text:
Logic, Game Theory, and the Real World. Arnis Vilks 1 Leipzig Graduate School of Management (HHL)
- Jordan Little
- 3 years ago
- Views:
1 Logic, Game Theory, and the Real World Arnis Vilks 1 Leipzig Graduate School of Management (HHL) Introduction Both Logic and Game Theory are fascinating fields. I for one have always been intrigued by the perennial philosophical puzzle of how reasoning works and which kind of reasoning is sound. How reasoning human agents interact with each other, and how they contribute to each other s well-being, and why they often harm each other, is a similar perennial puzzle, but for some reason its more explicit investigation has had to wait for the genius of John von Neumann. I am quite confident, however, that in the history of thought bright men or women before von Neumann must have thought about the I think that you think that he thinks that I think -loops that are so typical for game theoretic reasoning. In fact, this little observation about game-theoretic reasoning already makes clear why game theory cannot really live without including logic into its field of inquiry. Many years ago, when I was a student at Hamburg University, I was taught that Logic is the theory of valid or correct reasoning. One might perhaps use rational as opposed to factual reasoning as a third nearsynonym. My logic professors some 30 years ago made much of the point that logic is not psychology. The latter may try to investigate how people actually develop, i.e., modify and extend their belief systems, even if no external information arrives. That is, psychology may look at how people actually think. But Logic, I was told, is rather a normative discipline. It tells you, how you ideally ought to reason, what you are allowed or required to infer from given premises. Thus, it seems that Logic needs to prove that the inferences it singles out as correct, cannot lead you astray. As I assume - many other serious students of logic, I was somewhat puzzled by the fact that in proving the theorems of logic one frequently makes use of just those very modes of reasoning the validity of which one is proving - but of course the distinction between formal and informal proofs, between object- and metalanguage made that puzzle much less worrying. 1 This paper, presented at the opening ceremony of GloriClass, was written while I was visiting Waikato Management School in Hamilton, New Zealand, in the first months of 2006.
2 2 Some years later, I was taught, and many economics students all over the world are still taught today, that Game Theory studies the interaction of rational agents, where rationality has a double meaning. It covers both rationality of choice, and rationality of reasoning. Rationality of choice means that relative to the information you happen to have, you choose what you prefer most among the options you consider possible. If I observe you sitting and listening, I may thus infer by the rationality of choice principle that, however annoyed you may be by what I am saying, your observable choice reveals that right now you prefer sitting and listening to getting up and leaving. In making this inference, I certainly take for granted that you consider it possible to leave, but given this assumption, observed behaviour implies certain things about preferences. The second part of Game Theory s standard rationality assumption is more or less just the assumption that the players reasoning is correct, and that no relevant inference fails to be made. This is sometimes expressed by saying that game theory assumes players to be perfect logicians. Actually, they are often required not only to be logicians, but to know a good deal about higher layers of mathematics as well, but most game theorists don t know much about the distinction between logic and mathematics. Now, unlike the rationality of choice principle, logical omniscience seems a pretty bold assumption to make. After all, game theory is meant to elucidate actual behaviour of human beings in situations where they interact, and actually reason about each others reasoning. This brings me closer to one of the main points I would like to make. Game theory has become the most important tool kit for economists, and it is sometimes also used in political science, because it seems to elucidate real-world interactions. The world is of course full of interaction between humans. Every organisation or institution is brimming with interaction, every market is essentially interaction, not to mention international politics like the current scary escalation of violence between Islamic extremists and the George-W.-Bush-led Western alliances. Of course, as most of you know, game theory can also be applied to the interaction of machines and software agents, and John Maynard Smith has inspired the development of a whole new sub-discipline - evolutionary game theory - by showing that many game theoretic ideas can be applied to the interaction of animals without of course assuming them to be perfect mathematicians. Unlike its rationalistic ancestor, evolutionary game theory does not look at interaction between a few,
3 3 who consciously choose their respective strategies, but it looks at whole populations of agents who are genetically programmed to play particular strategies, and who may or may not have offspring with the same genes depending on how fit their strategy makes them to survive within the current population s mix of strategies. Of course, with certain modifications and reinterpretations, this nonrationalistic branch of game theory can also be applied to the interaction among populations of machines or computer programmes and it can also be applied to that particular species of animal that likes to think of itself as very different from all other species, because it has free will to choose and because it a mind to reason. I am getting even closer to the point I want to make. There are conflicts and interactions between humans in the real world out there that arguably cost many thousands of human lives each day. Nevertheless, the reasoning that apparently informs the most far-reaching strategic decisions of the political and business leaders in the real world, appears to be often so innocent of any decision-theoretic or game-theoretic wisdom, that one cannot but marvel at the lack of interaction between us thinkers, and those who move and often shake the world. Now, it is always easy to blame others, and intellectuals tend to underestimate the amount and complexity of reasoning that quite a few of the people in authority, actually do carry out before making their strategic choices. But if I am right that many important decisions out there lack all the insights that logic and game theory can provide, I think we intellectuals have to blame ourselves, too. I have the impression that both fields we are talking about today, both logic and game theory, often tend to ignore the important problems, and waste much time and effort in defining precisely, and then solving problems - which nobody had before they were invented by the logicians or game theorists. Even the terminologies used within our fields tend to be so idiosyncratic that members of one research group sometimes have great difficulties to even understand what is written by a member of another research group. Now, I am not, of course, urging the Amsterdam GloriClass to forego research on foundational issues, or to write popular expositions of logic and game theory for the politician. Actually, I try not to urge anybody to do anything. But I kindly invite you to consider the research you are doing in the context of the problems out there which urgently await if not solutions then at least informed advice on the soundness of reasoning and on the rationality of choice.
4 4 A simple game of some importance To illustrate, let me consider a very simple example. Assume there are two players, the rich civilization R, and the poor one P. Both have two strategies: To play aggressive A, or to play meek M. If both play meek, the rich civilization gets almost the whole pie, which I take to be 22 t USD, but the poor can improve a little against this allocation by playing aggressive. If the rich play aggressive they hurt the poor, but against a meek strategy by the poor, the rich loose only little. If both play aggressive well, humankind may not survive the ensuing nuclear war. A first distinction can be illustrated here, the one between decisiontheoretic rationality and game-theoretic rationality. While it is clearly the dominant strategy for the rich to play meek, the poor civilization s best response depends on its opponent s choice. If the poor do not know about the character of the rich, and therefore regard both strategies of the rich as equiprobable, the poor will be indifferent between its two strategies, and hence may well choose to play meek. Many other beliefs of the poor, represented by a probability distribution over its opponent s strategies, are of course just as consistent with playing meek. However, considering that the rich opponent is rational, and knowing about the structure of the game, the poor must conclude that the rich will not play aggressive, but meek. Therefore game theory recommends the aggressive strategy to the poor. P R A M 0 17 A M 1 2 Obviously, the strategy combination (M,A), where the first component denotes the rich player s strategy, is the only Nash equilibrium for this little game, and one might think this all one can say. Not so. Do you really think (M,A) is rational? As I just mentioned, there are different notions of rationality. Decision-theoretic rationality does not quite coincide with game-theoretic rationality. One is more demanding than the other, but both are treated as normative concepts in the sense I indicated by saying that game theory recommends M to R and A to P.
