Nature, Science, Bayes 'Theorem, and the Whole of Realityâ

Philosophy

Nature, Science, Bayes' Theorem, and the Whole of Reality Moorad Alexanian Department of Physics and Physical Oceanography University of North Carolina Wilmington Wilmington, NC 28403-5606 Abstract A fundamental problem in science is how to make logical inferences from scientific data. Mere data does not suffice since additional information is necessary to select a domain of models or hypotheses and thus determine the likelihood of each model or hypothesis. Thomas Bayes' Theorem relates the data and prior information to posterior probabilities associated with differing models or hypotheses and thus is useful in identifying the roles played by the known data and the assumed prior information when making inferences. Scientists, philosophers, and theologians accumulate knowledge when analyzing different aspects of reality and search for particular hypotheses or models to fit their respective subject matters. Of course, a main goal is then to integrate all kinds of knowledge into an all-encompassing worldview that would describe the whole of reality. A generous description of the whole of reality would span, in the order of complexity, from the purely physical to the supernatural. These two extreme aspects of reality are bridged by a nonphysical realm, which would include elements of life, man, consciousness, rationality, mental and mathematical abstractions, etc. An urgent problem in the theory of knowledge is what science is and what it is not. Albert Einstein's notion of science in terms of sense perception is refined by defining operationally the data that makes up the subject matter of science. It is shown, for instance, that theological considerations included in the prior information assumed by Isaac Newton is irrelevant in relating the data logically to the model or hypothesis. In addition, the concepts of naturalism, intelligent design, and evolutionary theory are critically analyzed. Finally, Eugene P. Wigner's suggestions concerning the nature of human consciousness, life, and the success of mathematics in the natural sciences is considered in the context of the creative power endowed in humans by God. I. INTRODUCTION In 1950, Albert Einstein gave a remarkable lecture (Einstein 2005, 46-8) to the International Congress of Surgeons in Cleveland, Ohio. Einstein argued that the 19th-century physicists' simplistic view of Nature gave biologists the confidence to treat life as a purely physical phenomenon. This mechanistic picture of Nature was based on the casual laws of Newtonian mechanics and the Faraday-Maxwell theory of electromagnetism. These causal laws proved to be wanting, especially in atomistic phenomena, which brought about the advent of quantum mechanics in the 20th-century. Einstein indicates that there are three principal features which science has firmly adhered to since Galileo Galilei. This includes not only physics, but also all natural sciences dealing with both organic and inorganic processes, "First: Thinking, alone, can never lead to any knowledge of external objects. Sense perception is the beginning of all research, and the truth of theoretical thought is given exclusively by its relation to the sum total of those experiences. Second: All elementary concepts are reducible to space-time concepts. Only such concepts occur in the 'laws of nature.' In this sense, all scientific thought is 'geometric.' A law of nature is expected to hold true without exceptions; it is given up as soon as one is convinced that one of its conclusions is incompatible with a single experimental fact. Third: The spatiotemporal laws are complete. This means, there is not a single law of nature that, in principle, could not be reduced to a law within the domain of space-time concepts. This principle implies, for instance, the conviction that psychic entities and relations can be reduced, in the last analysis, to processes of a physical and chemical nature within the nervous system. According to this principle, there are no nonphysical elements in the causal system of the processes of nature. In this sense, there is no room for 'free will' within the framework of scientific thought, nor for an escape into 'vitalism.' " (Einstein 2005, 46-8). Einstein understands by science the study of the physical aspect of Nature and denies the metaphysical doctrine of vitalism, viz. that living organisms possess a nonphysical aspect that gives them the property of life. In addition, 2 Einstein invokes a reductionist view that the laws of physics and chemistry alone suffice to explain life functions and processes. Of course, one cannot discern from Einstein's speech if he ascribes to the thesis that life emerges from a complex combination of organic matter, or more drastic still, inorganic matter. It is clear that the inferences that Einstein makes follow from a combination of known data and assumed prior information. Actually, the distinction one makes between what constitutes data and what constitutes prior information, or priors for short, is purely logical. Any additional information needed to make an inference beyond that provided by the data is by definition prior information. These concepts will be the topic of the next section. II. MATHEMATICAL MODEL OF REASONING The special theory of relativity is an often-cited example of inference based on purely deductive reasoning. The constancy of the speed of light in vacuum plus the invariance of the laws of physics for different inertial frames suffice to derive, together with the assumed uniformity and isotropy of spacetime, all the results in the special theory of relativity. Of course, inferences in science are mostly based on inductive or plausible reasoning where probability theory, not needed in deductive reasoning, is essential in the optimal processing of incomplete information as emphasized by Edwin Thompson Jaynes (Jaynes 2003, xix-xxix). It was the problem of how the longitudes of Jupiter and Saturn had varied over long times that led Pierre-Simon Laplace to the study probability theory. Although the latter was based on consideration of games of chance, Laplace saw early on that it would become the most important object of human knowledge. The following two quotes from Thorie Analytique des Probabilits, 1812 indicate Laplace's insight into the workings of the human mind, "The most important questions of life are indeed, for the most part, really only problems of probability," and "Probability theory is nothing but common sense reduced to calculation." The problem of induction has a long history. "Philosophers have argued over the nature of induction for centuries. Some, from David Hume (1711-76) in the mid-18th century to Karl Popper in the mid-20th century, have tried to deny the possibility of induction, although all scientific knowledge has been obtained by induction. D. Stove (1982) calls them and their colleagues 'the irrationalists' and tries to understand (1) how could such an absurd view ever have arisen? And (2) by what linguistic practices do the irrationalists succeed in gaining an audience?" (Jaynes 2003, 310). Scientists do not test their theories against an infinite number of alternatives in order to establish the absolute status of a hypothesis embedded in the universe of all conceivable theories. Instead, "The functional use of induction in science is not to tell us what predictions must be true, but rather what predictions are most strongly indicated by our present hypotheses and our present information?" (Jaynes 2003, 310). Jaynes (2003, 24) develops quantitative rules of inference by working out the consequences of the following desiderata: (I) Representation of degrees of plausibility by real numbers. (II) Qualitative correspondence with common sense. (III) Consistency. The fundamental principle underlying all probabilistic inferences is "To form a judgment about the likely truth or falsity of any proposition A, the correct procedure is to calculate the probability that A is true P (A|E1E2 * * * ) conditional on all the evidence E1E2 * * * at hand." (Jaynes 2003, 86). The symbol AB, the logical product or the conjunction, denotes the proposition that both A and B are true. The arguments A and B in the formal probability symbol P (A|B), which is a real number, are propositions and not numerical values. One deals always with a finite set of propositions and extension to infinite sets is permitted only when this is the result of a well-defined and well-behaved limiting process from a finite set. A. Bayes' Theorem As indicated by Laplace, what one wants is to use probability theory to indicate which of a given set of hypotheses {H1, H2, * * * } is most likely to be true in the light of the data and any other evidence at hand. For example, the hypotheses may be various suppositions about the physical mechanism that is generating the data. Fundamentally, physical causation is not an essential ingredient of the problem; "what is essential is only that there be some kind of logical connection between the hypotheses and the data." (Jaynes 2003, 88-9). If one uses probability theory as logic, then Bayes' theorem, first found by the amateur mathematician the Rev. Thomas Bayes (1763), can be used to make probabilistic inferences from incomplete information, say, data from the 3 observational or the experimental sciences, viz. P (H|DX) = P (H|X)P (D|HX)/P (D|X), where P (A|E) stands for probability that A is true conditional on the evidence E and X= prior information, H = some hypothesis to be tested, D= data. If the physical evidence D considered by different people is the same, then the real question is, what prior information X do different people consider in making logical inferences? The posterior probability P (H|DX) depends on the product DX and not separately on the data D and the prior information X. This indicates that the separation of the evidence into data and prior is one of convenience when organizing a chain of inferences. In the study of the physical universe, one may suppose that the prior information X be expressible in purely mathematical and physical terms. Of course, human consciousness and rationality enters in how and what type of data D is obtained and what sort of prior information X is used. However, a robot that reasons according to certain definite rules designed by us can make the reasoning and deduce the consequences that follow from Bayes' theorem, once such choices are made. Consider the following application of Bayes' theorem (Kahneman and Tversky 1973). Prior information: X = "In a certain city, 85% of the taxicabs are blue, 15% are green ." Data: D = "A witness to a crash who is 80% reliable (i.e., who in the lighting conditions prevailing can distinguish correctly between green and blue 80% of the time) reports that the cab involved was green." In this psychological test, the subjects are then asked to judge the probability that the cab was actually blue. The correct result for the probability that the cab was actually blue P (B|DX) is given by Bayes' theorem, where the hypothesis H is either B or G. Now the prior information gives that P (B|X) = 0.85 and P (G|X) = 0.15. In addition, the data D, given the hypothesis H and prior information X, yield P (D|BX) = 0.20 and P (D|GX) = 0.80. The probability P (D|X), needed in Bayes' theorem, follows from the normalization condition P (B|DX) +P (G|DX) = 1. Thus, P (D|X) = P (B|X)P (D|BX) +P (G|X)P (D|GX) = (0.85)(0.20) + (0.15)(0.80) = 0.29. Therefore, by Bayes' theorem, P (B|DX) = P (B|X)P (D|BX)/P (D|X) = (0.85)(0.20)/(0.29) = 0.59. It is interesting that the subjects in the psychological test tended to guess a value for P (B|DX) of about 0.20, which corresponds to ignoring the prior information X, viz., P (B|X) = P (G|X) = 1/2, thus P (D|X) = 1/2 and P (B|DX) = P (D|BX) = 0.20 as suggested by the data alone. An equally yet opposite error would be to cling solely to the prior information at the expense of the data, which may be common in certain circumstances in religion and politics or, at times, even in science. In this instance, P (D|GX) = P (D|BX) = 1/2 and so P (B|DX) = P (B|X) = 0.85. These two extreme cases make either the prior information or the data D irrelevant, thus drastically changing the inferences made. Human reasoning, if unfettered, can bring into a problem of inference prior information that is irrelevant to the data being considered. "Obviously, the operation of real human brains is so complicated that we can make no pretense of explaining its mysteries; and in any event we are not trying to explain, much less reproduce, all the aberrations and inconsistencies of human brains. That is an interesting and important subject; but it is not the subject we are studying here. Our topic is the normative principles of logic, and not the principles of psychology or neurophysiology." (Jaynes 2003, 8). The introduction of an imaginary being, a robot, is an attempt to guide human reasoning about propositions according to the given desiderata. The making of inferences must be based on a clear connection between the data one has plus the relevant prior information one uses in making logical inferences. Otherwise, data or prior information not explicitly stated may be used unknowingly. The best illustration of this caveat is provided by David Hilbert's systematic study of the axioms of Euclidean geometry, which led Hilbert to propose 21 such axioms rather than the usual 5 axioms of Euclid of Alexandria. Hilbert published Grundlagen der Geometrie in 1899 putting geometry in a formal axiomatic setting. It is important to remark that assigning prior probabilities to verbal statements, e.g., concerning purpose, design, intelligence, consciousness, etc., is an open-ended problem of logical analysis since there is no unique way to accomplish that. In fact, prior probabilities represent a state of knowledge rather than a physical fact. Presently, there are four general principles (Jaynes 2003, 88-9) for assigning priors, viz., group invariance, maximum entropy, marginalization, and coding theory. For instance, the question of macroscopic final causes, e.g., arranging a physical system in order to attain a given temperature and pressure, are accomplished by using the principle of maximum entropy. Of course, physicists have succeeded in handling also physical systems in order to obtain particular microscopic final causes. It is in this sense that there is indeed purpose and design in the Universe. However, the latter is a theologically neutral observation that does not invariably lead to the existence of supernatural contravention of the laws of physics. (Jaynes 2003, 614). 