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1

Hollander, Paul. Anti-Americanism: Irrational & rational. New Brunswick, NJ, USA: Transaction Publishers, 1995.

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2

Rational numbers: Poems. [Kirksville, Mo.]: Truman State University Press, 2000.

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3

Stein, Jeremy C. Rational capital budgeting in an irrational world. Cambridge, MA: National Bureau of Economic Research, 1996.

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4

Więsław, Witold. Liczby niewymierne. Warszawa: CODN, 1992.

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5

Flannery, David. The square root of 2: A dialogue concerning a number and a sequence. New York, NY: COPERNICUS, 2005.

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6

Antithetik neuzeitlicher Vernunft: "Autonomie-Heteronomie" und "rational-irrational". Göttingen: Vandenhoeck & Ruprecht, 1987.

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7

Bernard, Michael Edwin. Staying rational in an irrational world: Albert Ellis and rational emotive therapy. South Melbourne, Vic: McCulloch Publishing in association with Macmillan Australia, 1986.

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8

May, Leo. Empirical relations between some irrational transcendental mathematical universal constants. Regensburg: Roderer, 1997.

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9

S, Bezuk Nadine, ed. Understanding rational numbers and proportions. Reston, Va: National Council of Teachers of Mathematics, 1994.

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10

Pi. Greensboro, North Carolina: Morgan Reynolds Publishing, 2014.

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11

Daniel, Kent. Market efficiency in an irrational world. Cambridge, MA: National Bureau of Economic Research, 2000.

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12

Mary, Stroh, and Sopris West Inc, eds. TransMath: Making sense of rational numbers. Longmont, Colo: Cambium Learning/Sopris West, 2010.

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13

Rational number theory in the 20th century: From PNT to FLT. London: Springer, 2012.

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14

Lappan, Glenda. Bits and pieces I: Understanding rational numbers. Palo Alto, CA: Dale Seymour Publications, 1998.

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15

Lappan, Glenda. Bits and pieces I: Understanding rational numbers. Palo Alto, CA: Dale Seymour Publications, 1998.

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16

1948-, Silver Edward A., and Stein Mary Kay, eds. Improving instruction in rational numbers and proportionality. New York: Teachers College Press, 2005.

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17

Sublimity: The non-rational and the irrational in the history of aesthetics. New York, NY: Routledge, 2006.

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18

C, Passmore Gloria, ed. H.R.G. Howman on provincialisation in Rhodesia, 1968-1969, and rational and irrational elements. Cambridge: African Studies Centre, 1985.

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19

Caveing, Maurice. L' irrationalité dans les mathématiques grecques jusqu'à Euclide. [Villeneuve d'Ascq]: Presses universitaires du Septentrion, 1998.

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20

Graham, Bird. Rational decisions, irrational results: The economics of the LDC debt crisis and its resolution. Guildford: Department of Economics, University of Surrey, 1994.

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21

Bird, Graham. Rational decisions, irrational results: The economics of the LDC debt crisis and its resolution. [Guildford]: University of Surrey, Dept. of Economics, 1994.

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22

Rational investing in irrational times: How to avoid costly mistakes even smart people make today. New York: Truman Talley Books, 2002.

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23

Wired for survival: The rational (and irrational) choices we make, from the gas pump to terrorism. Upper Saddle River, N.J: Wharton School Pub., 2009.

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24

Gert, Joshua. Underdetermination by Reasons. Edited by Daniel Star. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780199657889.013.20.

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The norms of rationality determine whether an act is irrational, rationally required, or rationally optional. It has seemed theoretically difficult to make significant room for the last category, because rational status is typically taken to be a function of reasons, and reasons are typically taken to have univocal strength values. But there is also a strong intuition that normal choice situations present us with many equally rational options. If this intuition is correct, two questions arise. The first is how it could be true, assuming that rational status is indeed a function of reasons. The second is whether and how we can act in a non-arbitrary way when we are faced with a choice between a number of equally rational options. This chapter examines four strategies for addressing these questions: incommensurability of reasons, parity, the ubiquity of ties, and a distinction between the justifying and requiring roles of practical reasons.
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25

Landau, Edmund. Grundlagen Der Analysis: (Das Rechnen Mit Ganzen, Rationalen, Irrationalen, Komplexen Zahlen). 4th ed. Chelsea Pub Co, 1997.