5 5 But the more thoughtful game-theorists such as Harsanyi have been very aware of the fact that there is of course a still more demanding notion of rationality what one may call moral, ethical, or fully normative rationality. Assume for a moment that both civilizations have the same number of people, and that each poor life counts just as much as a rich one. Is there an outcome that is ethically rational? You think ethics is neither logic nor game-theory? But as long as both disciplines end up making recommendations, and tell you what you should infer from given premises, and what the rational strategy choice is, both disciplines are normative. So why stop at the conventional wisdom of a Nash equilibrium? You may say, none of the outcomes looks particularly ethical. Right, I agree. So, what about inventing a new strategy, call it the innovative one. P R A M I A M You might say, well that s a different game. Of course it is. Within the academic world of the game theorist, it may be considered cheating if, in the middle of an analysis, you all of a sudden add a new strategy. But imagine we are modelling a real world conflict. How do we know which strategies are available? What does it mean to claim that a real human in a particular situation has options A, B, C and no others? Both George W. Bush and Usama bin Laden may have thought that, in order to achieve their respective goals, they had no better option but to ask their followers to go to faraway countries, and to kill themselves and many others. But maybe they were just lacking creativity. I think it is a very relevant (and essentially open) question of logic in game theory what we take an option to be. (I do think it is easier to see the problem in the context of a serious application than in an Alice-and-Bob-type toy example, but I did not
6 6 necessarily mean to suggest that my model of the clash of civilizations is capturing all the essentials of that global problem. There is a folk metatheorem of game-theoretic modelling to the effect that for any given result there is a set of game-theoretic assumptions from which the result follows. It goes without saying that if I had wanted to praise the US president here, I could have designed a different little game than the one I just presented a game which would yield what I wanted to show: Not invading Iraq must lead to disaster.) Eight important logical problems of game theory I guess I have messed up things a little. So let me try to disentangle some of the logical problems of game theory which I see as really important. I will briefly explain eight such issues. 1. The distinction between a normative and a predictive (or descriptive) use of theory is of utmost importance in applications of game theory. Are the solutions we define in game theory what we ought to recommend? Or are they just some kind of predictions? Maybe this is more of a philosophical or methodological issue than a logical one, but it seems to be also very relevant to logic itself. I do not have to tell you about the plethora of logical systems which have been analysed in the learned monographs and journals. If that is not just playing around with symbols, than what is the status of those systems? Should we use classical or intuitionistic logic when we reason about games? Should we use a different one when we reason about quantum information? A Leipzig colleague of mine, Piero La Mura has recently generalized Aumann s concept of correlated equilibrium to allow for correlation by means of possibly entangled q-bits. Which logic should we use in reasoning about this? To ask the question again: what is the logical status of Logic and of GT? Normative, predictive, or what? Johan van Bentham has recently written that discussions of normative versus predictive views of logic have become predictable and boring. That may be so, but it is an issue which is can hardly be avoided unless one is happy to confine oneself to the narrow world of pure, academic, discourse. To my mind, game theory today should help to avoid World War III. 2. Of course one of the strategies academics use in order to answer a question consists of making distinctions. Of course one can begin to define normativity1 as opposed to normativity2 as distinct from rationality 4. I know full well, of course, that one often needs to make the right distinctions, if one wants to convince others. But even more important than making clever distinctions, and leave it at that, is to make a
7 7 difference. I very much hope, and I trust, that the research that is going to be done in the GloriClass is going to make a difference, but if it made a difference not only to some other members of GloriClass, that would be splendid. In the world of Business today, where game theory is used and applied, the importance of ethics is widely acknowledged. Scandalous behaviour by Top-Managers as exemplified by, e.g., the Enron and Worldcom cases, may have been the main reason for this, but the fact remains that Business Ethics is increasingly seen as necessary by quite sober-minded business people. There are of course applications of logic to ethics and law, which might well be reconsidered in the context of games. Or to put this as a question: What is the logic of fully normative or ethical recommendations? 3. More specifically, the logical relation between standard game-theoretic rationality and whatever one takes ethical rationality to be, needs to be addressed. Just as game-theoretic rationality is a special case of decision-theoretic rationality, one would expect moral or ethical rationality to be a special case of game-theoretic rationality. But look at my 3*2 example again. You may have noticed that inventing the innovative strategy did not really help at first glance. The extended game still has just one Nash equilibrium the one we had before. Can we expect anything else than (M,A) in the extended game? Maybe not, if game theory is interpreted as predictive, but if the model was used in normative sense, one might - perhaps - think up and defend an ethical justification for the outcome (11,11). Should we then recommend I to R, rather than M? As far as I am aware, such questions are not among the standard questions logicians are trained to think about. But who else if not logicians - or maybe philosophers with a good understanding of logic and game-theory - should be able to address them? 4. The notion of an option or feasible choice that is presupposed by game theory has puzzled me a lot. I made a suggestion before my 5- year excursion into the world of business to the effect that one can interpret the dual of the epistemic-logic knowledge operator, K, to express what a player subjectively considers possible. I still think that was a good idea. But when I presented it at a LOFT conference with Bob Aumann in the audience, he almost got angry with me, and repeated a couple of times that the feasible actions in a game are not those whereof one does not yet know that one will not carry them out. With his amazing mathematical intuition he had apparently deduced on the spot that all real decision problems would be reduced to trivial ones within his preferred framework of S5. The situation is quite close to the one in Fitch s paradox: If it is the case that I will choose M, but still consider it possible that I will not choose M, one would like it to be possible to know
8 8 this. In one of those most useful coffee breaks after my talk, Aumann very kindly approached me to say he was sorry about getting angry, and explained that he thought the feasible options in a game must be the objectively given, physically possible actions. Well, I like and respect Bob Aumann very much, he no doubt deserved the Nobel prize he got last year, but I find the idea that the feasible moves in a game are all the physically possible ones, outright grotesque. We never know all the physically possible actions we might carry out at any given instant, and if we did, and moreover could somehow specify all of them, there would just be one big game of life or Savage s grand world decision problem - left to consider, and any attempt to apply the tiny little textbook games we think are useful to analyse real-world conflicts and cooperation would at best be reduced to training material for students. So I challenge you logicians to think about what exactly turns a hypothetical action into one that has to be included as a move in the relevant game. 5. There is another problem that links game theory with logic. It is the problem of choosing the optimal logic. To take just epistemic logic as an example, most of you know that one can define somewhat different systems even within the narrow confines of Kripkean, or, say, neighbourhood, semantics. There are the systems K, KT, S4, S5, and many others. Of course, in a relaxed research environment there may be little need to choose one instead of the others. But in applications one would very much want to know which model of knowledge is the most appropriate one. In principle, decision or game theory should be able at least to give structure to the problem of rational choice between alternative logical options. But again - the devil is in the detail, and as soon as one looks closely at the basics of decision theory, the dividing line between logic and decision theory seems elusive. I mentioned the principle of rational choice in my introductory remarks. Let me repeat what it says. If one chooses an action, it must have been considered feasible by the agent, and there cannot be another feasible one that is preferred to the chosen one. Depending, of course, on a number of details about the notions of action and preference, non-logicians have criticized this principle of rational choice as an empty tautology. At least on a slightly naïve account of logic, it seems logically impossible to simultaneously claim that a certain behaviour is an intentionally chosen action, and that in the very moment of choosing this action - the chooser considers an alternative action feasible which he actually prefers to the chosen one. So is there a logic that connects actions, preference, and feasibility in such a way that the principle is valid? If so, there might be a grand unified theory of logic and games.
9 9 6. The next issue I would like to mention, is the notion of information, and its relation to the foundations of mathematics. Johan van Bentham has, I think quite rightly, emphasized that the notion of information may be a more basic notion for an adequate understanding of the world than the notions we have inherited from the logicians of 100 years ago. It may well be that I am just revealing my ignorance here, but I have not seen any theory of information that could aspire to be the foundation for, say, most of the mathematics applied in the sciences. I think it is fair to say that most applications of mathematics today take it for granted that mathematics rests on a fairly safe basis, and that this basis is the one thought up by Zermelo and Fraenkel, and later shown by the Bourbaki group to produce virtually all of known useful mathematics. If one asks why this basis is pretty safe, one can probably just point to the fact that the mathematics that can be derived from it, has not only proved very useful in combination with all sorts of non-mathematical ideas, but it has apparently nowhere collided with observations or ideas which could claim to be just as evident as the axioms of Zermelo-Fraenkel set theory. Now, you are probably familiar with the Quine-Duhem thesis, which roughly says that one can refute by observation only the conceptual apparatus used as a whole, but hardly ever a particular segment of that conceptual apparatus. Thus, it is essentially a matter of convention what is taken to be the infallible hard core of ones world view. It seems clear to me that taking set theory to be beyond reasonable doubt is such a convention. And conventions can and should be modified, if there are convincing alternatives one can choose - and good reasons to actually do choose some modification. Now, again, I may just be revealing my personal ignorance when I say I have not seen an alternative to standard set theory that could at least plausibly hold the promise to clear away some of the conceptual riddles in fields like logic and game theory - where in spite of the aforementioned zoo of logical systems, at the meta-level standard mathematical logic and set theory are treated almost as god-given. But there are such riddles, and somehow many of them seem to confirm that information is more basic than sets. Let me mention one from a field I know very little about, and explain another one that I know much better The field I know next to nothing about except that it seems to rely heavily on the right way of modelling information, is quantum mechanics. Recently, Conway and Kochen have discovered and proved a theorem that goes by the name of free-will theorem. It says, apparently, that if an experimenter has some free will, sub-atomic particles also have some free will. One of the assumptions in the theorem is that there is a finite upper bound on the speed with which information can be transmitted.
10 10 Although the speed of light seems a natural candidate for this upper bound, it seems that it is experimentally not that clear that nothing can travel faster than light. And what is there in the theory of information that tells us what the carrier of information must be? Is it absurd to say that I sometimes transmit information to myself? Is the speed of thought limited by the speed of light? Can we choose what to think next? Can we choose to focus on one thought, and suppress any new ideas for a while? The famous physicist Roger Penrose has argued forcefully that human thought is creative and therefore not algorithmic. But as far as I know, the physics of mind is still unknown There is another conceptual riddle that I am quite sure has not been answered in the learned literature. To me, it strongly suggests that the logical foundations of mathematics need modification if we want a satisfactory theory of reasoning about choice. Imagine one of the simplest games there is a one-player game with two strategies. Assume the strategies are actually given by their payoffs. Let these be monetary payoffs, and assume our agent prefers more to less money. Now, he is offered the choice between alternative payoffs which would be given to him as gifts. Either he can have 3 7 or 7 4. Our agent, like most of us, gets out his pocket calculator, types in the required calculations, and ends up with the information 3 7 = 2187 and 7 4 = According to the principle of rational choice, he chooses 3 7 instead of 7 4. So far, so good. What I need to tell you, perhaps, is that I cheated again. Actually, 7 4 =2401. The situation I had in mind is one where our agent is unaware of the fact that his pocket calculator has a defect. As it happens, the third digit from the right is always a 1. Now why is this a conceptual riddle? Well, standard predicate logic with equality has the axiom of substitutivity, or indiscernablility of identicals which says Y=X (P(Y) P(X)) for any predicate P. Now let P(X) be the predicate the agent has the information that 2187>X. As I assumed in my little fictitious story, P(7 4 ) is true. It is also true that 7 4 = The axiom thus allows us to deduce P(2401). But it seems plausible to assume that our fictitious agent is neither an idiot nor otherwise out of his mind, and that P(2401) is false. It seems that if we did not choose by convention to treat standard mathematical logic as irrefutable, we would have a nice Popperian falsification of a logical axiom here. 7. I do not know, of course, how to deal satisfactorily with these and the many other problems that arise in thinking about speed of thought, choice, free will, or the so-called propositional attitudes. It is certainly
11 11 easy to think up an ad-hoc logic that allows one to accommodate any one of these problems. But one certainly does not want to throw away the beloved, and essentially healthy, baby of mathematics with the bathwater of some stubborn anomalies. What seems needed is a theory - or logic - of information that is in accordance with our intuitions and observations about the nature of information, but which can still accommodate at least large parts of present-day mathematics. The problems of information, consciousness, free will, and choice seem to be so much at the intersection of quantum physics, logic, and decision theory that I for one would not be overly surprised if the next big step in the history of thought arose from a unified perspective on information and on how it is processed by the human mind. I mentioned already that because of creativity, human thought is not algorithmic. A fortiori, it is not isomorphic to a formal system, as this term is commonly defined. It may well be that a suitable modification of the definition of formal system will do the trick of understanding how the human mind works, and will allow one to defend the correspondingly reinterpreted strong AI thesis. In order to allow for creativity, one might try to investigate open systems instead of the usual formal ones. What do I mean by an open system? Well, it might look much like a standard formal system except that neither the alphabet nor the axioms are fixed once and for all. Thus, we might say, let O be a system which has an alphabet a,b,c,, and possibly also greek, Arabic, Chinese, or still other characters. These may be introduced if required, but not without giving reasons. We might specify a certain number of assumptions or axioms and rules of inference, but allow for other assumptions to be introduced if required but again not without mentioning that the formula or sentence written down is meant to be a new, additional, assumption. There is, of course, a notion of derived or inferred formula in O. A formula F is derived in O, if it is the last one of a finite sequence such that each element of the sequence is either an assumption or derived from previous elements. At any given moment, one can freeze an open system into the formal one that has as its alphabet and axioms only the signs and assumptions introduced so far. There may not be many other interesting things one can say about all open systems. But are there many interesting things one can say about all formal systems? In order to say something interesting, one needs to get more specific, but the only point I want to make here, is this: The notion of formal system is not one that cannot be modified in interesting ways. Certainly, it seems quite straightforward to develop standard mathematics within an open system I cannot see that anything would need to get lost. But of course, the associated philosophy of mathematics would be closer to Lakatos Proofs and Refutations than to Bourbaki s Théorie des Ensembles.