4 B. Hypothesis Testing The fundamental question in science, and for that matter, rational thinking in general, is how to decide between differing available models or hypotheses in order to account for the existing data. Of course, one has to be rather clear on what data is being considered and how the data is collected in that particular kind of knowledge. One best way to avoid confusion is to characterize a kind of knowledge according to a subject matter. The question is how does one do that in an unambiguous, operational fashion so that it is clear what kind of evidence would be necessary in order to establish the truth or falsehood of claims being made. Of course, what prior information is used to analyze such data is crucial. In order to keep track of what assumptions are being made in the process of developing scientific theories of Nature, one must specify what the data D is that one is taking into account and what prior information X one is assuming. Of course, the division of what is data and what is prior information is a purely logical one. In any case, any additional information beyond that provided by the data of the current problem is by definition prior information. Bayesian methods are used whereby the mathematical rules of probability provide consistent rules for conducting inferences. Einstein indicates that physical influences can propagate only forward in time (causality). However, logical connections, which may or may not correspond to causal physical influences, propagate equally well in either direction, viz., "one man's prior probability is another man's posterior probability." (Jaynes 2003, 88-9). In Bayes' theorem, the logical product, say, HX denotes the proposition that both propositions H andX are true. Therefore, in order to know the likely truth of H, viz. P (H|DX), given the data D and prior X, one needs not only the sampling probability P (D|HX) but also the prior probabilities P (D|X) forD and P (H|X) for H. All probabilities are necessarily conditional on the prior information X. If parts ofX are irrelevant to the problem at hand, then such parts of X will cancel out mathematically and so P (H|DX) will not depend on such parts of X and so are truly irrelevant in determining the likely truth of H. III. THE SCIENCE OF ISAAC NEWTON Humans are puzzled by two fundamental thoughts: the question of origins and/or existence and what sustains and/or controls that which already exists. Some may further question if entities can come into being that are not causally related to what already exists. Biblical answers to these questions are, the creation account by God (Genesis 1, 2) via Christ (John 1:3), Christ sustains the creation by the word of His power (Hebrews 1:3), and God entering His creation through the Incarnation of His Son (John 1:14). However, such answers still do not quench human curiosity and so further progress is attempted by the methods of science that may still be guided by theological considerations. Blaise Pascal summarized the human dilemma succinctly, "For in fact what is man in nature? A Nothing in comparison with the Infinite, an All in comparison with the Nothing, a mean between nothing and everything. Since he is infinitely removed from comprehending the extremes, the end of things and their beginning are hopelessly hidden from him in an impenetrable secret; he is equally incapable of seeing the Nothing from which he was made, and the Infinite in which he is swallowed up." (Pascal 1941, 23). The development by Isaac Newton of his gravitational theory illustrates how suppositions enter in our attempts to study Nature. In constructing his theoretical model of the solar system, Newton said nothing about the origin of the solar system; he simply assumed its existence and was concerned only with planetary motion. Is the origin of planets outside the confines of science? Of course not! However, if one wants to study the origin of planets, then one must consider a more encompassing model with new initial conditions that will allow predictions regarding the existence of planets and, in addition, successfully describe their motion as Newton accomplished. The process of extending the usefulness and predictability of a model can go on and on encompassing more and more of the description of Nature and leading to more predictions than given by previous theories. However, eventually one reaches a point where no further progress is possible and one would achieve the elusive, so-called Theory of Everything, which purportedly explains and links together all known physical phenomena. The suppositions and initial conditions made in this ultimate theory will invariably lie outside science and into the realm of the purely metaphysical. John Wheeler (Wheeler and Ford 1998, 262) asked, "How come existence?" and its subsidiary, "How come the quantum?" as an attempt to incorporate some deeper concepts into science. Wheeler's "It from bits" is an attempt to answer some of these fundamental questions but still within the confines of a science based on materialism. The data used by Newton in constructing his gravitational theory, obtained by the Danish astronomer Tycho Brahe, is summarized in Johannes Kepler's three laws that rule the motion of the planets around the Sun. What prior information did Newton use? Surely, Newton used all he knew and, in addition, created the calculus in order to derive the gravitational force between two spherically symmetric massive objects. Was all the prior information Newton had at hand relevant for the conception and construction of his theory of gravitation? Certainly not! Much of the prior information Newton had was irrelevant to his discovery since one is not here dealing with the origin of 5 ideas or the historical development of a theory. Rather, one is seeking the logical connection between the model or hypothesis and the data. Clearly, more than one model or hypothesis may be connected logically with the data. For instance, the Ptolemaic system, with the aid of epicycles, explained the apparent motion of the Moon, Sun, and the retrograde motion of the planets. In fact, more levels of epicycles (circles within circles) were added to the models to match more accurately the existing data. The important question is how does one compare different conceivable models, distinguishes their individual merits, and selects the best? The stakes are indeed high since a false premise built into a model that is never questioned cannot be removed by any amount of new data. The comparison of models in order to choose the best amongst a prescribed class of alternative hypotheses can be based on the principle of reasoning through modern Bayesian analysis. In fact, the Franciscan Monk William of Ockham may be considered a forerunner of modern Bayesians. It is interesting that Newton reconciled or integrated his scientific work with his theological beliefs: "A God who had been active in history, and who had communicated with mankind through the prophets, also might be expected to be active in Nature. When Newton was in a more speculative frame of mind, he often seemed to be exploring strategies that would heighten that sense of divine dominion and control. It would seem reasonable to suppose that this was one reason why he was reluctant to make the gravitational force an innate property of matter... Newton wrote, 'There exits an infinite and omnipresent spirit in which matter is moved according to mathematical laws.' " (Brooke 1988, 169-83). According to Newton, the biblical God interacts also with the physical aspect of His Creation via purely physical agencies: "Newton's universe needed to be tinkered with from time to time. He thought that the gravitational attraction of the planets would cause their orbits to accumulate deviations, and the constant radiation of matter from the solar system would have to be made up. (The degeneration of the cosmos is not merely the result of friction in the interplanetary ther.) As much as possible he introduced natural agencies, such as the passage of comets through the solar system, as the means by which God made corrections and restored mass." (Wilder 1991, 2-16). If the central problem for Newton was a theory that led to Kepler's three laws, then clearly invoking God amongst his prior information was certainly not relevant in order to make the logical connection of the model or hypothesis to the data. It is important to distinguish between the scientific model proposed and the actual, real solar system. A scientific model need not refer or invoke a Creator; however, all that is may be the action of a Creator, which both creates and sustains all that exists. Despite Newton's attempt of integrating his theology with science, his principle of universal gravitation is clearly a physical theory designed to describe the physical aspects of the solar system. Of course, any theory of the formational history of the universe would involve the whole of reality, which would include not only the purely physical, but also the existence of conscious, rational human beings. The fundamental question then becomes what kind of model or hypothesis, initial conditions, and prior information are suitable and sufficient for such an all-encompassing description of Nature? IV. SCIENCE AND THE WHOLE OF REALITY It is difficult to carry on constructive dialogue without defining the meaning of concepts like "reality," "natural," "science," etc. What is "natural" may mean all that exists in Nature but then what is "Nature"? One must have operational definitions of these concepts, as is the norm in the physical sciences, in order to attain objectivity. Witness the notion of time and the operational definition of time via clocks, which are purely physical devices. If such conceptual order cannot be established in physics, then confusion will reign in the study of all aspects of reality. For instance, philosophers have argued for millennia on the nature of time, in particular, whether time is real or a mere appearance. As Einstein would indicate, just thinking of what is time does not suffice and so time must be defined with the aid of physical clocks that establishes an unambiguous, objective meaning of time, which allows knowledge of external objects and their temporal behavior. Einstein (2005, 46-8) considers Nature to encompass both the organic and the inorganic and knowledge of natural phenomena is based on observations. In addition, the laws governing the workings of Nature are reducible to elementary, spatiotemporal, physical concepts. More importantly, Einstein denies the notion of the nonphysical in the causal development of Nature. However, how are observations to be conducted in order to collect the necessary data in the study of Nature? What entities or devices register observations as data? The subject matter of science is indeed the physical universe as posited by Einstein. It is clear that unless one defines science in terms of a subject matter, then all sorts of intractable confusion will arise as to the true nature of unadulterated science. Therefore, the data that is constitutive of the subject matter of science can be collected, in principle, solely by physical devices (Alexanian 2000, 80). This accords with Einstein's notion of science and makes precise his requirement that "sense perception is the beginning of all research.the sum total of those experiences" 6 (Einstein 2005, 46-8). However, is the whole of reality physical? It is not clear whether Einstein denies the existence of nonphysical elements in the whole of reality or only "in the causal system of the processes of nature." The metaphysical question regarding the nature of the whole of reality goes beyond the bounds of science (Alexanian 2002, 287-88). I for one believe that knowledge of