work would have minimal interaction with the wind. The caisson on the Brooklyn side had already reached depths capable of killing workers, and no one understood how to manage “the bends” (known at the time as caisson disease) when the other (Manhatten-side) caisson was slated to go deeper still. I do not think the New York caisson ever did reach bedrock as it was supposed to; Roebling made a judgement call, to rest the tower on the compressed sediment, as the Brooklyn tower rests on clay.
          As the bridge has aged and been renovated, it has been necessary to revisit and elaborate the models of how the bridge “works” as a system to understand the implications when steel rusts, cable strands break, sandstone crumbles. Inspections have been continuous on the Brooklyn Bridge since 1901 and numerous component failures have occured and political wrangles over deferred maintenance and renovations gone forward. The Williamsburg and Manhatten bridges were much less conspicuously robust designs — surely a testament to political possibilities opened by experience with suspension bridges.

          • I guess my question is, are there bridge designs existing today that are better theory than the current consensus, but which are dismissed for purely political reasons? The standard “factor of two” safety margin covers up enough faulty theory that you can get away with mocking better analyses on the grounds that “current models are just fine because bridges stay up, don’t they?” (Galloping Gertie excepted?)
            If economists want to be more like bridge builders, shouldn’t they at least double their poverty level estimates?

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