12 12 One would hope that logic and mathematics are capable of progress, and maybe the time is ripe for a step forward after 100 years of essentially refining the received view of Frege, Russell, Zermelo and Fraenkel. Why not think about how to do this big step in the Amsterdam GloriClass? 8. The eigths and last issue I would like to try and disentangle from the others hidden in my little clash-of-civilizations game, probably needs to be addressed jointly with the issue of what constitutes information. It is the issue of how one interprets some given information. There is of course much learned literature about both formal and informal semantics, but the basic idea seems to be that any given information typically admits of different interpretations. I think I do not overly stretch the ordinary usage of the English language when I say that the information we have about the clash can be interpreted as an indication that if the escalation continues, the American president may one day decide to sacrifice the people who crucified Jesus. Both George W. Bush and Usama bin Laden are known to interpret their respective holy books in a very literal - if not naïve way. One of the more obvious urgent things logicians should do, is telling the world out there that for any given information or book, no fallible human knows the only correct reading or interpretation. Educated men and women should know that both the Bible and the Qu ran have content that cannot be interpreted literally, even if one tries. The very concept of a God who is beyond human understanding makes the word god - a metaphor. Conclusion Now it seems, I have come full circle, as they say. To conclude, I suggest that logicians working on game theory should neither fall prey to the ever-present temptation of misplaced modesty in the choice of topics and issues, nor succumb to the pressure of publishing many instead of good papers. The LPU or least publishable unit of wisdom like other very small particles - may well be subject to Heisenberg s uncertainty principle: As soon as its content has been observed by careful reading, it has already sped into the forgotten prehistory of human thinking. And if you try to keep it in the present, its position reduces to an item in your list of publications that is not read or understood by anybody. Wisdom and courage are virtues that must not be separated by the societal division of labour wisdom and cowardice for the scholars and academics, as it were, and thoughtless bravery for those in authority. If nothing else, the need to convince those who allocate research funds
13 13 should make logic in game theory be aware of how relevant both fields are, or at any rate how relevant both fields might again become relevant both to quite down-to-earth issues of economics and international politics, and to seemingly remote academic disciplines like quantum physics or theology. References Bourbaki, N., Éléments de Mathématique, Théorie des Ensembles. Paris : Hermann, Clausing, T., and Vilks, A., Backwards Induction in General Belief Structures with and without Strategies. In: Bonanno, G., Colombatto, E., and van der Hoek, W. (eds.), LOFT 4, Proceedings of the 4 th Conference on Logic and the Foundations of Game and Decision Theory. Torino: ICER, Harsanyi, J., Morality and the Theory of Rational Behaviour, in: Sen, A. and Williams, B. (eds.), Utilitarianism and Beyond. Cambridge: Cambridge University Press, Lakatos, I., Proofs and Refutations. The Logic of Mathematical Discovery. Cambridge: Cambridge University Press, La Mura, P., Correlated Equilibria of Classical Strategic Games with Quantum Signals. In: International Journal of Quantum Information, Vol. 3, No. 1 (2005) Penrose, R., The Emperor s New Mind. Concerning Computers, Minds, and the Laws of Physics. London: Oxford University Press, Savage, L., The Foundations of Statistics. New York: Dover Smith, J.M., Evolution and the Theory of Games. Cambridge: Cambridge University Press, Van Benthem, J., What One May Come to Know. In: Analysis 64 (Issue 282, 2004), Van Bentham, J., Where is Logic Going, and Should It? In: Bencivenga, E. (ed.), What Is to Be Done in Philosophy? Vilks, A., What is a Game? In: Bolle, F., and Carlberg, M. (eds.), Advances in Behavioral Economics. Essays in Honor of Horst Todt. Heidelberg: Physica, Vilks, A., Rationality of Choice and Rationality of Reasoning, HHL Working Paper, 1996.
CHAPTER 7 GENERAL PROOF SYSTEMS 1 Introduction Proof systems are built to prove statements. They can be thought as an inference machine with special statements, called provable statements, or sometimesMore information
P vs NP problem in the field anthropology
Research Article P vs NP problem in the field anthropology Michael.A. Popov, Oxford, UK Email email@example.com Keywords P =?NP - complexity anthropology - M -decision - quantum -like game - game-theoreticalMore information
Last time we had arrived at the following provisional interpretation of Aquinas second way:
Aquinas Third Way Last time we had arrived at the following provisional interpretation of Aquinas second way: 1. 2. 3. 4. At least one thing has an efficient cause. Every causal chain must either be circular,More information
A brief history of type theory (or, more honestly, implementing mathematical objects as sets)
A brief history of type theory (or, more honestly, implementing mathematical objects as sets) Randall Holmes, Boise State University November 8, 2012 [notes revised later; this is the day the talk wasMore information
Time and Causation in Gödel s Universe.
Time and Causation in Gödel s Universe. John L. Bell In 1949 the great logician Kurt Gödel constructed the first mathematical models of the universe in which travel into the past is, in theory at least,More information
Pascal is here expressing a kind of skepticism about the ability of human reason to deliver an answer to this question.
Pascal s wager So far we have discussed a number of arguments for or against the existence of God. In the reading for today, Pascal asks not Does God exist? but Should we believe in God? What is distinctiveMore information
Chapter 21: The Discounted Utility Model
Chapter 21: The Discounted Utility Model 21.1: Introduction This is an important chapter in that it introduces, and explores the implications of, an empirically relevant utility function representing intertemporalMore information
Harvard College Program in General Education Faculty of Arts and Sciences Harvard University. A Guide to Writing in Ethical Reasoning 15
Harvard College Program in General Education Faculty of Arts and Sciences Harvard University A Guide to Writing in Ethical Reasoning 15 A Guide to Writing in Ethical Reasoning 15 Professor Jay M. HarrisMore information
WHAT ARE MATHEMATICAL PROOFS AND WHY THEY ARE IMPORTANT? introduction Many students seem to have trouble with the notion of a mathematical proof. People that come to a course like Math 216, who certainlyMore information
Biology X: Introduction to (evolutionary) game theory
Biology X: Introduction to (evolutionary) game theory Andreas Witzel see Gintis, Game theory evolving, Chapters 2, 3, 10 2010-09-20 Overview Evolutionary game theory: motivation and background ClassicalMore information
Does rationality consist in responding correctly to reasons? John Broome Journal of Moral Philosophy, 4 (2007), pp. 349 74.
Does rationality consist in responding correctly to reasons? John Broome Journal of Moral Philosophy, 4 (2007), pp. 349 74. 1. Rationality and responding to reasons Some philosophers think that rationalityMore information
Lecture 8 The Subjective Theory of Betting on Theories
Lecture 8 The Subjective Theory of Betting on Theories Patrick Maher Philosophy 517 Spring 2007 Introduction The subjective theory of probability holds that the laws of probability are laws that rationalMore information
Mathematical induction: variants and subtleties
Mathematical induction: variants and subtleties October 29, 2010 Mathematical induction is one of the most useful techniques for solving problems in mathematics. I m assuming you re familiar with the basicMore information
Descartes. Philosophy and Good Sense
Perspectives in Philosophy Rene Descartes Descartes Philosophy is the search for certainty the search to know, for yourself, what is really true and really false to know which beliefs are reliable. However,More information
It has been contended that it would be possible for a socialist economy to solve
THE EQUATIONS OF MATHEMATICAL ECONOMICS AND THE PROBLEM OF ECONOMIC CALCULATION IN A SOCIALIST STATE LUDWIG VON MISES I It has been contended that it would be possible for a socialist economy to solveMore information
Cosmological Arguments for the Existence of God S. Clarke
Cosmological Arguments for the Existence of God S. Clarke [Modified Fall 2009] 1. Large class of arguments. Sometimes they get very complex, as in Clarke s argument, but the basic idea is simple. LetsMore information
ON EXTERNAL OBJECTS By Immanuel Kant From Critique of Pure Reason (1781)
ON EXTERNAL OBJECTS By Immanuel Kant From Critique of Pure Reason (1781) General Observations on The Transcendental Aesthetic To avoid all misapprehension, it is necessary to explain, as clearly as possible,More information
I d Rather Stay Stupid: The Advantage of Having Low Utility
I d Rather Stay Stupid: The Advantage of Having Low Utility Lior Seeman Department of Computer Science Cornell University email@example.com Abstract Motivated by cost of computation in game theory,More information
AI Principles, Semester 2, Week 2, Lecture 4 Introduction to Logic Thinking, reasoning and deductive logic Validity of arguments, Soundness of
AI Principles, Semester 2, Week 2, Lecture 4 Introduction to Logic Thinking, reasoning and deductive logic Validity of arguments, Soundness of arguments Formal systems Axioms, Inference, and Proof PropositionalMore information
WEAK DOMINANCE: A MYSTERY CRACKED JOHN HILLAS AND DOV SAMET Abstract. What strategy profiles can be played when it is common knowledge that weakly dominated strategies are not played? A comparison to theMore information
Lecture Notes, October 30. 0. Introduction to the philosophy of mind
Philosophy 110W - 3: Introduction to Philosophy, Hamilton College, Fall 2007 Russell Marcus, Instructor email: firstname.lastname@example.com website: http://thatmarcusfamily.org/philosophy/intro_f07/course_home.htmMore information
CHANCE ENCOUNTERS. Making Sense of Hypothesis Tests. Howard Fincher. Learning Development Tutor. Upgrade Study Advice Service
CHANCE ENCOUNTERS Making Sense of Hypothesis Tests Howard Fincher Learning Development Tutor Upgrade Study Advice Service Oxford Brookes University Howard Fincher 2008 PREFACE This guide has a restrictedMore information
Janet E. Helms, Ph.D. Augustus Long Professor, Department of Counseling, Boston College
Janet E. Helms, Ph.D. Augustus Long Professor, Department of Counseling, Boston College Interviewed by Carlos P. Zalaquett, Ph.D., L.M.H.C Department of Psychological & Social Foundations University ofMore information
1/9. Locke 1: Critique of Innate Ideas
1/9 Locke 1: Critique of Innate Ideas This week we are going to begin looking at a new area by turning our attention to the work of John Locke, who is probably the most famous English philosopher of allMore information
Frege s theory of sense
Frege s theory of sense Jeff Speaks August 25, 2011 1. Three arguments that there must be more to meaning than reference... 1 1.1. Frege s puzzle about identity sentences 1.2. Understanding and knowledgeMore information
What is Undergraduate Education?