the true nature of humans, in particular the ability to know self and reason, involves more than the physical. Surely, human consciousness is not detectable by purely physical devices and only the nonphysical self in humans can "detect" or know consciousness. Of course, different levels of conscious experience are related to brain-states but self cannot be reduced to such physical states. Therefore, human consciousness is outside the purview of science (Alexanian 2002, 65), which allows humans to "detect" nonphysical entities such as self, information, mental constructs, mathematical abstractions, etc. It seems unlikely that the notion of life can be defined in terms of purely physical concepts and so it may be that the true essence of what life is lies outside the confines of science as well. In the process of developing scientific theories, human consciousness and reasoning summarizes the data into laws and creates the mathematical models with predictive power that describe Nature. However, the human elements of consciousness and rationality are not an integral part of the laws and models themselves. That is to say, human consciousness and rationality are not needed to connect logically the data to models or hypotheses and so are irrelevant as prior information. Theoretical models of Nature and the predictions that follow from them are exactly like mathematical systems with axioms and theorems. Einstein indicates (2003, 46-8) that all scientific thought is "geometric" and the abstract concepts exist only in conscious minds. It would be almost miraculous if a human being would be one of the predictions derived from a scientific theory envisioned by human beings themselves. Scientific studies need not invoke God, i.e. God does not form part of the prior information or data, provided one does not deal with ontological questions, in particular, regarding the origin of the assumed initial conditions of our spatiotemporal laws and the laws themselves. Additional prior information or data may be used to not only connect logically the new hypotheses with the original data but also to encompass additional prior information or data from a different kind of knowledge, say theology. The latter would represent an attempt to integrate science and theology and thus create a synthetic discipline that would explain scientific knowledge and theological issues like purpose, meaning, value, etc. A sensible definition of the whole of reality is then the realm of all data collected by purely physical devices and conscious, rational human beings. Consequently, the subject matter that encompasses the whole of reality goes beyond the subject matter of science, viz. the physical, and includes the nonphysical as well. Thus, the physical aspect of Nature is a subset of the whole of reality, which does not include the abstract concepts, like mathematics, information, etc. that exist in the human mind. One is dealing here only with science, which I have defined unambiguously and operationally, and not with other kinds of knowledge. For instance, the study of theology and/or history would require different, additional data and prior information. Of course, in the order of knowledge, "Metaphysics and theology constitute the two domains of the ontological context. Since metaphysics delimits the possible, and since theology may assert something as actual which from the standpoint of certain metaphysics is impossible, therefore there can be a conflict" (Martin 1957, 328-29). Therefore, the incompatibility between materialism and theology "arose not from metaphysics in a regulative function, but from metaphysics in a reductive function." (Martin 1957, 328-29). Many scientists are interested in the relationship of science and religion. In particular, Howard J. Van Till, a physicist and astronomer who is a founding member of the International Society for Science and Religion, is devoted to topics regarding the relationship of science and religion. Walter R. Thorson, a theoretical chemist, has deep interest in the philosophy of science and related issues in theology. Their proposed naturalism (Thorson 2004, 26-36) and (Van Till 2004, 292-5) are theistic owing to the prior information of a Deity and a Creator, respectively, in their initial conditions of their spatiotemporal laws. Clearly, the existing physical data does not lead to a specific metaphysics. Hence, choosing materialism as the correct metaphysics is a form of nihilism since it eliminates legitimate kinds of knowledge that deal with the nonphysical, say, theology, consciousness, etc. The study of the time development of the universe deals with both physical and historical sciences. (Alexanian 2007, 10, 12). The former are experimental in nature, whereas the latter are akin to forensic science, where the results of experimental sciences are used to validate an assumed sequence of unique events. Surely, interferences from the physical data can easily go beyond purely scientific descriptions into theological considerations. This was certainly the case in the work of Newton. Similarly in the naturalism of Thorson (Thorson 2004, 26-36) and Van Till (Van Till 2004, 292-5), as well as, in intelligence design (ID) (see O'Leary 2004, chaps. 13-6), where either explicitly or implicitly the notion of a Supreme or Superior being is introduced. However, such prior information is irrelevant in the description of the physical aspect of the universe where ontological questions are not addressed but may be necessary when dealing with the whole of reality-both physical and nonphysical. (Alexanian 2007, 85-86). These approaches are discussed in the light of Bayes' theorem in the following section. If materialism is equated to physicalism, then only the physical is real. Now materialism is obviously wrong since it denies the existence of nonphysical, abstract concepts needed and used in science. The very notion of creating theories to explain the physical goes beyond the physical owing to the need of nonphysical prior information. For instance, 7 there is no material or physical existence for the transcendental number? However, such a concept is indispensable in theoretical science. In addition, materialism denies the very notion of Deity, which transcends the physical yet is "detected" by the nonphysical in humans. (Alexanian, 2006, 254-255). V. NATURALISM, INTELLIGENT DESIGN, AND EVOLUTION The power of Bayes' theorem lies in making clear, in the logical chain of inferences, what constitutes the input, viz. data and prior information, and what constitutes the output, viz. the likelihood of a hypothesis from that of a given set. Still, it is an open and difficult problem of how to translate different verbal prior information into numerical prior probabilities. This makes one less able to deduce the likelihood of a hypothesis in the historical sciences from the data and assumed prior information than is the case in the physical sciences and thus more difficult to appraise the validity of different hypotheses conditional on the data and prior information. Nonetheless, Bayesian analysis allows us to clarify and evaluate the logical relation of different hypotheses to the data and the assumed priors. The following simple example illustrates the use of Bayes' theorem in cases of verbal prior information. Consider the statement "Doubt is an integral element of faith." How does probability come into the analysis of this statement? Surely, faith without doubt denotes certainty, which is contrary to its nature and indicates already a probability of one. What is the prior information that can account for the correctness of the statement? It is a matter of choice on what or on whom one puts one's faith. Therefore, the choice in the prior information is by necessity accompanied with doubts vis--vis the other, non-selected faiths. However, it is difficult to quantify such arguments. If all choices of differing faiths are equal, then one has Laplace's "Principle of Insufficient Reason." Scientific theories are like mathematical systems, say Euclidean geometry, with suppositions (axioms) and predictions (theorems). Of course, the logic can go both ways and so one can make some theorems axioms, etc. There is no designer in the theory except the human who created the mathematical scheme. If one wants to explain humans that created the mathematics and developed the scientific theories, then one has to unify science with some other kind of knowledge. It is in this sense that one infers a Creator from what exists. Thorson (Thorson 2004, 26-36) indicates that intelligent design (ID) is not a legitimate scientific agenda for biology and thus classifies ID as natural theology rather than a naturalistic approach to science. By "naturalism," Thorson means, "that in science we deliberately refrain from using explanatory paradigms or concepts that appeal either to divine agency itself or to any direct surrogate for such agency" (Thorson 2004, 26-36) . Thorson suggests a possible way ID may be made compatible with a "naturalistic" approach to biology. In particular, ID should focus on Thorson's "functional logic" that endows biological systems with "a logical organization toward achievement of certain tasks or functions" (Thorson 2004, 26-36). Such functional logic, although compatible with mechanistic logic, most likely is not derivable from it. Thorson proposes, in order to emulate the successes of physical science, deferring the question of origins, which may actually go beyond the bounds of science. On the other hand, Van Till believes that ID is "inherently incapable of developing a positive case for any particular non-naturalistic worldview" (Van Till 2004, 292-5). By "naturalism," Van Till means, "a world view (whether theistic or atheistic) that posits the sufficiency of the system of natural causes to bring about the actualization of the full spectrum of physical structures and biotic forms and systems that have appeared in the formational history of the universe" (Van Till 2004, 292-5). Van Till proposes that our universe is gifted by its Creator with a "robust formational economy." This would lack "nothing needed to actualize, without compensatory non natural action, every type of structure and organism that has appeared in its formational history." Van Till distinguishes "materialism" that denies the existence of any immaterial Deity from the theistic "naturalism" that he posits. However, in contrast to ID, which Van Till considers closely associated with Divine intervention, Van Till's naturalism comes dangerously close to Deism. The "naturalisms" of both Thorson and Van Till includes as prior information the notion of a Deity and a Creator, respectively. Yet, the data both are trying to explain are not theological but physical and biological in nature, and refer to a Deity or Creator to set up the initial conditions that purport to explain the history of the universe. Evolutionary theory comes in two main flavors according to the assumed initial conditions. One form supposes that initially there is nothing but nonliving matter, say, the Big Bang creation of the universe, and life and complex living organisms develop as the universe evolves by spatiotemporal laws. This is materialistic metaphysics, which violates the order of knowledge, where metaphysical propositions are regulative rather than constitutive of historical propositions (Martin 1957, 318). Alternatively, the initial state is taken to consist of simple, living organisms and the essential problem is how complex, living organisms arise in time. Theories with explicit mechanisms and predictive power that would achieve this sort of temporal behavior are rather difficult to construct since it would involve a thorough knowledge of experimental science and would have to possess the ability to describe the historical development of our universe. Both the "functional logic" of Thorson and the "robust formational economy" of Van Till are a form of evolutionary theory, albeit theistic. Thorson (Thorson 2004, 26-36) relegates the question of origins to a Deity and Van Till (Van 8 Till 2004, 292-5) ascribes his "robust formational economy" to a Creator. The theory of ID holds that certain features of the universe and of living organisms are best explained by an intelligent cause. On the other hand, evolutionary theory is based on undirected processes such as natural selection and so it supposes no known teleological content either in the initial state or in the temporal development of the universe. Therefore, it is not clear whether the intelligent cause in ID is solely in the initial state, as in Thorson and Van Till's theories, or else, as Van Till emphasizes (Van Till 2004, 292-5), it also appears in the dynamics of the system in the form of divine intervention. Intelligent design is based on the inference that certain biological information must be the product of an intelligent cause. This can be realized, for instance, if the designer arranges the information content of the initial condition so that the time development of the system would give rise to the observed complexity. A stronger version of the latter would posit that no physical theory could give rise to irreducible complexity if not