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In physics, the term 'bootstrap model' is used for the class of theories that assume that very general consistency criteria are sufficient to determine the whole theory completely.
In the 1960s and '70s, an ever-growing list of strongly interacting particles — mesons and baryons — caused some physicists to question the distinction between composite and elementary particles. In particular, Geoffrey Chew and others advocated "nuclear democracy", which foreswore the idea that some particles were more elementary than others. Instead, they sought to derive as much information as possible about the strong interaction from plausible assumptions about the S-matrix, which describes what happens when particles of any sort collide. It is so difficult to find formulas for a nontrivial S-matrix obeying these assumptions that some believed there might be a unique solution. This led to a bootstrap program often associated with the phrase "the analytic S-matrix".
This bootstrap program had limited success, and it fell out of favor with the rise of quantum chromodynamics. It is now believed that mesons and baryons are made of elementary particles called quarks and gluons.
These are a number of other more successful examples of using general principles to derive specific theories of physics, starting from Einstein's 1905 paper on special relativity. The form of general relativity is almost entirely specified from general principles including the principal of equivalence. There has also been partial sucess in deriving quantum theory from axioms of quantum logic.
Bootstrap principles related to the S-matrix also lie behind Gabriele Veneziano's early work on string theory, which began as an approach to the strong interaction.
More generally, "bootstrapping" refers to any method of reaching higher levels of understanding by building off of lower levels.

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References

R. J. Eden, P. V. Landshoff, D. I. Olive and
J. C. Polkinghorne, ''The Analytic S-Matrix'',
Cambridge U. Press, 1966.