Education as Degrees and Certificates What is Undergraduate Education? K. P. Mohanan For many people, being educated means attending educational institutions and receiving certificates or degrees. ThisMore information
THE REASONING ART: or, The Need for an Analytical Theory of Architecture
P ROCEEDINGS VOLUME I SPACE SYNTAX TODAY THE REASONING ART: or, The Need for an Analytical Theory of Architecture Professor Bill Hillier and Dr Julienne Hanson University College London, London, EnglandMore information
When Betting Odds and Credences Come Apart: More Worries for Dutch Book Arguments
When Betting Odds and Credences Come Apart: More Worries for Dutch Book Arguments Darren BRADLEY and Hannes LEITGEB If an agent believes that the probability of E being true is 1/2, should she accept aMore information
The Gospel & The Scholars. For most of us, our college days are a time in our lives centered around study, research,
1 The Gospel & The Scholars William K. Lewis Fairmont Presbyterian Church College Ministry Team For most of us, our college days are a time in our lives centered around study, research, and learning. WeMore information
Students in their first advanced mathematics classes are often surprised
CHAPTER 8 Proofs Involving Sets Students in their first advanced mathematics classes are often surprised by the extensive role that sets play and by the fact that most of the proofs they encounter areMore information
Argument Mapping 2: Claims and Reasons
#2 Claims and Reasons 1 Argument Mapping 2: Claims and Reasons We ll start with the very basics here, so be patient. It becomes far more challenging when we apply these basic rules to real arguments, asMore information
3. Mathematical Induction
3. MATHEMATICAL INDUCTION 83 3. Mathematical Induction 3.1. First Principle of Mathematical Induction. Let P (n) be a predicate with domain of discourse (over) the natural numbers N = {0, 1,,...}. If (1)More information
2. Propositional Equivalences
2. PROPOSITIONAL EQUIVALENCES 33 2. Propositional Equivalences 2.1. Tautology/Contradiction/Contingency. Definition 2.1.1. A tautology is a proposition that is always true. Example 2.1.1. p p DefinitionMore information
Kant s deontological ethics
Michael Lacewing Kant s deontological ethics DEONTOLOGY Deontologists believe that morality is a matter of duty. We have moral duties to do things which it is right to do and moral duties not to do thingsMore information
Week 7 - Game Theory and Industrial Organisation
Week 7 - Game Theory and Industrial Organisation The Cournot and Bertrand models are the two basic templates for models of oligopoly; industry structures with a small number of firms. There are a numberMore information
ANOTHER GENERATION OF GENERAL EDUCATION Peter K. Bol Charles H. Carswell Professor of East Asian Languages and Civilizations I was asked to set forth some personal reflections rather than to summarizeMore information
Are the truths of mathematics invented or discovered?
Are the truths of mathematics invented or discovered? By Vincent Wen Imagine you are a prehistoric caveman living a nomadic life. One bright sunny morning, a fellow caveman comes to you, borrows a fewMore information
The Philosophical Importance of Mathematical Logic Bertrand Russell
The Philosophical Importance of Mathematical Logic Bertrand Russell IN SPEAKING OF "Mathematical logic", I use this word in a very broad sense. By it I understand the works of Cantor on transfinite numbersMore information
There is a physics joke about the stages of learning quantum mechanics:
Preface The only way to learn physics is to do physics. However, almost all physics textbooks leave a huge gap between the level of the problems that they solve as examples, and the level of the problemsMore information
MAT2400 Analysis I. A brief introduction to proofs, sets, and functions
MAT2400 Analysis I A brief introduction to proofs, sets, and functions In Analysis I there is a lot of manipulations with sets and functions. It is probably also the first course where you have to takeMore information
6.207/14.15: Networks Lecture 15: Repeated Games and Cooperation
6.207/14.15: Networks Lecture 15: Repeated Games and Cooperation Daron Acemoglu and Asu Ozdaglar MIT November 2, 2009 1 Introduction Outline The problem of cooperation Finitely-repeated prisoner s dilemmaMore information
6.042/18.062J Mathematics for Computer Science. Expected Value I
6.42/8.62J Mathematics for Computer Science Srini Devadas and Eric Lehman May 3, 25 Lecture otes Expected Value I The expectation or expected value of a random variable is a single number that tells youMore information
DISCRETE MATHEMATICS W W L CHEN c W W L Chen, 1982, 2008. This chapter originates from material used by the author at Imperial College, University of London, between 1981 and 1990. It is available freeMore information
1 A project or simply a task?
1 A project or simply a task? The need for a clear definition In this chapter we focus on the basics of working on projects, namely the identification and the definition. We also cover the preconditionsMore information
Vagueness at the interface between logic, philosophy, and linguistics
LoMoReVI Cejkovice, September 17 Vagueness at the interface between logic, philosophy, and linguistics Pleasures and pitfalls of interdisciplinarity Chris Fermüller Vienna University of Technology TheoryMore information
MATHS B-DAY 2006 Friday 24 November IN THE HANDS OF TIME The Maths B-Day is sponsored by and Maths B-day 2006-1- Wiskunde B-dag 2006 0 Introduction The maths B-day assignment this year is totally focusedMore information
LOOKING FOR A GOOD TIME TO BET LAURENT SERLET Abstract. Suppose that the cards of a well shuffled deck of cards are turned up one after another. At any time-but once only- you may bet that the next cardMore information
For the purposes of this course, the natural numbers are the positive integers. We denote by N, the set of natural numbers.
Lecture 1: Induction and the Natural numbers Math 1a is a somewhat unusual course. It is a proof-based treatment of Calculus, for all of you who have already demonstrated a strong grounding in CalculusMore information
Program Level Learning Outcomes for the Department of Philosophy Page 1
Page 1 PHILOSOPHY General Major I. Depth and Breadth of Knowledge. A. Will be able to recall what a worldview is and recognize that we all possess one. B. Should recognize that philosophy is most broadlyMore information
13 Infinite Sets. 13.1 Injections, Surjections, and Bijections. mcs-ftl 2010/9/8 0:40 page 379 #385
mcs-ftl 2010/9/8 0:40 page 379 #385 13 Infinite Sets So you might be wondering how much is there to say about an infinite set other than, well, it has an infinite number of elements. Of course, an infiniteMore information
Introduction. Dear Leader,
Table of Contents Introduction...4 Meeting and Setting Goals...6 Week 1: The Great Human Questions...9 Week 2: Examining the Ways We Know...15 Week 3: The Christian Worldview...24 Appendix A: The DivineMore information
Artificial intelligence PHILOSOPHY OF ARTIFICIAL INTELLIGENCE. Strong AI Thesis. Weak AI Thesis. Can a machine think?
Artificial intelligence PHILOSOPHY OF ARTIFICIAL INTELLIGENCE Prof.Dr John-Jules Meyer Dr Menno Lievers Artificial Intelligence is the science of making machines do things that would require intelligenceMore information
Transcription of Questions and Answers from Virtual Open Event of Wednesday 23 rd February 2011
Transcription of Questions and Answers from Virtual Open Event of Wednesday 23 rd February 2011 Topic Question Answer Administration Administration Administration Administration/Entry Requirements Is itMore information
General Philosophy. Dr Peter Millican, Hertford College. Lecture 3: Induction
General Philosophy Dr Peter Millican, Hertford College Lecture 3: Induction Hume s s Fork 2 Enquiry IV starts with a vital distinction between types of proposition: Relations of ideas can be known a prioriMore information
Nash and game theory
Nash and game theory Antonio Cabrales 1 I am asked to give my view on the contribution of John Nash to the development of game theory. Since I have received most of my early influence through textbooks,More information
An Innocent Investigation
An Innocent Investigation D. Joyce, Clark University January 2006 The beginning. Have you ever wondered why every number is either even or odd? I don t mean to ask if you ever wondered whether every numberMore information
Introduction to computer science
Introduction to computer science Michael A. Nielsen University of Queensland Goals: 1. Introduce the notion of the computational complexity of a problem, and define the major computational complexity classes.More information
The Classes P and NP
The Classes P and NP We now shift gears slightly and restrict our attention to the examination of two families of problems which are very important to computer scientists. These families constitute theMore information
Teaching Writing and Teaching Philosophy
Teaching Writing and Teaching Philosophy Ray Perkins and Dan Kervick We would like to explore two questions concerning philosophy and writing: (1) How might the study of philosophy be used to teach goodMore information
DO WE REALLY UNDERSTAND QUANTUM MECHANICS? COMPRENONS-NOUS VRAIMENT LA MECANIQUE QUANTIQUE? VARIOUS INTERPRETATIONS OF QUANTUM MECHANICS IHES, 29 janvier 2015 Franck Laloë, LKB, ENS Paris 1 INTRODUCTIONMore information
S5 solution to the red hat puzzle
S5 solution to the red hat puzzle 1 Florida State University Abstract: I argue that the solution to the Red Hat Problem, a puzzle derived from interactive epistemic logic, requires S5. Interactive epistemicMore information
7 Conclusions and suggestions for further research
7 Conclusions and suggestions for further research This research has devised an approach to analyzing system-level coordination from the point of view of product architecture. The analysis was conductedMore information
! Insurance and Gambling
2009-8-18 0 Insurance and Gambling Eric Hehner Gambling works as follows. You pay some money to the house. Then a random event is observed; it may be the roll of some dice, the draw of some cards, or theMore information
Am I An Atheist Or An Agnostic?