designed to do so. If successful, then design would not rely on inference but would be a necessary condition of complex biological systems. This endeavor would be the biological equivalent of Gödel's incompleteness theorem in any axiomatic mathematical system (Nagel and Newman 1958). In the case of ID, the domain would encompass all conceivable physical theories of Nature. Accordingly, no hypothesis that does not include a designer in the prior information is able to explain the whole of biological data. The proof of such a proposition would constitute indeed a Herculean task. Darwinism presupposes a purely materialistic description of Nature whereas ID supposes the existence of an intelligent designer. As indicated above, ID cannot refute the naturalism of Thorson and Van Till. In fact, the difference between ID and Thorson and Van Till's theories is that ID claims to identify by means of scientific data the originator of the initial conditions as an intelligent agent. The whole gamut of possible initial states, which can range from the state of creation on the seventh day of Genesis 2 (or an earlier day) to the presently supposed Big Bang origin of the universe, are available to any theory. It is important to indicate that Thorson's, Van Till's, and ID's efforts of explaining what presently exists are purported to be scientific theories. Of course, in the true reductionist tradition of science, the goal is always to consider the simplest, least complex initial conditions together with a dynamical model that successfully describes the temporal behavior of an initially lifeless, physical universe. Accordingly, in such scenarios, life, rationality, and consciousness would be a consequence of the temporal evolution of the universe. VI. SCIENCE, LIFE, AND PHYSICS The division of Nature into the physical and nonphysical aspects raises the issue whether the nonphysical can be explained fully in terms of the physical or not. Humans possess both physical and nonphysical attributes and beyond Nature itself, there is the supernatural that transcends Nature. Eugene Paul Wigner observed, "There are phenomena what the present physics cannot describe. One of them is the life. This circumstance is as peculiar as if physicists did not consider gravity. However, gravity exists and life exists as well. Humans are here with all of their thoughts, joys and desires. It used to be said that humans obey the laws of physics and emotions do not count. This saying reminds me of the fact that 100 years ago the physics textbooks stated: 'Atoms may exist but that is irrelevant for physics.' Some scientists say that emotions may influence the soul but not the motion of our hands or feet. However, it is hard to accept that we are only machines. Consciousness may influence the events in the same way as gravity does. This means, however, that in shaping the future of our universe something plays a relevant role what physicists are not interested about, in a way as they were not interested about atoms 100 years ago" (Wigner 1999). Wigner was a mathematical physicist and Nobel Laureate in Physics who laid the foundation for the theory of symmetries in quantum mechanics and commented, "It was not possible to formulate the laws (of quantum theory) in a fully consistent way without reference to consciousness." If true, then the latter would provide a rather strong connection between the physical and the nonphysical aspects of Nature. The notion whether life itself can be understood or explained in terms of purely physical concepts or not is a rather complex problem to which all fundamental problems in physics pale in comparison. For instance, can life be the result of an emergent property just as wetness is an emergent property of water molecules when in the liquid state? Thorson is skeptical that "any purely physical model can explain biological organization" (Thorson 2004, 26-36). Therefore, in essence, Thorson's concern with a naturalistic approach to biology represents extending the definition of what science is to include the concept of life, whatever life is. Surely, the notion of life can be used in science as an unknown, phenomenological concept its true nature awaiting final understanding much as Thorson suggests regarding questions of origin. Wigner raises the question of human consciousness and life as possible scientific topics. Is it then possible to extend further the definition of science beyond the realm of the purely physical in order to encompass the notion of human consciousness as well? Alternatively, is human consciousness an emergent property of the purely physical? Positive answers to these questions would imply that Thorson and Van Till's naturalisms and ID theory could be reduced to materialism, since there would be no need of a Deity to neither posit the initial conditions nor contravene the laws 9 of physics. However, this leads to an intrinsic incompatibility with theology since materialism "does not allow the possibility of the truth of any strictly theological proposition" (Martin 1957, 326). However, the undetectable nature of self by purely physical devices indicates that naturalism cannot encompass the whole of reality, even if one supposes the existence of life and/or humans in the initial conditions. Consciousness may even be an emergent property of the physical yet the physical cannot detect it, much like the inability of a water molecule to detect the wetness of water, which would be rather puzzling. This conclusion does not invoke the incompatibility of materialistic metaphysics and theology but relies on the existence of conscious beings that "detect" nonphysical entities, even God, but are undetected by means of purely physical devices owing to the existence of nonphysical consciousness. Wigner (1960, 1-14) also examined how mathematics accurately describes physical phenomena thus affirming Galileo's tenet that "The book of Nature is written in the language mathematics." Wigner asserts, however, ".....the enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious and there is no rational explanation for it." It may be that mathematical descriptions of Nature work because the human mind creates mathematics. Now God created both humans and Nature. The circle is thus completed with the creative power of humans mimicking that of God and understanding Nature by the power of their intellect. Thus, the existence of self, which "detects" the spiritual, exemplifies the image of God in humans and points to the existence of theological and mathematical truths innate to humans. This resembles somewhat the theory of occasionalism of Nicolas Malebranche who claimed that the only causal power is God (Malebranche 1997). It is important to remark that the laws of experimental sciences, which underlie the laws of Nature, are generalizations of historical propositions and are quite consistent with most theological presuppositions. It is in the study of unique historical events, say in cosmology or abiogenesis, where the conflict, the so-called war between science and religion, truly arises. It is the historical presuppositions in the historical sciences, not the science used that is based on the findings of the experimental sciences, which gives rise to a possible discord. For instance, the Christian faith is based on the historicity of God incarnate in Jesus of Nazareth and the redeeming power of the cross. Experimental science has nothing to say regarding any particular historical event; least of all regarding the entering of the Creator Himself into His creation. Question of origins, in particular, the origin man, pose a most difficulty problem. Note that even though the results of experimental sciences are used to analyze extant data, the problem of origins is essentially a historical, not a scientific problem. Additionally, it confronts Christians with how to reconcile the origin and present moral status of man vis--vis the redeeming grace found in the death and resurrection of Jesus the Christ. "Then the Lord God formed man of dust from the ground, and breathed into his nostrils the breath of life; and man became a living being." (Genesis 2:7 NASB). Physical science has successfully developed paradigms to study nonliving "dust." However, can science make the "breath" of God part of its subject matter? Is the concept of life so elusive that it becomes scientifically indefinable? Perhaps the inability of nonliving matter to detect and identify life as well as consciousness indicates that only life itself can "detect" and know life. Similarly, only self can "detect" and know self. Consciousness presupposes rationality, rationality presupposes life and life presupposes God. Human rationality and consciousness is used to know both Nature and God yet paradoxically humans are unable to formulate a scientific theory of neither life nor self. VII. CONCLUSIONS The purely physical is the subject matter of physics, the prototype of all sciences. An extreme form of reductionism supposes that all that exists is the purely physical and the nonphysical aspect of reality follows from the purely physical and the laws governing their actions. This poses a gargantuan theoretical problem and so a more practical approach would built on less fundamental foundations by supposing the existence of more complex entities, even living beings, and explaining the remaining aspects of both the purely physical and nonphysical in terms of them. Therefore, a definition of science in terms of a subject matter is necessary; otherwise, the term would be as equivocal and meaningless as the term evolution has become. This is clearly not reductionism since one is not reducing all that exists to the physical; therefore, one is invoking neither physicalism nor materialism. Many consider such a definition of science as excluding, for instance, ID as science. However, if it does do that it would also exclude Darwinism as well. A definition of science based on the study of the physical aspect of Nature is a two-edged sword that exposes the nonscientific, philosophical baggage of Darwinism. If such a definition of science is unacceptable, then one has to extend the definition beyond that presently used by physicists, astronomers, chemists, neurophysiologists, molecular biologists, etc. The question is how does one do that in an unambiguous, operational fashion so that it is clear what kind of evidence would be necessary in order to establish the truth or falsehood of claims being made in the name of science. Surely, one can make higher order inferences from scientific data by using additional prior information than is required to do unadulterated science. Such higher order inferences are normally made in order to integrate scientific 10 data with evidence from other kinds of knowledge. An obvious example of this is, "The heavens are telling of the glory of God; And their expanse is declaring the work of His hands" (Psalm 19:1 NASB). One needs scientific data and prior information that would encompass both scientific and theological considerations. If living organisms and conscious beings are to be part of the subject matter of science, then how does one define these new concepts with some sort of scientific rigor? Physicists have studied the notion of life, witness the works of Erwin Schrödinger, Max Delbrück, etc., and are now considering the question of consciousness. It is doubtful that the definition of science as the study of the physical universe will be able to encompass the difficult concepts of life and consciousness. No one has any idea how the latter concepts can be made part of the scientific endeavor with the same rigor that characterized the concepts and science developed by Galileo, Newton, Planck, etc., whichever way science is defined. REFERENCES Alexanian, Moorad. 2000. "Teaching, Propaganda, and the Middle Ground." Physics Today 53, no. 11, 80. Alexanian, Moorad. 2002. "Physical and Nonphysical Aspects of Nature." Perspectives on Science and Christian Faith 54, no. 4, 287-288. Alexanian, Moorad. 2002. "Humans and Consciousness." Perspectives on Science and Christian Faith 54, no. 1, 65-65. Alexanian, Moorad. 2007. "Debate about science and religion continues." Physics Today, 60, no. 2, 10, 12. Alexanian, Moorad. 2007. "Theistic Science: The Metaphysics of Science." Perspectives on Science and Christian Faith 59, no. 1, 85-86. Alexanian, Moorad. 2006. "Set Theoretic Analysis of the Whole of Reality." Perspectives on Science and Christian Faith 58, no. 3, 254-255. Brooke, John. 1988. "The God of Isaac Newton." In Let Newton Be!, ed. R. Flood, J. Fauvel and R.J. Wilson, 169-83. Oxford University Press. Einstein, Albert. 2005. "Physics, Philosophy, and Scientific Progress." Physics Today 58, no. 6, 46-48. Jaynes, Edwin Thompson. 2003. Probability Theory: The Logic of Science. Cambridge University Press. Kahneman, Daniel, and Amos Tversky. 1973. "On the Psychology of Prediction." Psychological Review 80:237-51. O'Leary, Denyse. 2004. By Design or by Chance?: The Growing Controversy on the Origins of Life in the Universe. Castle Quay. Malebranche, Nicolas. 1997. "The Search after Truth: With Elucidations of The Search after Truth (Cambridge Texts in the History of Philosophy)." Eds. Thomas M. Lennon and Paul J. Olscamp. Cambridge University Press. Martin, William Oliver. 1957. The Order and Integration of Knowledge. The University of Michigan Press. Nagel, Ernest and James R. Newman. 1958. Gödel's Proof. New York University Press. Pascal, Blaise. 1941. Pensees, and The Provincial Letters. Random House. Thorson, Walter R. 2004. "Naturalism and Design in Biology: Is Intelligent Dialogue Possible?" Perspectives on Science and Christian Faith 56, no. 1, 26-36. Van Till, Howard J. 2004. "Is the ID Movement Capable of Defeating Naturalism? A Response to Madden and Discher." Perspectives on Science and Christian Faith 56, no. 4, 292-295. 11 Wheeler, John A. and Kenneth W. Ford. 1998. Geons, Black Holes, and Quantum Foam: A Life in Physics. W.W. Norton & Company. Wigner, Eugene P. 1999. "On the Future of Physics." Fizikai Szemle 5: http://www.kfki.hu/fszemle/archivum/fsz9905/wigner.html Wigner, Eugene P. 1960. "The Unreasonable Effectiveness of Mathematics in the Natural Sciences." Communications on Pure and Applied Mathematics 13, no. 1, 1-14. Wilder, T.E. 1991. "At the Origins of English Rationalism." Contra Mundum, No.1, 2-16. Available at: http://www.contra-mundum.org/cm/cm01.pdf


