Home > Uncategorized > On logic and science

## On logic and science

from Lars Syll

Suppose you conducted an observational study to identify the effect of heart transplant A on death Y and that you assumed no unmeasured confounding given disease severity L. A critic of your study says “the inferences from this observational study may be incorrect because of potential confounding.” The critic is not making a scientific statement, but a logical one. Since the findings from any observational study may be confounded, it is obviously true that those of your study can be confounded. If the critic’s intent was to provide evidence about the shortcomings of your particular study, he failed. His criticism is noninformative because he simply restated a characteristic of observational research that you and the critic already knew before the study was conducted.

To appropriately criticize your study, the critic needs to engage in a truly scientific conversation. For example, the critic may cite experimental or observational findings that contradict your findings, or he can say something along the lines of “the inferences from this observational study may be incorrect because of potential confounding due to cigarette smoking, a common cause through which a backdoor path may remain open”. This latter option provides you with a testable challenge to your assumption of no unmeasured confounding. The burden of the proof is again yours.

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.

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. January 1, 2021 at 6:54 am

As a description of the logic of science this is incorrect.

“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.”

Science theorising is indeed logical. The impact it has had over recent centuries should be sufficient proof of that. But there wouldn’t be anything particularly logical in “looking at” separate parts. And it is the antithesis of logic to “suppose” to be able to predict the behaviour of the whole. That is not logic and it is not how science theorises.

Now if someone makes a claim—as Lars here—it is up to them to support it, to provide some evidence or, at the very least, an illustrative example. However, since this misunderstanding of science is common among social scientists, let me provide an example to show how wrong it is.

Newton’s second law, F=ma, says force equals mass multiplied by acceleration. It is a theory which wonderfully predicts behaviour of rockets and so on.

Acceleration itself equals distance divided by time squared (near enough for present purposes). So the parts Newton should have “examined” are mass, distance and time. But there is no agreed definition of mass. You can examine it as you like; they built that Large Hadron Collider to examine it—long after Newton, moon landings etc, etc. Examining mass is evidently irrelevant to the behaviour of the whole.

What of distance? What is it that you will examine? Nowadays space is thought to mostly consist of dark matter and energy which, they tell us, can’t be examined.

And finally time. Nobody knows what time is.

So did Newton examine mass, time and distance and use this acquired atomistic knowledge to write his second law? It is, of course, nonsense. Parts are not examined to form a theory.

Yes, the whole is constituted from its parts. But science theory only says how those parts relate to each other. It never says what the parts “are.” For science theory, the parts only exist in their relationships, not on their own.

Everyone understands physics theory irrespective of language, religion, and political inclination. The same goes for economic theory—a common body of theory, the world over. How is this possible? Because the theory expresses relationships. Quarrelling over the definitions of the interrelated parts is just a distraction; it will deliver no new theory. If you do want to examine a part then you must find the relationships of its constituent parts.

Where does the logic come in? In the deduction of some consequences from the theory—which may then be sought in reality with a view to applying or testing the theory. Economic theory is successful (to the extent it is) because it is scientific and logical. The other social sciences never adopted the scientific method and have consequently failed to develop useful theory.

• January 3, 2021 at 4:52 am

I support pfeffertag. Economists who are critical of neoclassical economics often criticize that it is produced by physics envy. It is roughly right. But, the understanding of those criticizers is quite superficial. They do not understand the real nature how physics succeeded as a modern science and what its real nature is.

• January 4, 2021 at 7:30 pm

There is a huge difference between the “Demand function” x = f(p) and the Demand function p = f(x).

In his Principles of the Theory of Wealth Augustin Cournot, Chapter IV pp. 1-2 had this to say about subjective utility and market prices: ” “[I]f the price is to be considered at which each buyer is willing to buy, and the price at which each seller is willing to sell, what becomes of the pretended principle? It is not, we repeat, an erroneous proposition – it is a proposition devoid of meaning.”

A proposition devoid of meaning, not matter what logic follows from it, remains devoid of meaning.

I think I am agreeing with the gist of what Lars Syll is saying about science vs the axiomatic-deductive method of ‘Offer’ curves conjoined to market prices.

• January 5, 2021 at 3:09 am

What kind of logical relations between the difference of x =f(p) and p = φ(x) and your conclusion supporting Lars Syll? Would you explain in what context Cournot made the remark you have cited?

2. January 1, 2021 at 10:00 am

I don’t have any problems with Lars Syll’s analysis as it stands. In other word I agree but I would like to see an omission (at least as occurs here) addressed. To oversimplify, this is to do with the issue that;

(1) hard science studies the physis;
(2) social science studies the nomos; and
(3) economics studies the physis plus the nomos.