Am I An Atheist Or An Agnostic? A Plea For Tolerance In The Face Of New Dogmas by Bertrand Russell (1947) I speak as one who was intended by my father to be brought up as a Rationalist. He was quite asMore information
A Few Basics of Probability
A Few Basics of Probability Philosophy 57 Spring, 2004 1 Introduction This handout distinguishes between inductive and deductive logic, and then introduces probability, a concept essential to the studyMore information
Perfect being theology and modal truth
Perfect being theology and modal truth Jeff Speaks February 9, 2016 Perfect being theology is the attempt to use the principle that God is the greatest possible being to derive claims about the divineMore information
CHAPTER II THE LIMIT OF A SEQUENCE OF NUMBERS DEFINITION OF THE NUMBER e.
CHAPTER II THE LIMIT OF A SEQUENCE OF NUMBERS DEFINITION OF THE NUMBER e. This chapter contains the beginnings of the most important, and probably the most subtle, notion in mathematical analysis, i.e.,More information
Gibbs Sampling and Online Learning Introduction
Statistical Techniques in Robotics (16-831, F14) Lecture#10(Tuesday, September 30) Gibbs Sampling and Online Learning Introduction Lecturer: Drew Bagnell Scribes: {Shichao Yang} 1 1 Sampling Samples areMore information
On a Straw Man in the Philosophy of Science A Defense of the Received View
On a Straw Man in the Philosophy of Science A Defense of the Received View Sebastian Lutz Theoretical Philosophy Unit Utrecht University The Netherlands July 9 th 2010 Perception Assumption Suppe, TheMore information
A Working Knowledge of Computational Complexity for an Optimizer
A Working Knowledge of Computational Complexity for an Optimizer ORF 363/COS 323 Instructor: Amir Ali Ahmadi TAs: Y. Chen, G. Hall, J. Ye Fall 2014 1 Why computational complexity? What is computationalMore information
The Double Lives of Objects: An Essay in the Metaphysics of the Ordinary World
252 The Double Lives of Objects: An Essay in the Metaphysics of the Ordinary World, by Thomas Sattig. Oxford: Oxford University Press, 2015, 288 pages, ISBN 9780199683017 (hbk). In The Double Lives ofMore information
Betting interpretations of probability
Betting interpretations of probability Glenn Shafer June 21, 2010 Third Workshop on Game-Theoretic Probability and Related Topics Royal Holloway, University of London 1 Outline 1. Probability began withMore information
Science, Religion and the Limits of Knowledge
Santa Clara University Department of Electrical Engineering Dr. Aleksandar I. Zecevic Winter 2015 ENGR 343 Science, Religion and the Limits of Knowledge REQUIRED TEXT Aleksandar I. Zecevic, Truth, BeautyMore information
6.254 : Game Theory with Engineering Applications Lecture 10: Evolution and Learning in Games
6.254 : Game Theory with Engineering Applications Lecture 10: and Learning in Games Asu Ozdaglar MIT March 9, 2010 1 Introduction Outline Myopic and Rule of Thumb Behavior arily Stable Strategies ReplicatorMore information
Ethics: What Is Right?
8 Ethics: What Is Right? The word ethics comes from the Greek word ethos, meaning custom. The Latin equivalent of this term is mores (customs), from which we derive our words moral and morality. AlthoughMore information
1/10. Descartes 2: The Cogito and the Mind
1/10 Descartes 2: The Cogito and the Mind Recap: last week we undertook to follow Descartes path of radical doubt in order to attempt to discover what, if anything, can be known for certain. This pathMore information
Critical and creative thinking (higher order thinking) refer to a set of cognitive skills or strategies that increases the probability of a desired outcome. In an information- rich society, the qualityMore information
Descartes Handout #2. Meditation II and III
Descartes Handout #2 Meditation II and III I. Meditation II: The Cogito and Certainty A. I think, therefore I am cogito ergo sum In Meditation II Descartes proposes a truth that cannot be undermined byMore information
THE STATESMAN. A GWC Student Attends Law School. New 2005 George Wythe College Campus. Happy Holidays! From George Wythe College. On Campus Seminars:
THE STATESMAN Volume 8 Issue 12 December 2005 Happy Holidays! From George Wythe College On Campus Seminars: Dec 16-17 Mar 4-5 Mar 7-8 May 2-27 May 30-31 July 15-16 Roots of America How to Read a Book AMore information
How to start research and how to present it?
How to start research and how to present it? Peter Kondor Budapest, CEU, 2010 Introduction What is research? How to start? How to present it? How to make it a paper? The main purpose of workshop to provideMore information
Subject area: Ethics. Injustice causes revolt. Discuss.
Subject area: Ethics Title: Injustice causes revolt. Discuss. 1 Injustice causes revolt. Discuss. When we explain phenomena we rely on the assertion of facts. The sun rises because the earth turns on itsMore information
TEACHER IDENTITY AND DIALOGUE: A COMMENT ON VAN RIJSWIJK, AKKERMAN & KOSTER. Willem Wardekker VU University Amsterdam, The Netherlands
International Journal for Dialogical Science Spring 2013. Vol. 7, No. 1, 61-65 Copyright 2013 by Willem Wardekker TEACHER IDENTITY AND DIALOGUE: A COMMENT ON VAN RIJSWIJK, AKKERMAN & KOSTER Willem WardekkerMore information
Philosophy 1100: Introduction to Ethics
Philosophy 1100: Introduction to Ethics WRITING A GOOD ETHICS ESSAY The writing of essays in which you argue in support of a position on some moral issue is not something that is intrinsically difficult.More information
PHLA The Problem of Induction
Knowledge versus mere justified belief Knowledge implies truth Justified belief does not imply truth Knowledge implies the impossibility of error Justified belief does not imply impossibility of errorMore information
How an undergraduate education in philosophy has helped me in physics
Journal of the NUS Teaching Academy Volume 4 Number 1 March 2014 From the Desk of... How an undergraduate education in philosophy has helped me in physics A. J. Leggett 1 1 2003 Nobel Laureate in PhysicsMore information
(Refer Slide Time: 1:41)
Discrete Mathematical Structures Dr. Kamala Krithivasan Department of Computer Science and Engineering Indian Institute of Technology, Madras Lecture # 10 Sets Today we shall learn about sets. You mustMore information
What Is School Mathematics?