Psychology of Religion

Philosophy

© 2003 Psychological Understanding of Religion Domenic Marbaniang The word "psychology" is a combination of two Greek words psyche meaning "soul", "spirit", or "mind" and logos meaning "science" or "study of". The science of psychology tries to investigate every area of human experience and behavior. Psychology of religion tries to understand the cause-effect relationships of religious experiences and religious consciousness so as to be able to predict behaviors. It aims to study the religious consciousness with investigations in religious behavior patterns. The major systems of psychology are: structuralism, functionalism, behaviorism, psychoanalysis, and Gestalt School of Psychology. Obviously, each system has its own way of understanding religious consciousness. Psychological Definitions of Religion About a century ago, James Henry Leuba was able to select forty-eight definitions of religion to which he added two of his own to include in his famous Psychological Study of Religion (1912). Various psychologists have defined religion variously. The word "religion" poses the same problems as the word "God". Both of the above words act like an umbrella comprehending a multiplicity of meanings, some of which drastically contradict each other. © 2003 Leuba divided all his rich collection of definitions into two groups, to which he added his own third one: 1. Those definitions that treat religion as "the recognition of a mystery pressing for interpretation". 2. Those definitions which adopt Schleiermacher"s view that religion is "a feeling of absolute dependence on God." 3. Leuba"s definition that "religion is the propitiation or conciliation of powers which are believed to direct and control the course of nature and human life." The above classification cannot be regarded as final, since newer definitions like Leuba"s easily arise. The definitions seem to be descriptions that, arising through induction, are not always comprehensive. The variety of psychological perspectives and definitions are also an issue of philosophical investigation. As early as 1916, Professor C.C.J. Webb had said that "I do not believe that religion can be defined." This does not, however, mean that the psychological definitions of religion are of no practical value. We must distinguish between definitions and descriptions. While definitions give essential meanings, descriptions state the external appearances. Obviously, the attempts to define religion are not merely attempts to describe but attempts to point out the essence of religion. Psychology understands the various rites, beliefs, and expressions of religions as reflective of a religious consciousness which it tries to investigate. The psychological definitions of religion do try to locate the essence of religion in the consciousness and not in the external "symbols", which are only interesting as long as they lead to an understanding of religious consciousness. It is the © 2003 similarities rather than the differences which are the object of the study. Following are some psychological definitions of religion that help us to know what psychology reveals about religion: Sir James Frazer: Religion is a propitiation or conciliation of powers superior to man which are believed to direct and control the course of nature and of human life. Thus defined, religion consists of two elements, a theoretical and a practical, namely a belief in powers higher than man and an attempt to propitiate or please them. E. Durkheim: A religion is a unified system of beliefs and practices relative to sacred things, that is to say, things set apart and forbidden – beliefs and practices which unite into one single moral community called a Church, all those who adhere to them. The cognitive and practical sides or aspects of religion have been well related in a definition by Professor George Galloway. Prof. George Galloway: Religion is that which refers to man"s faith in a power beyond himself whereby he seeks to satisfy emotional needs and gain stability of life, and which he expresses in acts of worship and service. The cognitive side of the religious consciousness is represented by faith, and faith is stimulated by emotion and posits the object which will satisfy the needs of the inner life.... The practical aspect is denoted by the acts of worship and service which belong to the nature of religion. © 2003 "Faith is stimulated by emotion and posits the object which will satisfy the needs of the inner life" reveals that religion is that to which a person recourses to find fulfillment which he cannot find through mere physical products – terrestrial products. Needs may be divided into two: a. Viscerogenic needs. For nourishment, rest, sex, and physical safety. They are considered as subjective. b. Psychogenic needs. For goodness, beauty, truth, holiness. They are considered as objectified. Religion, then may be called the individual reaching out to find fulfillment for his psychogenic needs. Faith in the supernatural or the mysterious, awesome, Great becomes essential to religion. J. Bissett Pratt: Religion is the serious and social attitude of individuals or communities toward the power or powers which they conceive as having ultimate control over their interests and destinies... This definition defines religion as an attitude, which is used to cover that responsive side of consciousness which is found in such things as attention, interest, expectancy, feeling, tendencies to action, etc. The advantages of defining religion as an attitude are sufficiently manifest. It shows that religion is not a matter of any one "department" of psychic life but involves the whole man. It includes what there was of truth in the historical attempts to identify religion with feeling, belief or will. And it draws attention to the fact that religion is immediately subjective, thus differing from science (which emphasizes "content" rather than "attitude"); and yet it points to the other fact also that religion involves and presupposes the acceptance of the objective. Religion is the attitude of © 2003 a self towards an object in which the self genuinely believes. The concept of religious attitude as a response or consciousness leading to religious practices is important in the study of the psychology of religion. In Frazer"s thought, "belief clearly comes first, since we must believe in the existence of a divine being before we can attempt to please him. But unless the belief leads to a corresponding practice, it is not a religion but merely a theology." Since the psychological method can be implemented with the availability of observable data, symptoms, practices, behavior, etc, observable practices are crucial for any possibility of the psychology of religion. Religious behavior is important to be identified and studied before any psychology of religion can be formulated. Dr. R. H. Thoules: Any definition of religion to be adequate must include at least three factors: a mode of behavior, a system of intellectual beliefs and a system of feelings... Religion is a felt practical relationship with what is believed in as a superhuman being or beings. Beliefs, feelings, and behavior are the three minimum factors that compose religion. Behavior includes things done and things-not-to-be-done, ritual and taboo. Thoules goes on to say: ... The main business of the psychology of religion is to study the religious consciousness. But it is impossible to study that alone; we must investigate religious behavior as well. All the above and the many definitions of religion point to the fact that man has a particular bend toward the © 2003 "Higher-Superhuman". Archaeology, anthropology, ethnology and sociology have greatly contributed towards the field of psychological study of man. It is not the diversity of religions but the similarities between them that point towards the "religiousness" of the human in any context, whether he is a remote tribal or a sophisticated urban. Psychologists agree that these similarities spring from such facts as the universality of human needs, spiritual no less than physical; from the same impulse towards unity and completeness; and from the same awareness of powers that appear to operate within the world and yet are external to it. Though the study of human religious behavior is important in psychology, it is not all. Religious behavior is only a door towards the opening of real understanding regarding the mind of man which by its bend towards the mysterious incomparably differs from the brutes. The varieties of rituals and taboos (religious behavior) point towards something common to every man. In addition to religious behavior, a study of the beliefs is also important. Beliefs are important to the understanding of behavior. Linguistic researches have shown that the meaning of the word "soul" etymologically means similar in most of the known languages. In Assyrian, Hebrew, Arabic, Greek, Stoic, Latin and Sanskrit it means breath, spirit, or wind. The various taboos and rituals cannot be studied in isolation from their related beliefs. The belief in soul or souls is characteristic of most religions. Psychology tries to explain the origin of the idea of the soul in relation to the survival instinct of man and also his possible cogitations on the dream, waking, and unconscious states. The soul"s relation to breath might have been thought on the differentiation of a corpse (that doesn"t breathe) and a © 2003 living person (who breathes). The relation between soul and breath is a concept not alien to even the primitive tribes. This belief expresses itself in certain rituals and taboos. Thus, psychology reveals that religious beliefs and religious rituals and taboos are closely related. This relation has been a regular feature of any religion. For instance, the belief of the identity of breath with soul is illustrated in a living example which Jung found during his researches among the mountain triebesmen of the Elgony; who, in the morning at the rising of the sun, "hold their hands before their mouths and spit or blow into them vigorously. Then they turn their hands round and hold the palms forward to the sun. Jung explains that this particular ceremony is an offering to the sun which for these natives is mungu. If they have spittle on their hands, this is the substance which, according to primitive belief, contains the personal mana, the force that cures, conjures and sustains life. If they breathe upon their hands, breath is wind and spirit. The action means "I offer my living spirit to God." It is a wordless, acted prayer, which could equally well be spoken: "Lord, into thy hands I commend my spirit." Perhaps the command "not to eat strangled meat" in the Bible is based on the assumption that strangling stifles the breath while the outflow of blood (in which the soul dwells) pours the soul out, a requisite of every sacrifice of blood in Judaism, at least symbolically. Thus, whether it is manmade ritual or a "divinely" commanded taboo or ritual, psychological connexions between attitudes, beliefs, feelings, and behavior can be found through the study of beliefs and behaviors. The strength of the connexion in a person depends on the time and degree he/she has been connected to the religion. Age and context do matter. © 2003 Psychology reveals that the human soul is religious. Human beings consciously and unconsciously respond to the mystery of the Supernatural, the mystery of life and death. Psychological experiences may be behind certain beliefs regarding self and the universe. These beliefs lead to certain practices of ritual and taboo. As far as the validity of the beliefs is concerned, that is not the domain of psychology; it is the domain of philosophy and science. For psychology it is the responses that are focal. And a psychological perspective of religion often views it as man"s responsive attitude to the "sacred". Resource: Spinks, G. Stephen. Psychology and Religion, Margaret Gorman (ed), New York: Paulist Press, NA.


