## malachite

## computer

## arithmetic Quick reference

### The Oxford Dictionary of Philosophy (3 ed.)

...The study of the natural numbers, which are 0, 1, 2, 3…and their successors. Arithmetic is characterized by Peano ’s postulates. Philosophical questions include the nature of our knowledge of those postulates; the nature of the numbers, which are apparently the objects of which arithmetic treats; and the relation of arithmetic to empirical science. See also abstract/concrete ; conventionalism ; formalism , logical ; logicism...

## arithmetic, foundations of Reference library

### The Oxford Companion to Philosophy (2 ed.)

...non-logical terms, from which other sentences can be deduced. The primitive terms used are ‘0’ (0 is the first natural number), ‘successor’ (the successor of 0 is 1, the successor of 1 is 2, etc.) and ‘natural number’, and the five axioms are: 1. 0 is a natural number. 2. The successor of any natural number is a natural number. 3. No two natural numbers have the same successor. 4. 0 is not the successor of any natural number. 5. For any property P , if (i) 0 has P and (ii) the successor of any natural number which has P also has P , then every...

## Jeffrey, Richard Carl (1926–2002) Reference library

### The Dictionary of Modern American Philosophers

...’s theory, preferences in The Logic of Decision determine utility functions only up to fractional linear transformation. For two such functions U 1 and U 2 , we have U 1 = [(aU 2 + b)/(cU 2 + d)], where ad-bc>0, cU 2 (A) + d>0, and cU 2 (T) + d = 1 for any proposition A for which U 2 is defined and T is the necessary proposition. Probabilities vary across such transformations: P 1 = P 2 (cU 2 + d). Probabilities are unique if the utility function is unbounded. This unified theory attributes probabilities and utilities to the same objects...

## Smeaton, John (1724–92) Reference library

### The Continuum Encyclopedia of British Philosophy

...mv 2 . Again, before collision, m 1 v 1 2 + m 2 v 2 2 = ( 8 × 20 2 ) + ( 8 × 0 2 ) = 3200. After collision, if mv 2 is conserved we must have ( m 1 + m 2 ) × v 3 2 = 3200 16 v 3 2 = 3200 v 3 2 = 200 v 3 = 10 × √ 2 = 14.142 … So the velocity is increased in the collision by a factor of √2 and this, says Smeaton, implies the possibility of perpetual motion. The conception of perfectly hard bodies is therefore ‘repugnant’, that is, incoherent. According to the old opinion, it is mv that is conserved. Before collision, m 1 v 1 + m 2 v 2 = ( 8 × 20 ) + ( 8 × 0 )...

## philosophy and science Reference library

### The Oxford Companion to Philosophy (2 ed.)

...to science for a technology of happiness and have therefore been especially keen that the social sciences should emulate, wherever possible, the style and method of the natural sciences and attain a comparable level of success at prediction and explanation. And even though a deontological ethics does not normally require assistance from science in order to achieve the realization of what it values, it does not repudiate such assistance either.Some philosophers, on the other hand, have actually adopted a negative attitude to science, or part of science, as...

## Cohen, Laurence Jonathan (1923) Reference library

### The Continuum Encyclopedia of British Philosophy

...prove each of two or more independent contentions. Supposing that this requires proof at a level of confidence greater than 0.5, then the plaintiff could separately prove each of the two contentions – say, with a level of confidence of 0.6 for each of the contentions – but, because of the conjunction rule, lose the case because of the fact that the conjunction thus has a level of confidence only of 0.36, well below the threshold of above 0.5. Further, mathematicist accounts of probability would fail to yield the right answer, according to Cohen, in the paradox...

## Boole, George (1815–64) Reference library

### The Continuum Encyclopedia of British Philosophy

...law was peculiar to Boole's new logical algebra: xx = x , considered by Boole as ‘the fundamental law of thought’ and commonly referred to as the ‘index law’. The two roots, 1 and 0, of x 2 = x are the only numerical values interpretable in Boole's algebra, which is thus distinguished from the ordinary numerical algebra. Boole was impressed by the fact that x (1 − x ) = 0, expressing ‘the principle of contradiction’ – traditionally viewed as fundamental – can be derived from his index law. Logical inference is achieved by performing algebraic...

## Peirce, Charles Sanders (1839–1914) Reference library

### The Oxford Companion to Philosophy (2 ed.)

...on the correct value for the chance of a member of the population having the property in question. The pragmatist principle teaches that probability is a propensity : if the chance of a coin coming up heads is 0.43, then, if we were to continue to toss it fairly, the proportion of times on which it comes up heads would converge on 0.43. The logic of abduction is a logic of discovery: it studies how we are guided in constructing new hypotheses from the ruins of defeated ones; and it examines the norms guiding us in deciding which hypotheses are...

## epistemology Reference library

### The Continuum Encyclopedia of British Philosophy

...no.2 (1997). ——, Openness to Argument (Chicago, forthcoming). Pinker, Steven , How the Mind Works (1998). Polanyi, M. , The Logic of Liberty: Reflections and Rejoinders (Chicago, 1951). ——, Personal Knowledge (1958). ——, The Study of Man (1959). ——, The Tacit Dimension (1966). ——, Knowing and Being , ed. M. Grene (1969). Popper, K. R. , The Logic of Scientific Discovery (1934; 1st English edn, 1959). ——, Conjectures and Refutations (1962). ——, Objective Knowledge (Oxford, 1972). Routledge Encyclopedia of Philosophy , Version 1.0...