What Is School Mathematics? Lisbon, Portugal January 30, 2010 H. Wu *I am grateful to Alexandra Alves-Rodrigues for her many contributions that helped shape this document. The German conductor HerbertMore information
Review. Bayesianism and Reliability. Today s Class
Review Bayesianism and Reliability Models and Simulations in Philosophy April 14th, 2014 Last Class: Difference between individual and social epistemology Why simulations are particularly useful for socialMore information
How Psychology Needs to Change
How Psychology Needs to Change Lois Holzman, Talk given at Vygotsky Today Symposium, Faculty of Philosophy, University of Banja Luka, Bosnia-Herzegovina, November 2004. I am a psychologist and I am proudMore information
CHAPTER 7 ARGUMENTS WITH DEFIITIONAL AND MISSING PREMISES What You ll Learn in this Chapter In Chapters -5, we developed a skill set that s sufficient for the recognition, analysis, evaluation and constructionMore information
Arguments and Dialogues
ONE Arguments and Dialogues The three goals of critical argumentation are to identify, analyze, and evaluate arguments. The term argument is used in a special sense, referring to the giving of reasonsMore information
Mathematics Undergraduate Student Learning Objectives
Mathematics Undergraduate Student Learning Objectives The Mathematics program promotes mathematical skills and knowledge for their intrinsic beauty, effectiveness in developing proficiency in analyticalMore information
6.254 : Game Theory with Engineering Applications Lecture 2: Strategic Form Games
6.254 : Game Theory with Engineering Applications Lecture 2: Strategic Form Games Asu Ozdaglar MIT February 4, 2009 1 Introduction Outline Decisions, utility maximization Strategic form games Best responsesMore information
Approaches to Apologetics
Approaches to Apologetics By John McClean Matthias Media (The Briefing #119; www.matthiasmedia.com.au/briefing). Used with permission. A poverty stricken student reaches the end of her financial resourcesMore information
Compass Interdisciplinary Virtual Conference 19-30 Oct 2009
Compass Interdisciplinary Virtual Conference 19-30 Oct 2009 10 Things New Scholars should do to get published Duane Wegener Professor of Social Psychology, Purdue University Hello, I hope you re havingMore information
Iterated Dynamic Belief Revision. Sonja Smets, University of Groningen. website: http://www.vub.ac.be/clwf/ss
LSE-Groningen Workshop I 1 Iterated Dynamic Belief Revision Sonja Smets, University of Groningen website: http://www.vub.ac.be/clwf/ss Joint work with Alexandru Baltag, COMLAB, Oxford University LSE-GroningenMore information
Marketing Automation And the Buyers Journey
Marketing Automation And the Buyers Journey A StrategyMix White Paper By Jonathan Calver, Managing Director, StrategyMix About this Paper This paper will first introduce you to the principles and conceptsMore information
1 Nonzero sum games and Nash equilibria
princeton univ. F 14 cos 521: Advanced Algorithm Design Lecture 19: Equilibria and algorithms Lecturer: Sanjeev Arora Scribe: Economic and game-theoretic reasoning specifically, how agents respond to economicMore information
Descartes Meditations Module 3 AQA. Meditation I Things which can be called into Doubt
Descartes Meditations Module 3 AQA Meditation I Things which can be called into Doubt Descartes rejects all his beliefs about the external world because they are doubtful and he wants to find a foundationMore information
Science, Religion and the Limits of Knowledge
Santa Clara University Department of Electrical Engineering Dr. Aleksandar I. Zecevic Winter 2013 ENGR 343 Science, Religion and the Limits of Knowledge REQUIRED TEXT Aleksandar I. Zecevic, Truth, BeautyMore information


text: Adaptive optics has a record of success with regard to improving the performance of optical systems in high-aberration environments. Whether correcting for atmospheric turbulence, thermal gradients or aberrations in the cornea and lens of the human eye, the technique has demonstrated the ability to remove moderate-order aberrations from propagation paths. As adaptive optics devices become more accessible, their range of potential applications grows.Researchers are now contemplating the use of adaptive optics in the microscopic imaging of biological specimens. The first step in designing an adaptive system is to understand its performance requirements. However, not much is known about the character of aberrations introduced by biological specimens. Tony Wilson, a professor of engineering science at Oxford University in the UK, has taken that first step by quantifying the aberrations that typical biological specimens introduce into an optical path.His team constructed a Mach-Zehnder interferometer operating at 633 nm to investigate a cross section of specimen types from rats, mice and C. elegans, including brain cells, organ and muscle tissue, and egg cells. In the object leg of the interferometer, the beam was transmitted through a sample, which was sandwiched between two Zeiss 1.2-NA water-immersion microscope objectives. The reference beam was stepped to provide three relative phases, and the beam was scanned across the sample in a 16 × 16 grid. The sample and reference beams were recombined at a CCD camera, and the data were processed to produce both an intensity and a phase map of each sample.Aberrations within a specimen become important when imaging a point within a cell. Confocal-fluorescence and two-photon microscopy scan a small focal spot across a sample. The excitation beams at high numerical aperture enter covering a wide area, but they rapidly come to a focus. The optical path within the specimen, prior to focus, contains elements that may differ significantly in their index of refraction, from as low as 1.3 to as high as 1.7. These differences cause phase delays that vary on a spatial scale, dependent upon the particular arrangement of elements within the cell.The question is: Is the scale of these aberrations amenable to correction by adaptive optics? To represent a worst-case scenario, the team collected measurements with the object beam focused on the far side of the specimens -- that is, after it had propagated through the maximum tissue depth.To quantify the scale of the aberrations, the researchers decomposed the measured wavefronts into Zernike modes. They ignored the lowest-order terms -- tip, tilt and defocus -- because they do not contribute to loss in signal or resolution in real confocal-fluorescence and two-photon microscopy systems.Spherical aberration was particu-larly important because a relatively large component can be introduced by the typical specimen geometry: a converging beam propagating through a cover slide layer of one index to a specimen layer of another index. Care was taken to eliminate the component that was not directly dependent on the sample.They calculated the Zernike terms and applied corrections to simulate the effect of an adaptive optical system employing Zernike modal correction. By calculating the Strehl ratios for different orders of correction, they could predict the signal improvement for different specimens and correction settings.The median signal improvement factor for 22 Zernike terms varied from a low of 1.6 in a mouse oocyte to a high of 4.4 in mouse liver tissue. In general, increasing the spatial frequency of the correction to include the first 37 Zernikes improved the signal collection only marginal-ly. In many cases, correction of 18 Zernikes compensated for the bulk of the aberrations. This is good news, because higher-frequency corrections are more difficult to realize in actual adaptive optics systems.

subset: commoncrawl


text:
|10 Oct 2011
Windows 7 Ultimate x64
Windows 7 boot fail
Hello, sorry for my english but This forum is probably the last thing that could help me.
I rode other topics about this problem. When I start computer it stops right before "Starting Windows" and there is only a black screen. I cant start windows any way.
So i put a disc with windows and try to repair but it said: "there is no problem with windows starting"
Than I started a console and try to insert c: and then
bootrec /fixmbr and fixboot
but fixboot doesn't work - I dont remember literally but it said something like: there is no filesystem/wrong filesystem
when i try to scanos it say that there is 0 operating systems.
Then I tried to run gparted to flag a disc, but it showed me different partitions configuration then ive got on windows - there is no windows disc!
oo.. i tried also to build BCD but when i had to put command: cd boot it said there is no comand like that
Please help me... I dont want to make a format...
Are there any different ways of fix it?
Sorry sorry from my english
|My System Specs
|10 Oct 2011
Does the HD register in BIOS setup? Is it set first to boot in BIOS setup, after CD/DVD drive? Try booting HD maker's diagnostic/repair CD to run extended scan: HD Diagnostic
Check for infection by installing, updating and running full scan with Malwarebytes in Safe Mode with networking. If no Safe Mode then download, burn to CD or write to flash stick, boot and run a full scan with Microsoft Standalone System Sweeper.
Boot back into the DVD REpair console or Repair CD to see if it discovers an installation to repair. If not, click through to Recovery Tools list to open command Prompt, type bootrec /fixboot and bootrec /fixmbr to see if it will now show an installation to repair. Do not change the drive letter as you say you did. If it now finds an installation to repair run Startup Repair repeatedly regardless of its finding at first. Next try System Restore from the Repair tools list, then using Command Line SFC -SCANNOW Run in Command Prompt at Boot
Next boot free Partition Wizard bootable CD to see if the 100mb System Rserved partition (preferred) or Win7 partition are still marked Active. If not, rightlick to Modify>Set to Active, then highlight the HD, from Disk tab select "Rebuild MBR", apply steps, reboot to see if it will start. You can also Explore the partitions to see if your files are intact; if so the OS should be reparable unless you damaged it with previous repair attempts.
You can copy out your files using DVD/Repair CD: Copy & Paste - in Windows Recovery Console or using Paragon Rescue CD.
Then if all else fails run Factory Recovery from boot using its Fkey given on first screen, or Recovery Disks you've made or order from manufacturer, or find a Win7 isntallation DVD to clean reinstall with Product Key on COA sticker following these steps: Reinstalling Windows 7
|My System Specs
|Thread Tools
|Similar help and support threads
Windows boot fail: Boot selection failed because a required device is
Hi there, I've recently built a new rig and I've had continuous problems trying to boot. I have two HDDs and one SDD. It seems when the two HDDs are plugged in, i can sometimes boot ok, and most times i get: Or Please select a boot device, or something to the affect. I've updated to the...
|Hardware & Devices
Computer or Windows 7 fail to boot.
I had to do a clean install of Windows 7, because while trying to fix dual boot with Windows 8 problem, after I no longer wanted dual boot with Windows 8. My main HDD failed, I had to install another HDD, tested it, checked good, I then installed Windows 7 on it, also I used other software and...
|General Discussion
Windows Boot Manager FAIL!
Hello Everyone. I had a dual boot with Win7 and Win8. I wanted to remove Win8 cause I was bored and didn't need it. So I used a method on this forum. I did everything right. https://www.sevenforums.com/tutorials/210983-dual-boot-delete-os.html But the boot manager failed. When I restarted...
|General Discussion
INTEL to AMD Windows Boot Fail
Alright guys, this is gonna be a fun one. I bought a new AMD AM3+ 8 core processor and Asrock mobo from Microcenter tonight, got home and stripped the old outdated Intel gear, for the AMD. I've got all of my AMD setup wires tucked neatly, get it to it's bay, turn it on and fail.. It...
|Hardware & Devices
Why did my windows 7 boot fail?
Recently I just tried starting my computer on and it wouldn't boot. I left my computer in locked mode then it eventually went to sleep. I kept trying to restart it and had no luck, I checked inside the cpu was running and the dvd drive was still able to open and close. My USB mouse or...
|General Discussion
|Our Sites
|Site Links
|About Us
|Find Us
Windows 7 Forums is an independent web site and has not been authorized, sponsored, or otherwise approved by Microsoft Corporation. "Windows 7" and related materials are trademarks of Microsoft Corp.
© Designer Media Ltd
All times are GMT -5. The time now is 09:14.


text:
Laurance S. Rockefeller founded Caneel Bay in the belief on the restorative power of Nature, a place where guests can relax and recharge, then return to their daily lives. Today, more than ever, we at the Massage Program encourage each person to invest in their Well Being. We hope you will join us in recognizing and receiving the restorative value of our services.
A variety of therapeutic and relaxing massage techniques are available from our qualified staff of skilled licensed massage therapists. Contact the Concierge Desk for information and appointments at 340.776.6111 x7218.
Raindrop Technique
Hot Stone Massage
Caribbean Bliss *
*Minimun of 6-full session appointments
Bee-utiful Facial
Please note: An additional 20% gratuity is added for all Spa Treatments.
Click here for more information on Caneel Bay
Uzzell, LLC
2009 - 2014 Copyright


text:
ACHI creates issue briefs, fact sheets, and reports about our current health system and why its transformation is important in Arkansas. Selected documents are organized here to create a more complete picture of the innovative and interrelated work taking place in Arkansas to improve the health and productivity of Arkansans.
The following resources have been made available as part of this project page. Resources are typically files like PDFs or Word documents, and will be downloaded when you click them.
Arkansas Center for Health Improvement
1401 West Capitol
Suite 300 (Victory Building)
Little Rock, AR 72201


text:
RideOn is the First-Ever Outdoor Mixed Reality Sports Headset
We see a lot of indoor VR simulation experiences for sports. There are flying machines, being a bird, rowing experiences and various biking and riding experiences. Some of these indoor VR sports simulations are pretty fun, but all have a similar limiting factor. You have to be confined to an indoor experience. RideOn see the world in really cool way and have decided to take a different route.
RideOn have built the first-ever active sports goggles for mixed reality. The goggles provide you a mixed reality experience outdoors and are designed for extreme light conditions. If you imagine comparing this to other Augmented and Mixed Reality products on the market, they all have a common problem: you really need to be indoors or in "normal" light conditions to use them.