Grounding, Contingency and Transitivity

Philosophy

GROUNDING, CONTINGENCY AND TRANSITIVITY Roberto Loss Forthcoming in Ratio Penultimate draft-Please refer to the published version Abstract Grounding contingentism is the doctrine according to which grounds are not guaranteed to necessitate what they ground. In this paper I will argue that the most plausible version of contingentism (which I will label 'serious contingentism') is incompatible with the idea that the grounding relation is transitive, unless either 'priority monism' or 'contrastivism' are assumed. 1. Introduction The fact that Frida Kahlo's Casa Azul is blue depends on the fact that it is of the specific cobalt-blue shade typical of the historic centre of its borough, Coyoacán. The fact that the current Finance Minister of Greece Yanis Varoufakis is European depends on the fact that he is Greek. The fact that it is true that the average temperature of the Earth's atmosphere is increasing depends on the fact that the average temperature of the Earth's atmosphere is indeed increasing. These all appear to be grounding claims, that is, claims of non-causal dependence, determination and explanation between the more fundamental and the less fundamental: it is because Casa Azul is of that specific shade of cobalt-blue that it is blue; it is in virtue of being Greek that Varoufakis is European; it is the actual increase in the average temperature of the Earth's atmosphere that explains why it is true to say that the average temperature of the Earth's atmosphere is increasing. In general, to say that the fact that p ('[p]') is grounded in the plurality of facts Γ ('[p] ← ')1 is to say that [p] either (metaphysically) depends on, is (metaphysically) determined by, or is (metaphysically) explained by Γ. If this is the case, then [p] is a derivative fact. If, instead, there is no plurality of facts grounding [p], then [p] is a fundamental fact, that is, a fact belonging to the fundamental level of reality.2,3 1 '←' stands here for full grounding. The notion of partial grounding ('|←') can be defined as follows: Partial grounding: f |←  =df for some Γ: f ← Γ and   Γ See, for instance, Gideon Rosen, 'Metaphysical Dependence: Grounding and Reduction' in Bob Hale and Aviv Hoffmann (eds.) Modality: Metaphysics, Logic, and Epistemology (Oxford: Oxford University Press, 2010) pp. 109–36, p.115; and Kit Fine, 'Guide to Ground' in Fabrice Correia and Benjamin Schnieder (eds.) Metaphysical Grounding: Understanding the Structure of Reality (Cambridge: Cambridge University Press, 2012), pp. 37-80, p. 50. 2 Although I wish to remain neutral about what kinds of entities facts are, for simplicity's sake I will follow Rosen, 'Metaphysical Dependence', and take facts to be true propositions 'individuated by their worldly items and the manner of their combination' (p. 124). 3 For an introduction to the notion of grounding and its relation to the notion of determination, dependence and explanation see, among others: Fabrice Correia and Benjamin Schnieder (eds.) Metaphysical Grounding: Understanding the Structure of Reality (Cambridge: Cambridge University Press, 2012); Kelly Trogdon, 'An Introduction to Grounding' in Miguel Hoeltje, Benjamin Schnieder and Alex Steinberg (eds.), Varieties of Dependence: Ontological Dependence, Grounding, Supervenience, ResponseDependence (Basic Philosophical Concepts). (Philosophia Verlag, 2013), pp. 97-122; Ricki Bliss and Kelly Trogdon, 'Metaphysical Grounding' in Edward N. Zalta (ed.) Stanford Encyclopedia of Philosophy (Winter 2014 Edition), http://plato.stanford.edu/archives/win2014/entries/grounding; and Michael J. Raven, 'Ground', Philosophy Compass (forthcoming). 2 The notion of metaphysical grounding lies at the centre of an intense discussion in the current debate in metaphysics. Among many others, the following is a list of questions that have attracted attention in the literature: (Q1) Do grounds necessitate what they ground? (Q2) Are universal or negative facts fundamental? (Q3) Is grounding transitive? (Q4) Is grounding a 'contrastive' notion? (Q5) Are the parts more fundamental than the whole they compose? (Q1) concerns the so-called Entailment Principle: Entailment: If [p] ← , then □(  p) (where '' is the conjunction of all the propositions corresponding to facts in ) Necessitarians hold that Entailment is valid and, thus, that (full) grounds necessitate what they ground.4 For example: the existence of Socrates appears to ground and necessitate the existence of its singleton {Socrates}; the fact that this flag is red grounds and necessitates the fact that something is red; the fact that p, and the fact that q jointly ground and necessitate the fact that p & q. Contingentists, on the other hand, hold that Entailment admits of counterexamples.5 The typical putative case of a contingentist grounding fact brings us to question (Q2). Consider what we might call the 'abundant totality fact' A that (say) a, b, and c are all the existing entities (supposing, of course, that a, b, and c are indeed all the existing entities). Since the joint existence of a, b, and c fails to necessitate A,6 necessitarians appear to have three main options at their disposal for what concerns the question of what, if anything, grounds A: (N1) A is fundamental ~f (A←f)7 4 Grounding necessitarians include, among others: Fine, 'Guide to Ground'; Rosen, 'Metaphysical Dependence'; Kelly Trogdon, 'Grounding: Necessary or Contingent?', Pacific Philosophical Quarterly 94 (4) (2013), pp. 465-485; Paul Audi, 'Grounding: Toward a Theory of the In-virtue-of Relation', Journal of Philosophy 109 (12) (2012), pp. 685-711; and Fabrice Correia, Existential Dependence and Cognate Notions (Philosophia Verlag, 2005). 5 Grounding contingentists include, among others: Jonathan Schaffer, 'The Least Discerning and Most Promiscuous Truthmaker', Philosophical Quarterly 60 (239) (2010), pp. 307-324; Stephan Leuenberger, 'Grounding and Necessity', Inquiry 57 (2) (2014), pp. 151-174; Alexander Skiles, 'Against Grounding Necessitarianism', Erkenntnis (forthcoming). 6 Unless we assume, with Timothy Williamson (Modal Logic as Metaphysics, Oxford: Oxford University Press, 2013), that necessarily, everything is necessarily something. In this paper I assume Williamson's 'necessitism' to be false. 7 This position is considered, for instance, by Fine, 'Guide to Ground', p. 62. 3 (N2) A is grounded in the facts [a exists], [b exists], [c exists], and (what we might call) the 'sparse totality fact' that everything is either identical to a, b or c. A← [Ea],[Eb],[Ec],[x(x=a v x=b v x=c)]8 (N3) A is grounded in the facts [a exists], [b exists], [c exists] and every 'nonexistence fact' about contingently non-existing entities A← [Ea],[Eb],[Ec],[~Ez1],[~Ez2],[~Ez3],[~Ez4],...,[~Ezn],...9,10 Contingentists, on the other hand, do not need to posit either fundamental totality facts or fundamental non-existence facts at the fundamental level of reality. Since they reject Entailment, they can simply claim that what grounds the fact that a, b and c are all the entities that exist are simply the facts [a exists], [b exists], [c exists] taken together: (C) A← [Ea],[Eb],[Ec] In other words, whereas necessitarians appear to be forced to take either some universal facts (such as abundant and sparse totality facts) or some negative facts (such as nonexistence facts) to be fundamental, contingentists can ban both from the fundamental level of reality and please the aesthetic sense of those who have a taste for desert fundamental landscapes. Therefore, although contingentists are not committed to answering negatively to (Q2), it seems that they would lose much of their dialectic leverage against necessitarians, were they to admit either universal or negative facts at the fundamental level of reality. For this reason, in what follows I will call the version of contingentism that bans universal and negative facts from the fundamental level of reality, 'serious contingentism'. As for (Q3), the idea that the grounding relation is transitive has been criticised in the literature11 by means of putative counterexamples like Jonathan Schaffer's famous case of the dented sphere (which will be discussed in section 5).12 Since, however, transitivity appears to be a 'natural, plausible, and useful assumption', Schaffer has proposed an interesting 'replacement which not only avoids the counterexamples but [also] explains why transitivity seemed plausible, while preserving its use in generating structure'.13 The main idea-which brings us to (Q4)-is that grounding should be taken to be a contrastive notion, and thus a quaternary relation having the form: 8 See, for instance, Rosen, 'Metaphysical Dependence'. 9 To my knowledge, nobody upholds this (rather uneconomical) option in the literature (at least explicitly). 10 For simplicity's sake I am not considering whether the facts [a exists], [b exists], and [c exists] are derivative or fundamental. If, for instance, [b exists], and [c exists] were derivative on [a exists] then [b exists], and [c exists] would not feature among the fundamental grounds of A (if any). This issue is not crucial to the argument I will present in section 2 and can thus be left aside. 11 See, for instance: Jonathan Schaffer, 'Grounding, Transitivity, and Contrastivity' in Correia and Schnieder, Metaphysical Grounding, pp. 122-38; and Gonzalo Rodriguez-Pereyra, 'Grounding is not a Strict Order', Journal of the American Philosophical Association (forthcoming). Notice, however, that Rodriguez-Pereyra argues that grounding is not transitive because it takes truthmaking not to be transitive and to be a case of grounding. Therefore, it is not clear whether his counterexamples could show that also the more specific notion of grounding discussed in this paper is not transitive. 12 For a discussion of Schaffer's counterexamples to transitivity, see: Michael J. Raven, 'Is Ground a Strict Partial Order?', American Philosophical Quarterly 50 (2) (2013), pp. 191-199; Jon Litland, 'On Some Counterexamples to the Transitivity of Grounding', Essays in Philosophy 14 (1) (2013); Amir A. JavierCastellanos, 'Some Challenges to a Contrastive Treatment of Grounding', Thought: A Journal of Philosophy 3 (3) (2014), pp.184-192; and Rodriguez-Pereyra, 'Grounding is not a Strict Order'. 