By Alfred North Whitehead

Symbolic Reasoning allied to dull A lgebra. the manager examples of such platforms are Hamilton sQ uaternions, Grassmann sC alculus of Extension and Boole sS ymbolic common sense. Such algebras have an intrinsic worth for separate special examine; they are also worthwhile of a comparative research, for the sake of the sunshine thereby thrown at the common conception of symbolic reasoning, and on algebraic symbolism particularly. The comparative examine unavoidably presupposes a few earlier separate learn, comparability being most unlikely with no wisdom. therefore after the final ideas of the total topic were mentioned in booklet I. of this quantity, the rest books of the quantity are dedicated to the separate learn of the Algebra of Symbolic good judgment, and of Grassmann sC alculus of Extension, and of the tips serious about them. the belief of a generalized perception of house has been made well-known, within the trust that the homes and operations keen on it may be made to shape a uniform approach to interpretation of a number of the algebras. hence it really is was hoping during this paintings to express the algebras either as platforms of symbolism, and in addition as engines for the research of the chances of idea and reasoning attached with the summary normal proposal of house. A ordinary mode of comparison.between the algebras is hence instantly supplied by way of the cohesion of the subject-matters in their interpretation. The designated comparability in their symbolic buildings has been adjourned to the second one quantity, during which it truly is meant to accommodate Quaternions, Matrices, and the final concept of Linear A lgebras. This comparative anatomy of the topic used to be originated by way of B. Peirce spaper on Linear Associative A lgebra, and has been carried ahead by means of more moderen investigations in Germany. Firat learn prior to theN ational Academy of Soienoes in Washington, 1871, and repabliahed within the American magazine of M
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The policy options inevitably must fall into one of two categories: increasing tax collection or decreasing benefits. Immigration falls into the first category, as do increased fertility, greater labor force participation, longer careers, employment of retirees, and higher tax rates. In the second category are such options as raising retirement ages, indexing benefits to prices rather than wages, limiting health care benefits, requiring greater cost-sharing for health care, and means-testing. At RAND, we hope to determine the best ways forward.

In China, it will nearly triple, from 11 percent to 31 percent; in Europe, it will climb from 21 percent to 34 percent. As graying workers exit the workforce, new workers will be needed to replace them. In this respect, the United States should fare relatively well. To maintain a constant labor force between now and 2050, the United States will need to “import” only 330,000 immigrants a year; currently, the United States adds about 1 million immigrants to its population annually. But maintaining a constant labor force will be a huge The policy options inevitably must fall into one of two categories: increasing tax collection or decreasing benefits.

The policy options inevitably must fall into one of two categories: increasing tax collection or decreasing benefits. Immigration falls into the first category, as do increased fertility, greater labor force participation, longer careers, employment of retirees, and higher tax rates. In the second category are such options as raising retirement ages, indexing benefits to prices rather than wages, limiting health care benefits, requiring greater cost-sharing for health care, and means-testing. At RAND, we hope to determine the best ways forward.

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