Check out our video demonstration of the RideOn Ski Goggles
The product inspiration came from their background in flying planes in the military and using various forms of Augmented Reality. The founder, Alon Getz, who is an avid skier and loves sports, realised the potential and set out to develop the RideOn products.
The First Mixed Reality Ski Goggles with Tons of Features
Having completed a successful round of funding on Indiegogo, the team at RideOn have been working round-the-clock to get their first product, a Mixed Realty Ski Goggle, out onto the market. The goggles are built with an onboard computer with 1.2 Ghz dual-core processor and an ARM Cortex 9. In addition, goggles come with an onboard camera that can record up to 3 hours of footage. They also have built-in bluetooth so that you can be connected to the internet with your phone. Controls within the goggles are managed using your eyes which is both practical and very cool as well.
What makes these goggles so interesting is that you can create a slalom or obstacle course experience while skiing. You select the course and then find a series of rings appearing in front of you in the snow. You are then timed and measured for your accuracy as you ski through the rings. In addition, you can coordinate with your friends to meet them and maintain contact while skiing or snowboarding. If you have been skiing, you probably know how annoying it is to pull off your gloves and dig out your phone to find out where your friends are. With the RideOn goggles, you can avoid much of this hassel by contacting them straight through the goggles without having to use your hands.
The Sports Market Remains Completely Untapped
Going beyond skiing and snowboarding, market research shows that the Augmented and Mixed Reality market is really in its infancy. Analysts in the industry have speculated that it could reach $20B by 2020. And within that there is a huge market for a variety of sports and uses such as motorbike helmets, bicycle glasses, sky diving goggles to even displays for boating and flying.
So is this Just the Ultimate Gadget or is it Practical?
The potential uses for making sports more engaging, fun and social certainly is more than appealing. Its both practical and also can enhance our entire sporting experience. There is also the potential that with more information available you can make better decisions and even train better or harder. Imagine having your heart rate on display while you are running or having information available to help you optimise your workout. All of this is possible and certainly part of the RideOn mission.
Having spent time analysing their product, researching the market and speaking with their team, there is a lot more to come from RideOn. We are excited and anxiously await to see what their product roadmap delivers in the near future. And until then…RIDE ON!
Follow us for the latest and coolest news, previews, trailers and sneak peaks into the exciting world of Augmented, Mixed and Virtual Reality.
Apple News: IamVR
Facebook: IamVRNews
Flipboard: IamVR Official
Google+: IamVR Official
Instagram: IamVR_Official
Medium: IamVR
Pinterest: IamVROfficial
Tumblr: IamVROfficial
Twitter: @IamVROfficial
Youtube: IamVROfficial


text:
Camp Info
Each camp will offer a unique learning experience that will enhance summer time and enrich child development. Outdoor activities are varying by seasonal themeWe offer adult supervision from 4 PM to 6 PM for an additional charge of $10/hr
All activities will be hosted weekly inspired on the 4 seasons of the year!
The camper will develop a creative character by artistic expression activities which include; making collages with magazines and construction papers, acrylic paintings, 3D frames, abstract projects, marbling with paper, painted pots, and others.
Convert something old to a new and useful one! Join us for a magical day of imagination and creation. We'll be using disposable materials to create masks, storage boxes, desk organizers, cd mosaics, plastic bottle containers and bird houses, bottle caps art. Campers will enjoy going green through their art! Campers will become familiar with concepts of reducing, reusing, and recycling while expressing creativity.
Does your kiddo like to create and decorate things? We will develop their creativity to create handicrafts with paper, use different materials to make flowers, bottles and boxes decoration, cards and tags, ornaments, and signs made out of beans!
A day full of wild and crazy experiments awaits! We will discover how things work and interact with one another, we will make experiments, exploring the wilderness, and planting seeds.
Join us in becoming amazing chefs this summer! We will cook up lots of delicious food, snacks, and desserts. Our kitchen will be filled with lot of stuff like cookies decoration, making and decorating cake pops, jell-o designs and pizza making. Come join in on all the cooking fun!
Game On! We are going to stay busy all day playing games! We're going to do sack races, treasure hunting, table games, obstacle courses, hula hoop games, and a splash zone a waits for you, to refresh at the end!
Let's play as a team to win! We'll be playing soccer, basketball, backyard baseball! The winning team will receive an insignia which could be used to win prizes at the end of the week!


text:
View the best solar energy companies currently servicing Pine Bluff, CA
Our 1,713 reviews of the 164 solar power companies servicing Pine Bluff in 2018 shows you the best 10 local solar panel installation companies by reputation. Enter your zip code and bill into the solar cost and savings calculator above to also see the cost of installing solar with the best solar companies near you and to get free quotes if you wish.
Firstly, no solar contractors can pay to get listed at the top of our search results.
The order of our list of best solar installers is displayed based on a formula balancing reviews number and reviews score only from the last two years. If a company has a lot of reviews and a higher average reviews score, but is below another company in the list, it is because most of their reviews are old and the company above them has more reviews at a better average reviews score in the last two years (even if overall they have fewer reviews or a lower all time average reviews score).
We show all solar energy contractors that have received reviews of solar panel installation work they have done in Pine Bluff even if they don't have an office in Pine Bluff. There are a lot of renewable energy companies in the solar industry in the United States that service areas in which they don't have offices via contract installation teams. Some of these companies receive a lot of complaints (see the big national installers reviews like Vivint Solar, Sunrun and Solar City), but others have really good reviews and so we don't exclude them from our top solar companies lists. They often bring price competition to smaller cities where the local solar companies are so busy they need to put their prices up. It is up to you how much weight you put on a local office when choosing between solar companies.
Services: Commercial Solar Electric, Residential Solar Electric, Energy Monitoring, Storage, Energy Audits
Office location: Canoga Park, CA 91303
I can not enough good things about NRG. Price was the best, organization, communication and professionalism was outstanding and superb.
Sunpower by Hooked On Solar
Services: Residential Solar Electric, Energy Monitoring, Storage, Energy Audits
Office location: Lincoln, CA 95648
Mitzi was great to work with! Patient, thorough in explaining options, and best of all, the system recommended has produced as promised (after one year).
Services: Residential Solar Electric, Energy Monitoring, Storage, Commercial Solar Electric
Office location: Tempe, AZ 85282
Our experience with Sunny Energy was excellent, for every question I had was answed either by email or by phone call
Services: Commercial Solar Electric, Residential Solar Electric, Energy Monitoring, Storage, Wind Turbines
The install process was perfect. No problems and no worries. Even came back to make sure system was running tip top. I would recommend this company to my friends and family.
See the best offers available in your city
Services: Commercial Solar Electric, Residential Solar Electric
Joanna was very knowledgeable and she knows how many panels you know. What kind of package best suits your family need. She is been working with the company for more than ten years.
Services: Residential Solar Electric
Ok lets first say this, Solar is a bad industry, The companies out there are like a bait and switch, Just want to get you to sign on the bottom line and don't care about you what so ever. Not true with Yancey, Joe Hess came out to the house and spent about 4HRS going over all the power needs I had. I thought the other companies I had tried to get quotes from were being thorough. But they weren't. Joe made sure I understood every part of this process.Solar is not cheap by any means. It will take you many years to recover. If its done right it should be 7-10Yrs. Yancey is a roofing company. This is important. I have watched my neighbors getting solar installed and they don't seem to care about tile roofs. They walk all over probably cracking your roof tiles and don't tell you about it. Yancey inspected mine before installation, discovered some that were cracked and I got the tiles and they replaced them for me. Also the other companies don't care how it looks either. They go around your vents leaving a checker board appearance on your house. Yancey actually came out and re-located my vents so when we put the solar on it was nice and clean. even went the extra steps to paint the conduit to match my house. Of course you have to have the paint for them. But they will do it. All said and done I feel confident that I chose the BEST solar people around. I did not feel cheated, manipulated, or coerced into doing this. I feel very GOOD about my choice. Also another thing to consider is the fact that there are many different types of solar panels out there, You think solar is solar, But in the end its not. For instance there different panels that look the same but produce at a different level. More power less panels. Panels that work in line. One goes down all go down. Or were they are each independent and one can go offline but your still producing. These guys explained all to me. and then I chose. With there recommendation of course. Do I feel I paid a lot. YES. But I also think this is a investment and over time I will get my money back. By the way all my estimates were all within 5k of each other. But other quotes were for lesser quality and no extras, slap em up and get out of there type attitudes. Yancey stood by, made sure I was satisfied. and I am confident that they will be there for me if anything goes wrong in the system. I cant say that about the other companies that quoted me. So all in all am I happy i can say Confidently YES i am. You cant go wrong by getting a quote by Joe Hess or Yancey. You will learn a lot from them.... read more
Services: Storage, Commercial Solar Electric, Residential Solar Electric
Last year we moved into a house that already had 24 old Sharp monocrystalline panels that were working fine but produced insufficient power for our 2 electric cars and new, energy-efficient electric appliances. Ilum Solar had been recommended by a friend, so we contacted them to add 7 Trina Solar, each nearly twice as efficient as our old Sharp panels. Ilum's installers did a neat, effective installation on our tricky roof and we couldn't be more pleased! Clean, professional, and reasonably priced installation! We would definitely recommend Ilum to anyone, but especially folks who want to add-on but don't know if it will be viable and economical. You're likely to be pleasantly surprised!... read more
Installed SunPower 2 1/2 years ago. Could not be happier with the crews at Capitol City... friendly, professional.. always answered my questions.. always there to resolve whatever issues I had. Even on subsequent maintenance work (minitor unit died), crew showed when they said they would and took the time to explain everything they were doing and the changes being made.. just were great to work with. Highly recommend Capital City Solar and SunPower.... read more
See the best offers available in your city
Services: Commercial Solar Electric, Residential Solar Electric
Company was very easy to work with and professional from the bid process through install. Neighbor and I both went with them and have no regrets from the price to service. The wife and I both like their business/sales style. Give them a shot!