13 Schaffer, 'Grounding, Transitivity, and Contrastivity', p. 129. 4 Contrastive Grounding: The fact that φ rather than φ* grounds the fact that ψ rather than ψ* While standard binary grounding is not transitive, claims Schaffer, contrastive grounding is, at least if transitivity is defined as follows: Differential Transitivity: If the fact that φ rather than φ* grounds the fact that ψ rather than ψ*, and the fact that ψ rather than ψ* grounds the fact that ρ rather than ρ*, then the fact that φ rather than φ* grounds the fact that ρ rather than ρ* Finally, (Q5) addresses the relation between grounding and mereology. This table is composed of a certain number of particles arranged table-wise. It seems thus correct to say that the fact that there is a table depends on the fact that there are particles arranged table-wise. Furthermore, this train of thought can be generalised to the idea that every mereological composite entity at least partially depends on the existence of its parts. This quite widespread idea, which can be labelled 'priority pluralism', has been attacked by Schaffer, who has argued for the 'priority monist' thesis, according to which there is only one fundamental entity, the cosmos, which is the mereological fusion of every concrete entity, and such that each one of its parts is metaphysically dependent on it.14 Schaffer takes grounding to be a relation that can hold between entities from different ontological categories, and thus also between individuals. However, if we take grounding to be a relation between facts (as I will be doing in this paper), then the central claim of Schaffer's 'Priority Monism' can be formulated as follows: Priority Monism: There is exactly one fundamental existence-fact about a concrete object and it is the fact that the cosmos exists. In what follows I will argue that there is an interesting and so far unnoticed relation between (Q1)-(Q5), that is, that (serious) contingentism appears to be incompatible with the idea that the grounding relation is transitive, unless either priority monism or contrastivism about grounding are assumed. I will thus conclude that philosophers endorsing priority pluralism and the idea that grounding is transitive and non-contrastive appear to have good reasons to also endorse necessitarianism and the validity of Entailment. 2. Serious contingentism and a counterexample to transitivity Suppose serious contingentism is true and consider the possible world w. In w, a1, a2, a3, ..., an ('the as') are all the entities that exist, b is a contingently non-existing object, and there is an entity a1, such that the fact that b does not exist is not even partially grounded in the fact that a1 exists. (1) The fact that b does not exist is not even partially grounded in the fact that a1 exists ~([~Eb] |← [Ea1]) Consider now the abundant totality fact saying that a1, a2, a3, ..., an ('the as') are all the entities that exist (call it 'T'). Qua serious theorists, serious contingentists take T to be a 14 Jonathan Schaffer, 'Monism: The Priority of the Whole', Philosophical Review 119 (1) (2010), pp. 31-76; Schaffer, 'The Least Discerning and Most Promiscuous Truthmaker'. 5 derivative fact. The fact that T is not necessitated by the existence of the as (as I am here assuming) is not a problem for them, since, qua contingentists, they can consistently take abundant totality facts like T to be fully grounded by the totality of existence facts. Therefore, serious contingentists can claim that we also have the following, in w: (2) T is fully grounded in the plurality of facts: [a1 exists], [a2 exists], [a3 exists], ...[an exists] T ← [Ea1],[Ea2],[Ea3],...,[Ean] Given the definition of partial grounding Partial grounding: f |←  =df for some Γ: f ← Γ and   Γ,15 it follows that T is partially grounded in the fact that a1 exists (3) T is partially grounded in fact that a1 exists T |← [Ea1] According to serious contingentists, also negative facts are not fundamental. Therefore, the fact that b does not exist must be a derivative fact. On what is this fact derivative? A prima facie plausible option for contingentists might be to say that the fact that b does not exist depends (at least partially) on T, that is the fact that the as are all the entities that exist: (4) The fact that b does not exist is grounded in the (abundant totality) fact (T) that the as are all the existing entities [~Eb] ← T This idea seems to have the ring of intuitiveness to it, at least from the point of view of those (like serious contingentists) banning non-existence facts from the fundamental level of reality.16 However, if partial grounding is transitive, it follows from (3) and (4) that the fact that b does not exist is indeed partially grounded in the fact that a1 exists (5) The fact that b does not exist is partially grounded in the fact that a1 exists [~Eb] |← [Ea1] thus contradicting (1). 3. Two non-starters There are two possible responses to the argument above presented that can be dismissed straight away. The first is to claim that the possible world w is not a genuine possibility and, therefore, that, for every possible world v, every entity x existing at v, and every possible entity y not existing in v, y's non-existence in v is partially grounded in x's existence in v. This would entail, for instance, that even the tiniest and most insignificant 15 Rosen, 'Metaphysical Dependence', p. 115; Fine, 'Guide to Ground', p. 50. 16 A second option is to take non-existence facts to be grounded in the sparse totality fact that everything is identical to one of the as. Since serious contingentists can take also sparse totality facts to be grounded in the totality of existence facts, the choice between these two options makes no difference to the argument I am presenting. For this reason, I will ignore the distinction between sparse and abundant totality facts until section 7. 6 entity in the remotest corner of the universe, such as a speck of dust on a remote planet, would be such that, if I existed without it existing, then its non-existence would have at least partially depended on my existence. This is, however, clearly false, as my existence (or non-existence) appears to be irrelevant to the non-existence (or existence) of a speck of dust on a remote planet on the other side of the universe. The second possible response is to deny that negative facts are grounded in totality facts. Here serious contingentists embracing transitivity would face a choice: (i) either they could claim that there is indeed a single fact that grounds every non-existence fact (but one that-unlike totality facts-is not grounded in any existence fact whatsoever), or (ii) they could claim that there is no single fact that grounds non-existence facts because each of them possesses some 'specific' ground. In our case, for instance, contingentists might respond that there must be some fact f such that f grounds the fact that b does not exist and the fact that f grounds b's non-existence cannot be 'generalised out'17 to any non-existence fact.18 However, the prospects of both choices appear to be pretty dim. On the one hand, it is really hard to see what kinds of facts could 'generically' ground non-existence facts beyond totality facts. On the other hand, the idea that in every possible world nonexistence facts always possess specific grounds strikes one as metaphysical wishful thinking. Consider, in particular, the case of fundamental and contingent entities: what can guarantee that it is necessarily the case that, if a certain fundamental and contingent entity were not to exist, the fact that it does not exist would possess a specific ground? Not only is the burden of proof on the contingentist's shoulder in this case, but the order to fill appears to be a pretty tall one. I conclude, therefore, that serious contingentists endorsing transitivity had better look elsewhere to respond to the objection advanced in section 2. 4. Transitivity and priority monism The intuition behind the argument of section 2 is that non-existence facts are grounded in 'the totality of what exists', so to say. However, there appear to be at least three main ways to precisely articulate this idea. The first is the one considered in section 2, according to which [b does not exist] is grounded in the abundant totality fact T (4) [~Eb] ← T The second is to say that [b does not exist] is grounded in the plurality of existence facts taken together: (6) [~Eb] ← [Ea1],[Ea2],[Ea3],...,[Ean] 17 On this notion of 'generalisation' see Kit Fine, 'Ontological Dependence', Proceedings of the Aristotelian Society 95 (1995), pp. 269-290, p. 277. 18 This would be equivalent to claiming the following: (*) [~Eb] ← f & ~∀x(~Ex → ([~Ex] ← f )) Admittedly, the definition of specificity as 'non-generalisability' is clearly wanting: on the one hand, it appears to be inadequate when the fact [φ(a)] in question is such that a is the only entity x such that φ(x); on the other hand, the fact that a grounding fact about an entity x cannot be generalised to any entity whatsoever is hardly sufficient to make it really 'specific' to x. Even so, it seems to be good enough for the purpose at hand, since it appears that, at least in worlds like ours in which (as it appears plausible to suppose) non-existence facts abound, contingentists would be committed to say (in this case) that non-existence facts possess grounds that are 'specific' at least in this sense. 