More abstractly, one talks about the product in category theory, which formalizes these notions.

Domain theory formalizes the intuitive ideas of approximation and convergence in a very general way and has close relations to topology.

SCOT is not only a theory, but also a methodology: it formalizes the steps and principles to follow when one wants to analyze the causes of technological failures or successes.

an isomorphism ) between individual objects ( not entire categories ) is referred to as a " natural isomorphism ", meaning implicitly that it is actually defined on the entire category, and defines a natural transformation of functors ; formalizing this intuition was a motivating factor in the development of category theory.

In Carl Jung's theory of the ego, described in 1921 in Psychological Types, intuition was an " irrational function ", opposed most directly by sensation, and opposed less strongly by the " rational functions " of thinking and feeling.

Indeed, one of Hilary Putnam's arguments for his version of functionalism relied on the intuition that such alien creatures would have the same mental states as humans do, and that the multiple realizability of standard functionalism makes it a better theory of mind.

That's not a serious issue for a modern axiomatic mathematician, since the implication of axiom is now a starting point for theory rather than a self-evident plank in a platform based on intuition.

The above intuition of domains being information orderings will be emphasized to motivate the mathematical formalization of the theory.

For most of their time, marketing managers use intuition and experience to analyze and handle the complex, and unique, situations being faced ; without easy reference to theory.

Order theory captures the intuition of orders that arises from such examples in a general setting.

Recent ideas about higher algebraic stacks and homotopical or derived algebraic geometry have regard to further expanding the algebraic reach of geometric intuition, bringing algebraic geometry closer in spirit to homotopy theory.

More generally " action at a distance " describes the break between human intuition, where objects have to touch to interact, and physical theory.

This intuition, in the context of denotational semantics, was the motivation behind the development of domain theory.

String theory, a leading candidate for a quantum theory of gravity, uses the term quantum geometry to describe exotic phenomena such as T-duality and other geometric dualities, mirror symmetry, topology-changing transitions, minimal possible distance scale, and other effects that challenge our usual geometrical intuition.

Stephen Yablo's ( 1998 ) response is to provide an error theory to account for the intuition that zombies are possible.

When reviewed in the light of contemporary standards of logical precision, it becomes clear that Lewin had the correct intuition, even though he did not have the benefit of a highly developed terminology of definition theory or modern day symbolic logic.

In the first chapter, he distinguishes two broad schools of ethical theory — those whose principles are defended by appeals to intuition and those whose principles are defended by appeals to experience.

One can also construct relationships which are made to agree with constraint restrictions arising from theory or to agree with common sense / intuition.

Until experimental proof of atoms was later provided in the 20th century, the atomic theory was driven largely by philosophical considerations and scientific intuition.

The semantic theory of humour is designed to model the native speaker's intuition with regard to humor or, in other words, his humor competence.

procedures change rapidly and parental confidence probably exceeds anything warranted by established psychological theory.

To guard against the tyranny of a numerical majority, Calhoun developed his theory of `` concurrent majority '', which, he said, `` by giving to each portion of the community which may be unequally affected by the action of government, a negative on the others, prevents all partial or local legislation ''.

And it is clearly argued by Lord Percy of Newcastle, in his remarkable long essay, The Heresy Of Democracy, and in a more general way by Voegelin, in his New Science Of Politics, that this same Rousseauan idea, descending through European democracy, is the source of Marx's theory of the dictatorship of the proletariat.

Analogously, anyone who argues that Einstein's theory of gravitation is simpler than Newton's, must say rather more to explain how it is that the latter is mastered by student-physicists, while the former can be managed ( with difficulty ) only by accomplished experts.

That such deficiencies existed within Ptolemy's theory was not discovered de novo by Copernicus.

In his study Samuel Johnson, Joseph Wood Krutch takes this line when he says that what Aristotle really means by his theory of catharsis is that our evil passions may be so purged by the dramatic ritual that it is `` less likely that we shall indulge them through our own acts ''.

In the face of a clear judgment from archaeology, therefore, it became impossible for a time for scholars to re-adopt the `` shore settled by '' theory.

J. T. Shotwell was appalled by such spurious history as that which attributed the fall of the Carolingian empire to the woolen trade, and he urged Adams to `` transform his essay into a real history, embodying not merely those facts which fit into his theory, but also the modifications and exceptions ''.

However, they do demonstrate the presence of large normal pressures in the presence of flat shear fields which were forecast by the theory in the first part of the paper.

Sample areas in the new investigations were selected strictly by application of the principles of probability theory, so as to be representative of the total population of defined areas within calculable limits.

A state, the highest form of human organization in fact and theory, could be subjected to Law only by a manifestation of self-will, or consent.

The displacement ( at least to a considerable extent ) of the ethical jurisprudence of the seventeenth and eighteenth centuries by positivism reshaped both international law theory and doctrine.

Philosophy can prevent the working scientist from becoming slothful and self-content by noting the assumptions and level at which a hypothesis or theory is framed.

The theory claims to show by analysis that when we say, `` That is good '', we do not mean to assert a character of the subject of which we are thinking.

On the positivist theory, everything I sought to express by calling it evil in the first case is still present in the second.

In these circumstances, since what was expressed by the remark when first made is, on the theory before us, simply absent, the remark now expresses nothing.

-- On the basis of a differentiability assumption in function space, it is possible to prove that, for materials having the property that the stress is given by a functional of the history of the deformation gradients, the classical theory of infinitesimal viscoelasticity is valid when the deformation has been infinitesimal for all times in the past.

But then this theory confesses that it is completely at a loss as to how the image can possibly be received by the brain.

It is borne out also by the absence of any developed theory about how sin passes from one generation to the next.

Thus, while altruistic persons may under some circumstances be outcompeted by less altruistic persons at the individual level, according to group selection theory the opposite may occur at the group level where groups consisting of the more altruistic persons may outcompete groups consisting of the less altruistic persons.

Group selection theory has criticized by many other evolutionary scientists.