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While studying science I have come across many times loops in logic.for example in survival of the fittest who is fit~who survives and who survives~who is fit. My question is how to deal with these loops.

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  • Sometimes by examining categories. Chicken-and-the-egg problems can be overcome by adding additional information. Natural selection says the egg came before the chicken, because the category chicken is a recent development that evolved from prior, egg-laying categories like dinosaur. Other circular reasoning can be made foundational. Fit survive. Survival is reproduction. Reproduction is self-replication. Self-replication is biological duplication. Biological duplication is biochemical replication. Ad nauseum.
    – J D
    Commented Aug 15, 2022 at 22:05
  • Survival of the fittest was a loose phrase invented by Spencer and used to popularize Darwin's theory. The conceptual loop played no role in the theory itself, so there was no need to deal with it. Nonetheless, Popper took it at face value ("If, more especially, we accept the statistical definition of fitness which defines fitness by actual survival, then the theory of the survival of the fittest becomes tautological, and irrefutable") and had to reverse himself later.
    – Conifold
    Commented Aug 15, 2022 at 23:09
  • A more substantive circularity occurs for some theoretical notions in scientific theories, such as force in Newtonian mechanics, where the laws of the theory have to be assumed to test its claims about them, see How did Newton measure forces in his experiments to establish the laws of motion? Sneed called this the problem of theoretical terms, and various approaches have been proposed to resolve it, e.g. by relating the terms to complementary experimental models.
    – Conifold
    Commented Aug 16, 2022 at 7:02

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There are cases in science where it is hard to say where the reasoning is grounded. For example, "survival of the fittest" is meant to convey an impression of general sorts of advantages, but evolutionary theory has come up with so many different and contrasting aspects of evolutionary fitness that "fitest population" has come to be more or less defined as "whatever population survived". However, it doesn't really matter that there is no a priori notion of fitness to appeal to, because fitness is really just a conceptual hook--a way to think about natural selection; it's not essential to the theory. All the theory requires is that sometimes when two populations have minor genetic differences one population thrives and the other fails. There doesn't have to be some overarching universal quality that the surviving populations all have. In some cases it was just the luck to be on the non-volcanic island instead of the volcanic island.

You see similar issues in physics. For example Alfred North Whitehead noted that in Newtonian physics, at the highest level of generality, magnitude of a force is determined by how much it accelerates a given mass, and at the highest level of generality, mass is determined by how much it is accelerated by a given force. This is a form of conceptual circularity, but it isn't a problem in practice, because in any application, you have some grounding notion of force or some grounding notion of mass that you can appeal to.

There have also been efforts to break the force/mass loop by defining one independently of the other. Whitehead had a proposal to define magnitude of mass without force by the action of two rotating masses at either end of a tether in empty space. Of course it was generally impossible to carry out experiments like this, so it was more of a conceptual solution than a practical one.

So there are three examples of ways scientists have dealt with a loop:

  1. define it away,
  2. ignore it because it don't matter in practical cases,
  3. or come up with a conceptual way to break the loop, even if there is no practical way to do so.

Scientists are generally concerned with understanding nature rather than with understanding their own methods, so they often give idealized and unrealistic accounts of how science works, and those accounts make their way into popular understanding of science. But the history of science is full of epistemological and foundational difficulties that have to be worked around, often in an ad hoc manner.

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