## Post, Emil Leon (1897–1954) Reference library

### The Dictionary of Modern American Philosophers

...(Solution to Post’s Problem, 1944), ” Proceedings of the National Academy of Science 43 (1957): 236–8. Grattan-Guinness, Ivor O . “ The Manuscripts of Emil L. Post, ” History and Philosophy of Logic 11 (1990): 77–83. Menger, Karl . Reminiscences of the Vienna Circle: A Mathematician’s View (Dordrecht, 1944). Quine, W. V. . The Time of My Life: An Autobiography (Cambridge, Mass., 1985). Rine, David C. , ed. Computer Science and Multiple-Valued Logic: Theory and Applications , 2nd edn (Amsterdam, 1984). Swieczkowska, Halina , ed. “ Emil L. Post and the...

## Turing, Alan Mathison (1912–54) Reference library

### The Continuum Encyclopedia of British Philosophy

...index number of the Turing machine it is investigating and, second, the input which is going to be fed to the target machine. T then outputs 1 or 0 depending on whether the target machine halts or not. That is, T(n,m) = 1 if Turing machine number n halts with input m and T(n,m) = 0 otherwise. Now, it can be easily shown that there is a Turing machine, call this one S, which generates an output of 1 when given input 0, and which responds to an input of 1 by simply filling its tape endlessly with 1s (that is, S fails to halt if it gets input (1). It can also...

## Wallis, John (1616–1703) Reference library

### The Continuum Encyclopedia of British Philosophy

...parabolas ( p 3 = l 2 d and p 4 = l 3 d ). Despite its merits this work was overshadowed by the other early work, Arithmetica infinitorum ( 1655 ), which was the result of his introduction to Cavalieri's infinitesimal methods in his reading of Torricelli's Opera geometrica ( 1644 ). His aim was to find a quadrature of the circle, which he proposed to solve by finding the area of one quadrant of a circle of unit radius, thus finding the value of π/4. Wallis's task, then, was essentially to integrate (1 – x 2 ) 1/2 between x = 0 and x = 1. To begin...

## logic Reference library

### The Continuum Encyclopedia of British Philosophy

..., ‘ Logic: In Reference of the Recent English Treatises on that Science ’, Edinburgh Review 66 (1833), pp. 194–238. van Heijenoort, Jean , From Frege to Gödel: A Source Book in Mathematical Logic, 1879–1931 (Cambridge, Mass. and London, 1967). Jevons, William Stanley , Pure Logic , or the Logic of Quality apart from Quantity with Remarks on Boole's System and the Relation of Logic and Mathematics (London and New York, 1864). ——, The Principles of Science: A Treatise on Scientific Method , 2 vols (1874). Joachim, Harold Henry , The Nature of Truth ...

## Otto, Max Carl (1876–1968) Reference library

### The Dictionary of Modern American Philosophers

...Wisc., 1970). The Max C. Otto Jubilee Dinner Addresses (Madison, Wisc., 1947). Taha, Intissar . Pragmatism and the Concept of Freedom in the Writings of Boyd H. Bode, William H. Kilpatrick, and Max C. Otto . PhD dissertation, Ohio State University (Columbus, Ohio, 1958). Marcus G.0...

## analytic philosophy Reference library

### The Continuum Encyclopedia of British Philosophy

...be illustrated by considering the statement that the average British mother has 2.2 children. Clearly, there can be no actual person with 2.2 children, and the fact that such a statement may be true (let us assume) does not justify us in inferring any such person as the average British mother. What such a statement means, of course, is that if we add up the total number of children of British mothers and divide by the total number of British mothers, then we get a figure of 2.2. All this commits us to is the existence of (normal) British mothers and their...

## Neuroaesthetics Reference library

*Anjan Chatterjee and G. Gabrielle Starr*

### Encyclopedia of Aesthetics (2 ed.)

...images or visual art is striking; natural scenes often result in cross-subject correlations in the range of 0.4 to 0.6 ( Vessel and Rubin, 2010 ; Biederman and Vessel, 2006 )—higher numbers indicate greater agreement with 1.0 being perfect concord; faces are even higher—0.8 to 0.9 in one analysis ( Langlois et al., 2000 ). By contrast, for paintings, correlations are approximately 0.14 ( Vessel et al., 2012 ) and for abstract images, 0.2 ( Vessel and Rubin, 2010 ). Many commentators assess this relative consensus by positing that certain perceptual...

## Synaesthesia Reference library

*John Gage*

### Encyclopedia of Aesthetics (2 ed.)

...Medical Mystery Offers Revolutionary Insights into Emotions, Reasoning, and Consciousness . New York: Putnam, 1993. Fechner, Gustav Theodor . Vorschule der Ästhetik . 2 vols. Leipzig: Breitkopf & Härtel, 1876. Franssen, M. “The Ocular Harpsichord of Louis-Bertrand Castel: The Science and Aesthetics of an Eighteenth-Century Cause Célèbre .” Tractrix: Yearbook for the History of Science, Medicine, Technology, and Mathematics 3 (1991): 15–77. Gage, John . Color and Culture: Practice and Meaning from Antiquity to Abstraction . Boston: Little, Brown, 1993...

## Schultz, Johann (1739–1805) Reference library

### The Dictionary of Eighteenth-Century German Philosophers

...reinen Vernunft , 2 vols (Königsberg, 1789/92; repr., Brussels, 1968). Other Relevant Works Betrachtungen über den leeren Raum (Königsberg, 1758). De geometria acustica seu solius auditus ope exercenda (Königsberg, 1775). De geometria acustica nec non de ratione 0:0 seu basi calculi differentialis (Königsberg, 1787). Elementa theologiae popularis theoreticae (Königsberg, 1787). Versuch einer genauen Theorie des Unendlichen (Königsberg, 1788). ‘Review of Immanuel Kant, Metaphysische Anfangsgründe der Naturwissenschaft (Riga, 1786; 2nd edn 1787)’, ...