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26

Irrational Numbers. London, England: Antitype Press, 2010.

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27

Spiller, Robert. Irrational Numbers. Brand: Medallion Press, 2008.

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28

Scott, Cyril. Medicine Rational and Irrational. Kessinger Publishing, 2003.

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29

Bruce, Steve. Action Rational and Irrational. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198786580.003.0009.

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The model of human action as resting on rational choices between alternative opportunities for maximizing our utility has been borrowed from liberal economics by social scientists keen to refute the conventional explanation of secularization. This chapter considers whether we can treat religion as a commodity that people buy more or less of according to individual rational choice. It argues that religion differs from soap powder both extrinsically (because we cannot readily compare its costs or benefits) and in terms of its social roots: in most societies switching religion threatens social bonds far more than does changing car brands. Finally, it advances an important general principle: that we should be very reluctant to impute to other people motives that we would not impute to ourselves.
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30

Angel of Irrational Numbers. Beach Holme Pub Ltd, 1991.

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31

Carpenter, Thomas P., Elizabeth Fennema, and Thomas A. Romberg, eds. Rational Numbers. Routledge, 2012. http://dx.doi.org/10.4324/9780203052624.

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32

Staying Rational in an Irrational World. Australia in Print, 1989.

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33

Richard, James. Rational Numbers Workbook. Independently Published, 2020.

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34

Irwin, William, and Luke Cuddy. BioShock and Philosophy: Irrational Game, Rational Book. Wiley & Sons, Incorporated, John, 2015.

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35

Sarangi, Shriya, and Shriya Sarangi. Two Sides: The Rational and Irrational Mind. Independently Published, 2020.

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36

Irwin, William, and Luke Cuddy. BioShock and Philosophy: Irrational Game, Rational Book. Wiley & Sons, Incorporated, John, 2015.

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37

Meierhenrich, Jens. “A Rational Core within an Irrational Shell”. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198814412.003.0007.

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This chapter turns from the making of The Dual State to its theoretical significance. Fraenkel’s principal argument had three parts. The first part comprised several counterintuitive propositions about the nature of the institutional design of the Nazi political order. Fraenkel argued that this structure consisted of two interacting states: a prerogative and a normative state. The second part of his argument revolved around the institutional effects of this bifurcated state. Fraenkel claimed that it facilitated not only violent domination but also allowed for an orderly transition to and consolidation of authoritarian rule. The third part of Fraenkel’s argument concerned the institutional origins of the dual state. I elaborate and critically evaluate each of these arguments in turn. Through an in-depth engagement with the strengths—and weaknesses—of The Dual State, I prepare the ground for the remainder of the analysis.
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38

Irwin, William, and Luke Cuddy. BioShock and Philosophy: Irrational Game, Rational Book. Wiley & Sons, Incorporated, John, 2015.

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39

Havil, Julian. Irrationals: A Story of the Numbers You Can't Count On. Princeton University Press, 2012.

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40

Havil, Julian. Irrationals: A Story of the Numbers You Can't Count On. Princeton University Press, 2012.

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41

Irrationals: A Story of the Numbers You Can't Count On. Princeton University Press, 2014.

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42

Flannery, David. The Square Root of 2: A Dialogue Concerning a Number and a Sequence. Copernicus, 2010.

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43

Coleman, Mark. Dignity Doctrine: Rational Relations in an Irrational World. SelectBooks, Incorporated, 2020.

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44

Bernard, Micahel E. Staying Rational in an Irrational World: Albert Ellis and Rational Emotive Therapy. Carol Publishing Corporation, 1991.

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45

Pfenninger, David T. The developmental mediation of irrational thought. 1986.

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46

Wu, Hung-Hsi. Rational Numbers to Linear Equations. American Mathematical Society, 2020.

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47

Irrational Numbers. The Mathematical Association of America, 2005.

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48

Dr, David Daniel, Lynn Steven J, and Ellis Albert 1913-2007, eds. Rational and irrational beliefs: Research, theory, and clinical practice. New York: Oxford University Press, 2009.

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49

The Irrationals: A Story of the Numbers You Can't Count On. Princeton University Press, 2012.

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50

Romberg, Thomas A., Thomas P. Carpenter, and Elizabeth Fennema. Rational Numbers: An Integration of Research. Taylor & Francis Group, 2015.

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