7 The third is to take [b does not exist] to be grounded in the existence of the mereological sum of every existing thing, that is, in the Schafferean cosmos ('k'):19,20 (7) [~Eb] ← [Ek] The fact that the non-existence of b is grounded in the existence of a1 follows from (4) (and (3)) by the transitivity of grounding and from (6) by the very definition of partial grounding. Instead, if (7) is assumed, we need the further pluralist assumption that every entity is partially grounded in all of its proper parts ('xPPy' stands for 'x is a proper part of y'): (8) xy(xPPy  ([Ey] |← [Ex])) As a matter of fact, it follows from (8) that (9) [Ek] |← [Ea1] and, hence, by (7) and (9) and the transitivity of partial grounding, that (5) [~Eb] |← [Ea1] If, instead, we embrace priority monism and take the cosmos to be the only fundamental entity (that is: the only entity x such that the fact that x exists is a fundamental fact), then from the fact that b's non-existence is grounded in the existence of the cosmos it does not follow that the fact [b does not exist] also depends on the fact that a1 exists. According to priority monism, it is a1 that depends on k, not the other way around: (10) [Ea1] ← [Ek] Therefore, within a monist setting no contradiction can follow from transitivity in our case. Monists can consistently claim that the fact that the cosmos exists grounds (i) every existence fact, (ii) every non-existence fact, and (iii) the totality fact. The fact that b does not exist and the fact that a1 exists are thus both derivative facts grounded in the fact that the cosmos exists and cannot, thus, form a chain of grounding relations threatening the idea that grounding is transitive. 5. Transitivity and contrastivism. By embracing priority monism serious contingentists can successfully respond to the objection advanced in section 2 without rejecting the transitivity of grounding. This is, however, not their only option, as they can instead use the argument of section 2 to bolster the idea that grounding is a contrastive notion, without the need of embracing monism. Consider, for instance, Schaffer's case of the dented sphere.21 The fact that a certain sphere s is more or less spherical does not obtain in virtue of the fact that it has a certain dent d, but in spite of it, claims Schaffer. However, on the one hand, the fact that it is more or less spherical clearly depends on its having a specific (more or less spherical) 19 See Schaffer, 'Monism: The Priority of the Whole'. For simplicity's sake, I am here ignoring the restriction to concrete entities. Nothing of substance will hang on this. 20 A variation of the first option consists in taking [b does not exists] to be grounded in the sparse totality fact that everything is identical to one of the as (see above, footnote 16). 21 Schaffer, 'Grounding, Transitivity and Contrastivity'. 8 shape H; on the other hand, it clearly has that specific shape partly in virtue of being dented in the way it is, that is, by having d. Counter-example: (D1) The sphere s has the shape H partly in virtue of being dented in the way it is, that is, by having d; (D2) The fact that a certain sphere s is more or less spherical is grounded in its having a specific (more-or-less spherical) shape H. Imagine, however, that you take the sphere s (which has the dent d) and start exerting some pressure on its dent d until the sphere is e-dented. As soon as you modify d, s will lose its original shape H. When the original dent is completely transformed into e, s has the shape I. However, both H and I are more-or-less spherical shapes. So, if we take s (that is H-shaped) and we slowly modify it so as to make it assume the shape I, we are not thereby making any difference to the fact that s is more-or-less spherical. In order to make such a difference a more radical change is needed (from H to, say, the non-spherical shape Z). Therefore, concludes Schaffer, the case of the dented sphere is not a counterexample to the transitivity of differential grounding. Contrastivist solution: (D1C) The fact that the sphere has the (d-dented) shape H instead of the (edented) shape I is grounded in the fact that it has the dent d instead of the dent e; (D2C) The fact that the sphere is more-or-less spherical rather than not is grounded in the fact that it has the (more-or-less spherical) shape H instead of the (not more-or-less spherical shape) Z. The same kind of contrastive treatment can also be applied to our counterexample (in a serious contingentist and priority pluralist setting) to the transitivity of grounding: Counter-example: (E1) The fact that the as are all the existing entities is partially grounded in fact that a1 exists; (E2) The fact that b does not exist is grounded in the fact that the as are all the existing entities. Imagine, in fact, that in the world w God intervenes and eliminates a1, without doing anything else. In such a case T would not be the abundant totality fact anymore. As an effect, the abundant totality fact would be the fact ('T-1') that the as minus a1, are all the entities that exist. However, the variation between T and T-1 would make no difference whatsoever to the non-existence of b in w. In order to make such a difference, God should intervene and change the abundant totality fact from T to a totality fact saying that b exists, like, for instance, the fact ('T+1') that the as plus b are all the entities that exist. Therefore, within a contrastivist framework, also the case of b's non-existence appears to be no counter-example to the (differential) transitivity of the grounding relation. 9 Contrastivist solution: (E1C) The fact the as rather than the as-minus-a1 are all the existing entities is partially grounded in the fact that a1 exists rather than not; (E2C) The fact that b does not exist rather than it does is grounded in the fact that the as rather than the as-plus-b are all the existing entities. To say that a1's existence partially grounds T-says the contrastivist-is to say that a1's existence makes a difference with respect to T, and so that an intervention with respect to a1's existence would change which fact is the abundant totality fact. However, while removing a1 from existence would indeed change the abundant totality fact from T to T1, this would not make the faintest difference as to the non-existence of b, which is why the case at hand-concludes the contrastivist-is not a counter-example to the differential transitivity of grounding. 6. Necessitarianism and transitivity Before concluding, it is worth mentioning how necessitarians can respond to the argument of section 2 (assuming they want to maintain both pluralism and transitivity without having to resort to contrastivism). In fact, while necessitarians have many options to choose from when it comes to the question as to what grounds non-existence facts, the argument presented in section 2 shows there is at least one option that is unavailable even to them. In fact, it should be now clear how necessitarians cannot both embrace option (N2), according to which abundant totality facts like T are grounded in the totality of existence facts together with a sparse totality fact (see above, section 1), and together claim that non-existence facts are grounded in abundant totality facts. In fact, this would entail in our case that, since a1's existence helps ground T, and T grounds b's nonexistence, so the fact that b does not exist is partially grounded in the fact that a1 exists, contradicting thus (1) (see above). However, necessitarians appear to have at least three other consistent options to account for what grounds the fact that b does not exist: (Nw1) The fact that b does not exist is fundamental ~f ([~Eb]←f) (Nw2) T is fundamental and the fact that b does not exist is fully grounded in T ~f (T←f) & [~Eb]←T22 22 It is worth mentioning, however, that, since T cannot obtain without the as existing, (Nw2) is problematic if a seemingly plausible principle of free modal recombination between fundamental and contingent facts is assumed. On the validity of modal recombination at the fundamental level see: Karen Bennett, 'By Our Bootstraps', Philosophical Perspectives 25 (1) (2011), pp. 27-41 ( '[...] it is plausible to think that whatever the fundamental elements of the world are, they are open to free modal recombination [...] In the absence of a reason to constrain their possible combination, it should be assumed that there is no such constraint; they are freely recombinable.', p. 27); Ross Cameron, 'From Humean Truthmaker Theory to Priority Monism', Noûs 44 (1) (2010), pp.178-198 ('There must be free recombination amongst the fundamental existents; whenever there is a necessary connection, there must be ontological dependence to explain the necessary connection.', p. 188); and Schaffer, 'Monism: The Priority of the Whole' ('[...] fundamental actual concrete objects should be freely recombinable, serving as independent units of being (building blocks, as it were). [...] If entities are metaphysically independent, then they should be modally unconstrained in combination.', p. 40). For a recent criticism of principles of modal recombination in general see: Jessica Wilson, 'What is Hume's Dictum, and Why Believe It?' Philosophy and 10 (Nw3) The fact that b does not exist is fully grounded in the fundamental sparse totality fact that everything is identical to either a1, or a2, or a3, ... or an. ([~Eb] ← [x(x=a1v x=a2 v x=a3 v ... x=an)]) & ~f ([x(x=a1v x=a2 v x=a3 v ... x=an)] ← f) Therefore, necessitarianism does not appear to be threatened by the argument of section 2 and appears thus to be at least a less committal alternative to its serious contingentist counterpart. 7. Conclusion. In this paper I have argued that, if grounding is a transitive notion, serious contingentists must choose between priority monism and contrastivism. Since non-serious contingentism does appear to be a far less philosophically appealing theory than its serious version, it follows that, if the argument presented in this paper is on the right track, priority pluralists and 'orthodox devotees of ground'23 have some good reasons to prefer necessitarianism to its contingentist alternative.24 Instituto de Investigaciones Filosóficas, Universidad Nacional Autónoma de México Circuito Maestro Mario de la Cueva Mexico City, 04510, Mexico. email@example.com Phenomenological Research, 80 (2010), pp. 595–637; and 'Three Dogmas of Metaphysical Methodology' in Matthew Haug (ed.), New Essays on Philosophical Methodology (Routledge, forthcoming). 23 Raven, 'Is Ground a Strict Partial Order?'. 24 Many thanks to the Programa de Becas Posdoctorales en la UNAM, Instituto de Investigaciones Filosóficas, Universidad Nacional Autónoma de México (UNAM), for academic and financial support.