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Conservatism is a political philosophy based on skepticism of both the abilities and motives of human beings. Conservatives therefore oppose institutions that have been designed by (fallible) human reason, in favor of institutions that evolved gradually over hundreds and thousands of years.
Most conservatives are inimical to government solutions to society's problems because these solutions rely on the ability of bureaucrats to make decisions for millions of strangers. Even if a bureaucrat had the vast knowledge and superior reasoning necessary to make those decisions, which he doesn't, he could not be trusted with the power that would be necessary to implement them. Being human, he would be naturally susceptible to abuse and corruption. Far better to leave things to the traditional and more-or-less decentralized institutions of church, family, and marketplace, and to the individual.
(There is a strain of conservative that, in contrast, is fine with using the power of the state to strengthen the authority of traditional institutions: it’s just a matter of having the right people in charge of the state. They are backbenchers, outside both the leadership and the mainstream of the conservative movement, but they do exist.)
Some activities, by their nature, must be carried out by government, so we have to have one. But since humans cannot be trusted with power, governmental authority should be limited to enumerated powers and subject to checks and balances. Federalism is the ideal form of government because solutions evolve via trial, error, and competition between the states, rather than being designed and imposed from above.
These ideas were prominent in the thinking of the Founding Fathers, hence the reverence for those worthy gentlemen. Madison put it best in The Federalist #51, where he wrote, “If men were angels, no government would be necessary. If angels were to govern men, neither external nor internal controls on government would be necessary. In framing a government which is to be administered by men over men, the great difficulty lies in this: you must first enable the government to control the governed; and in the next place oblige it to control itself. A dependence on the people is, no doubt, the primary control on the government; but experience has taught mankind the necessity of auxiliary precautions.”
The modern conservative agenda, to reign in the Federal Government where it has usurped powers rightfully belonging to states, churches, families, markets, and individuals, flows logically from this philosophy.