Now of course, I said this was an oversimplification as other social sciences (not just economics) can study physis plus nomos. But in economics, the complexities implied in the “physis plus nomos” conglomerate have perhaps thew most extensive, ramifying, reflexive, feed-back implications. To redo economics properly, so far as is humanly possible, will be an enormously difficult undertaking at the theoretical level.

In economics, we think of the physis as the real economy and we should turn think of this real economy as a complex, adaptive, dissipative system within the real environment. In turn, we should think of the nomos as culture, custom, legal law, institutions, administration and procedures as a “pure” and formal/social nomological machine (following Nancy Cartwright and Lars Syll) but which as a “pure” nomological machine follows said custom, legal law, regulation etc, and and either self-references or tends to refer/defer to ideology and dogma as further parts of the nomos. The full nature of economics is thus the study of the interaction of the (culturally sanctioned and formal, the nomos and the real, the physis. It is only by conceptualizing economic ontology in this fashion (I argue) that we can systematically and scientifically analyze it.

Again to keep it much simplified, we are in economics pitting rules and precepts (of the nomos or culture) against the discovered fundamental laws of the real world up to and including the arenas of biology and ecoology. Where a precept of the prescriptive nomos (like endless capitalist growth) comes into collision with fundamental laws of earth systems and ecology (in this case) then the precept of the nomos must be abandoned and the principle of the fundamental law of nature obeyed.

Francis Bacon already knew this: “Nature to be commanded must be obeyed..”

But it seems that the hardest thing for humans to do is to abandon beliefs and face real facts.

• January 3, 2021 at 4:14 am

In economics, we think of the physis as the real economy and we should turn think of this real economy as a complex, adaptive, dissipative system within the real environment. (Ikonoclast on January 1, 2021 at 10:00 am)

The full nature of economics is thus the study of the interaction of the (culturally sanctioned and formal) nomos and the (real) physics. (Ikonoclast on January 1, 2021 at 10:00 am, partly modified by me)

Ikonoclast seems to grasp the real problem for economics, but he may be considering only the ontology. It is necessary to know the real difficulty of attacking this complex system and think of the strategy how to overcome it with our limited capabilities of logic and analysis. This is the question of epistemology. We should create (or invent) appropriate tools to break through these difficulties.

We have discussed this problem as comments in Asad Zaman’s blog article. They count more than 119 to date.

3. January 1, 2021 at 12:41 pm

Lars says: “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”

Pfeffertag says: “As a description of the logic of science this is incorrect”.

Lars actually agrees with this. He goes on advocate ‘human logic’, which is what pfeffertag is saying real scientists use The issue then comes back to whether model-pushing economists are real scientists.

I join the argument in that I’ve been in the scientific business of exploring the logic of logic and over 65 years coming to some understanding (doubtless imperfect but better than none) first of what ‘science ‘ is, then ‘scientific logic’ and then ‘human logic’, and finally of what google suggests many people have described as “the art of living together”.

Lars say: “Mathematics and logic cannot establish the truth value of facts. Never has. Never will”. Quite right. Even true logic can only establish the truth value of facts if its premises are true, and as Ken Zimmerman insists, the facts are manufactured: put into language by us.

Pfeffertag says: “there wouldn’t be anything particularly logical in “looking at” separate parts. … And finally time. Nobody knows what time is”. Exactly. Logic is about words. We have the word ‘time’ but we don’t know what it means. We have the word ‘part’ but see parts as things rather than relationships within and communication between subsystems of systems.

I say: science cannot be what scientists do when even scientists do not recognise the significance of their own use of language, dismissing information science as a mere artifact of a specialist technology and likewise the physiological justification of psychological differences.

What has come out of information science has been the possibility of using spare capacity to allow each other to pursue our own dreams by cutting each other (and our environment) a bit of slack: hence the development of broadband digital technology on the internet and the Christian virtue of a paradigmatic family, prioritising mercy and brotherhood over physical enforcement of what the enforcer regurgitates as ‘justice’.

Fashionable misinformation and denial of the difficult is of course much easier than trying to think creatively about how to resolve the difficulty. If you have never grappled with the technical difficulty of Algol68 computer programming you will not understand how it made intractable problems resolvable, nor probably have noticed how cars became easier to drive as more and more of their functions were automated. As G K Chesterton famously put it, “Christianity has not been tried and found wanting: it has been found difficult and never tried”.