Energy Expert Solutions Inc (Formerly Known as Sol Power Development, LLC)
Services: Energy Audits, Residential Solar Electric, Wind Turbines, Solar Pool Heating, Energy Monitoring, Solar Hot Water (Thermal), Storage, Commercial Solar Electric
Deciding to install Solar was a no brainer considering the fact that I live in a hot climate that requires a lot of AC to be comfortable. Choosing a solar contractor was a bit more challenging - trying to weed out the good and reasonably priced companies. I decided go with Patrick Weller - he is a C-46 contractor - one who has the credentials specific to design and installation of solar systems. He is very professional and knowledgeable and was able to easily answer all my questions (I have a Electrical Engineering degree so I had many). I highly recommend Patrick - He and his crew get a 5-star++ rating.... read more
Search by city
Average rating for solar companies in Pine Bluff, CA
Popular solar installation facts
Top 100 residential solar installers 2018
Top 100 most reviewed installers
Best solar companies in Pine Bluff, CA offering quotes online
Highest rated solar companies in Pine Bluff, CA
Pine Bluff covers the following zip codes:
Back to list of Cities in California


text:
Last Updated: 3 days ago
2204 Edgelands Drive, Reno NV 89521
From $592,995
Why 'From' pricing?
New homes can be personalized to your needs and taste.
Builders pricing can vary greatly. Builders display base pricing because you have not selected your options and upgrades yet and some homes may indicate that the land cost is not included.
Meribel (3733 sq. ft.) is a home with 5 bedrooms, 3 bathrooms and 3-car garage. Features include living room and master bed upstairs.
Builder Community Sales Office Map
2204 Edgelands Drive, Reno, NV 89521
Sales Agent: Jenny Evans & Melissa Miller
Hours: Mon 1 pm to 6 pm; Tue-Sun 10 am to 6 pm
Diamond Crest at Bella Vista Ranch
Diamond Crest is in the Bella Vista Ranch master plan and offers two-story living with expanded covered deck and bonus room options. Home designs display open concept floor plans with an upstairs master bedroom and 3-car garage. Diamond Crest is a short drive from Lake Tahoe and is located near world-renowned ski resorts including Mt. Rose, Heavenly, Squaw Valley, Northstar, Boreal, and Diamond Peak. Residents will enjoy resort-style living with amenities including a community clubhouse, outdoor swimming pool, fitness center, and more.Visit the website Free brochure
Actual schools may vary. Contact the builder for more information.
Get the latest Reno news and deals delivered weekly!
We will never share your email address.
Privacy policy


text:
I am a member of BzzAgent and was lucky enough to be a part of the Hill's Science Diet pet food campaign. For being a member, I was sent a free bag of pet food to test out and review. I chose to test out the cat food because we did an earlier campaign for pet food that Mason got to participate in and we like to be all equal opportunity in this household....
I used to work for a Veterinarian....one that sold Hill's Science Diet in his clinic. I know how strongly he recommended it to his clients...but I also know how expensive it is. And, if your animals are anything like MY animals (and kids for that matter)...they can be picky eaters at times. Some days they chow down like they haven't been fed in WEEKS and other days they just pick at their food like they think it's laced with arsenic or something (and yes...this applies to both the pets AND the children).
So, needless to say, I've always been a bit reluctant to dole out wads of cash for pet food that may or MAY NOT be eaten by my pets. I don't like to buy the cheapest food on the shelf for my cat...I like to buy her something that I feel enhances her health and helps her live a more meaningful INDOOR life. With that said, I was SO incredibly happy to be chosen for this campaign so that I could test to see if she liked it or not.
And she did...boy did she ever. I poured some in her bowl the night I received it and she had pretty much eaten the entire bowl of food in the time it took me to run 3 miles on the treadmill (ok...so that might be a bit of time but whatever). No hesitation to the food whatsoever...she just dug in. Since then, I have been mixing it with my normally purchased food and she has been eating it all up like I'm treating her to fresh fish or something quite as delectable.
Will I continue to buy it? The jury is out. It IS quite a bit more expensive...but it will last longer if I mix it with her normal food. She doesn't really have any medical issues right now...so we don't need speciality food at this point (for overweight, hairball, old age, etc). But you can bet I won't hesitate to turn to Science Diet if the need arises...because I have nothing to worry about in terms of her rejecting it...and that was my main concern.
Do you have a pet and would you like to try it to? Well YOU are in luck!!
Just go to: www.hillspet.com/idealbalance to check out their Competitive Cat and Dog Food Comparison tools, an easy way to compare your current pet food to Ideal Balance™, and download a Free Bag Rebate!!!


text:
LAHORE: Prime Minister Nawaz Sharif has invited Turkish businessmen to invest in energy, agriculture, textile, tourism and infrastructure building sectors in Pakistan. Meanwhile Pakistan and turkey have sighed three MOUs for cooperation between the two countries in different fields.
Addressing Pak-Turk Business Forum in Lahore on Monday he said his Government would ensure full protection and support to the Turkish investment.
The Prime Minister asked Turkish enterpreneurs to explore the possibility of investment in the energy sector in Pakistan which has wide-ranging potential in thermal, hydel and alternative sources.
He said Pakistan has also embarked upon an ambitious programme of infrastructure development and Turkish cooperation would be welcome. He said the programme includes construction of motorways, highways, airports, theme parts and Economic Corridor linking Pakistan and China.
The Prime Minister noted that Turkish businessmen have expressed their desire to invest in Diamer-Bhasha and Bunji dams, Lahore-Karachi motorway and Gaddani Power Park.
He said Board of Investment of Pakistan is also working with Pak-Turkey Business council in promoting cooperation in textile, automobile and communication sectors.
He said there is vast potential in tourism development in Pakistan and Turkish firms can join their Pakistani counterparts for the purpose.
Mian Nawaz Sharif also recounted the incentives that Pakistan offers to foreign investors including repatriation of the capital, profit, and tax breaks, concessions in custom duties and special economic zones where one window facility is offered.
The Prime Minister said economic prosperity of people remains the top priority of the present government. He said our economic framework is based on sound macro-economic policies and accelerated economic growth, alleviate poverty and creating new jobs.
Addressing the Pakistan-Turkey Business Forum, Turkish Prime Minister Recep Tayyip Erdogan said Turkey attaches great importance to its relations with Pakistan.
He said Turkey will take benefit of investment opportunities in Pakistan.
The Turkish Prime Minister said with the visit of Turkish businessmen to Pakistan, a new chapter of trade will be opened between the two countries.
He said he is thankful of the Pakistan Government for encouraging the Turkish businessmen. He said people of Turkey and Pakistan are brothers and the Turkish people takes Pakistan as their second home.
Recep Tayyip Erdogan said Turkey wants to enhance trade volume with Pakistan. He said his country to increase cooperation between Turkey and Pakistan in different fields including agriculture and tourism.
Three MOUs were signed on the occasion for cooperation between the two countries in different fields.
Meanwhile Chief Minister Punjab Mian Shahbaz Sharif recalled the close and historic bonds between the two countries but emphasized the need to go beyond to forge a strong economic partnership to the mutual advantage.
He said Turkey has achieved all round progress and Pakistan has much to learn from the brotherly country.
He pointed out that there was time when exports of the two countries stood at the same level of four billion dollars but now Turkey has achieved the miraculous export figure of 150 billion dollars through hardwork and innovations.
He thanked Turkey for extending meaningful assistance in the implementation of Metro Bus project in Lahore.
Addressing Pakistan-Turkey Business Forum in Lahore this evening, Finance Minister Ishaq Dar said the structural reforms and the macro economic stability programme of the government have shows impressive results during the last five years.
He said tax collection grew by 17%; 7% increase in remittances and stock market capitalization increased by 22 percent.
The Finance Minister said international credit rating agencies are projecting positive outlook for Pakistan and all major donors including IFC, OPIC, World Bank, Asian Development Bank and Islamic Development Bank are happily dealing with Pakistan.
He pointed out that Pakistan has recently been given GSP plus status by the European Union and the country certainly has an edge over many countries of the region as far as labour cost is concerned.
Ishaq Dar said according to authentic reports, investors who invested in Chdina re thinking to relocate their businesses in this region particularly in Pakistan.
He said Pakistan has a lot of positive things to offer on the investment side, adding that it guarantees hundred percent repatriation of the capital and profit, dividends, capital gains, technical feel and royalties.


text:
French billionaire Paul Louis Halley, 69, was killed when his light aircraft went down near Oxford airport in 2003.
The same verdict was ruled on the deaths of his wife, Annik Jacqueline, 63, and Belgian pilot Hans Frans Walter Brams, 46, who were also killed.
The inquest, at Oxford Coroner's Court, lasted a day.
Mr Halley was the seventh richest man in France with a fortune estimated at £2.2bn.
Shortly after the accident, the then French prime minister, Jean-Pierre Raffarin, paid tribute to him as a "shining personality" and brilliant businessman.
An earlier investigation by the Air Accidents Investigation Branch into the crash on 6 December 2003 reached no definite conclusion.
The Socata TBM 700 aircraft was preparing to land at Oxford Airport after arriving from Brussels.


text:
Pete Wicks And Megan McKenna Are Over??
- BREAKING NEWS! Love Island Winners Jack And Dani Have SPLIT!
- Katie Price Make's Deal With Creditors To Avoids Bankruptcy
- Celebs Go Dating 2019 Series Announced With Pete Wicks, Kerry Katona, Georgia Steel And Chelsee Healey All Leading The Lineup!
- Anne Hegerty Screams Her Head Off As She Takes Part In Second Bushtucker Trial Of New I'm A Celeb Series
- Marvin And Rochelle Humes To Host New BBC Saturday Night Music Quiz Show
- Second Late Arrival On I'm A Celebrity Scrapped After ITV Pay Noel Edmonds £600,000
- Inbetweener's Beauty Emily Atack Stripps Off In The Jungle Shower On I'm A Celebrity
- Endemol To 'Meet' With Netflix Next Week About Them Buying Rights For Big Brother
- Emma Willis Weeps As She Presents The Last Ever Big Brother Final