For our New Year resolution I propose we all stop arguing and start learning from each other,: not so much what we think as why we think it. [As against what most of us think others think].

Most of my own arguments are spelled out in Chesterton’s “Orthodoxy”, which I found difficult, but tried over twenty years and still don’t really find wanting. The bits I would like to dwell on are his introduction of pfeffertag’s ‘time’ to the defence of democracy: “tradition asks us not to neglect a good man’s opinion, even if he is our father”. (The “our father’s father …” argument takes us back to evidence persisting from the beginning of time). The second bit concludes a
defence in chapter V of his “primarily loyalty” [to men rather than money?]. “Men did not love Rome because she was great. She was great because they had loved her”.

4. January 1, 2021 at 1:24 pm

Happy New Year to you too, Ikonoclast. As it was unsaid, I hope it goes without saying that that goes for Lars, Pfeffertag, other contributors to this blog and “all men of good will”.

And a final thought about Chesterton. “Men did not love him because he was right. He was, but was humorous and kind because he loved them”.

5. January 1, 2021 at 3:44 pm

pfeffertag. To mass, time and distance, Newton needed Kepler’s laws. In addition, his formula gives answers accurate up to 7 decimals and yet it is wrong; there is no such force of gravity. Anyway, happy New year.

6. January 2, 2021 at 9:00 am

Dominique, your saying “there is no such force of gravity” suggests you may have missed my earlier sharing of someone referring to “second-order cybernetics”: the point being our discussion of reality is “second-order” in that it is in terms of words.

‘Force’ is a word that Newton associated with ‘mass’, but to cut a long story short, the mass has evolved from localisation of ‘energy’ (a word used to explain change) and it is a philosophical decision (a logical rather than a scientific one) whether to root what we call ‘evolutionary change’ in the Conservation of Energy or in a localised God (explaining that localisation as a trinitarian cycle of internal changes, much like the solid-liquid-gas phases we see as ice-water-vapour). Einstein didn’t prove that force doesn’t exist: he just explained the effects of Newtonian energy of motion more accurately in terms of energy density, which is more consistent with an expanding universe, evolution and a Big Bang form of Creation.

7. January 2, 2021 at 8:01 pm

Davetaylor: ” Einstein didn’t prove that force doesn’t exist: he just explained the effects of Newtonian energy of motion more accurately in terms of energy density, which is more consistent with an expanding universe, evolution and a Big Bang form of Creation.”

I do not claim that Einstein prove that force does not exist but rather a force with infinite range holding the planets in their orbits does not exist. However his space-time paradigm runs into trouble in quantum gravity. Elsewhere when we map a 3-D reality into a 2-D surface of a black hole, gravity disappears. Now does a 2-D configuration is a true representation of a 3-D world remains to be seen. Hopefully, the Holographic Principle will shine more light on the subject.

8. January 3, 2021 at 6:48 pm

Logic is an effective tool of science…and a potentially destructive means of its search for truth.

The willingness and ability to consider conceptual opposition/illogical thinking regarding present orthodoxy and the means of resolving orthodoxy’s problems has historically been a primary signature of accomplished paradigm change.

9. January 4, 2021 at 1:21 pm

Mainstream’s obsession with the “scientific” approach is not without irony. Despite the fact that this methods presupposes a design of the economy that is static in its dynamics, researchers try to outwit one another with ever fancier twists and tweaks to their models to keep up with latest actual events (such as the Covid pandemic) thus implying that the economy is, in fact, not static at all.
It is thus really fun to observe the passion and eagerness with which mainstream economists invalidate their own models of the past and also (unconsciously) invalidate their pet rational expectations approach when ignoring the fact that (promised) changes to their models that are not relayed to their “rational” agents ridicule the whole idea of forward lookingness and rational expectations. It is also easy to spot why they are not aware of the irony of their doing. Listening, for example, to the ongoing AEA presentations you realise that researchers and discussants are so absorbed with formulating and “solving” their models that there is no capacity left for reflecting on what they are actually doing.

10. January 5, 2021 at 12:19 pm

Dominique, Craig and Christian are all saying interesting things here. Dominique, I accept your clarified reading of Newton, and comment about 3D gravity disappearing when mapped into 2D. Chesterton’s argument for being able to judge depth by triangulation or “stereoscopic vision” doesn’t work when the focus is so far away, but I think Craig’s ” willingness and ability to consider conceptual opposition/illogical thinking” helps. It is illogical to assume that because gravity disappears off our map it therefore ceases to exist, but the conceptual opposition to light going into the black hole is to see it as coming out: our seeing light being formed from homogeneous dark energy,or in biblical language God saying “Let there be light”. Christian is spot on when he says “Listening, for example, to the ongoing AEA presentations you realise that researchers and discussants are so absorbed with formulating and “solving” their models that there is no capacity left for reflecting on what they are actually doing”.

That was what Chesterton was complaining of in 1908 in terms of his 1904 physiological psychology: academics using only half of their brain. “Reason seeks to cross the infinite sea, and so make it finite. The result is mental exhaustion. … The madman of experience … is in the clean and well-lit prison of one idea … That unmistakable mood or note I hear from Hanwell [a lunatic asylum] I hear also from half the chairs of science and seats of learning today”.

Though intentionally humorous, the point of this is not to ridicule science but to suggest the cure: looking at the real world as well as the map. “[The ordinary man’s] spiritual sight is stereoscopic: he sees two different pictures at once and yet sees all the better for that.
… The circle returns upon itself and is bound. The cross [the Argand diagram map of the complex number field] opens its arms to the four winds; it is a signpost for free travellers”.

• January 5, 2021 at 12:47 pm

Reading back, I see my “map” and “reality” are more or less what Ikonoclast referred to above as “nomos” and “physis”, i.e. both dimensions of the complex number, not one or the other. What Ikonoclast might reflect on is mistaking the one for the other leading to paradox rather than “collision”, and on the meaning of the negatives: misinformation in the nomos and debt or shortage in the physis, perhaps both in a complex reality.

11. January 13, 2021 at 4:37 pm

The complexity you mention is nowhere better illustrated than in this from Bertrand Russell on the ‘first cause’ debate. The first cause argument asserts that everything we see around us is causal in nature, therefore if one goes up the chain of causality, one will encounter the First Cause, and that would be God.

Russell criticizes this argument by quoting a story from his days of youth.

To come to this question of the existence of God, it is a large and serious question, and if I were to attempt to deal with it in any adequate manner I should have to keep you here until Kingdom Come, so that you will have to excuse me if I deal with it in a somewhat summary fashion. You know, of course, that the Catholic Church has laid it down as a dogma that the existence of God can be proved by the unaided reason. That is a somewhat curious dogma, but it is one of their dogmas. They had to introduce it because at one time the Freethinkers adopted the habit of saying that there were such and such arguments which mere reason might urge against the existence of God, but of course they knew as a matter of faith that God did exist. The arguments and the reasons were set out at great length, and the Catholic Church felt that they must stop it. Therefore, they laid it down that the existence of God can be proved by the unaided reason, and they had to set up what they considered were arguments to prove it. There are, of course, a number of them, but I shall take only a few. [I include just one, here.]

THE FIRST CAUSE ARGUMENT

Perhaps the simplest and easiest to understand is the argument of the First Cause. (It is maintained that everything we see in this world has a cause, and as you go back in the chain of causes further and further you must come to a First Cause, and to that First Cause you give the name of God). That argument, I suppose, does not carry very much weight nowadays, because, in the first place, cause is not quite what it used to be. The philosophers and the men of science have got going on cause, and it has not anything like the vitality it used to have; but, apart from that, you can see that the argument that there must be a First Cause is one that cannot have any validity. I may say that when I was a young man and was debating these questions very seriously in my mind, I for a long time accepted the argument of the First Cause, until one day, at the age of eighteen, I read John Stuart Mill’s Autobiography, and I there found this sentence: ‘My father taught me that the question, “Who made me?” cannot be answered, since it immediately suggests the further question, “Who made God?” That very simple sentence showed me, as I still think, the fallacy in the argument of the First Cause. If everything must have a cause, then God must have a cause. If there can be anything without a cause, it may just as well be the world as God, so that there cannot be any validity in that argument. It is exactly of the same nature as the Hindu’s view, that the world rested upon an elephant and the elephant rested upon a tortoise; and when they said, ‘How about the tortoise?’ the Indian said, ‘Suppose we change the subject.’ The argument is really no better than that. There is no reason why the world could not have come into being without a cause; nor, on the other hand, is there any reason why it should not have always existed. There is no reason to suppose that the world had a beginning at all. The idea that things must have a beginning is really due to the poverty of our imagination. Therefore, perhaps, I need not waste any more time upon the argument about the First Cause.

Russell’s attack on the ‘First Cause Argument’ appears to be inconclusive at best. But his correction to all those who know logic and science always provides some remedy is staggeringly direct and useful.