Thursday, June 25, 2015

Chapter 9_Theism and the Deep Roots of Science

I. Science and the Divine Image

Plantinga: Modern Western empirical science originated and flourished in the bosom of Christian theism and originated nowhere else…All of the great names of early Western science, furthermore – Nicholas Copernicus, Galileo Galilei, Isaac Newton, Robert Boyle, John Wilkins, Roger Cotes, and many others – all were serious believers in God…This is no accident: there is deep concord between science and theistic belief.[1]

Plantinga: How should we think of science?
(1) Realists – science is an effort to learn something of the sober truth about our world
(2) Instrumentalists – the value of science lies in its ability to help us get on in the world
(3) Constructive empiricists – The point of science is to produce empirically adequate theories; the question of the truth of these theories is secondary[2]

à Science is at bottom an attempt to learn important truth about ourselves and our world…More specifically, science is a disciplined and systematic effort to discover such truths, an effort with a substantial empirical involvement.[3]

Q1: Is everyone ok with Plantinga’s characterization of science, developed to this point? If not, how would you prefer we characterize it?

Plantinga: What sorts of conditions would be required for the success of science?
(1) There must be a match between our cognitive faculties and the world[4]

Science, clearly, is an extension of our ordinary ways of learning about the world. As such, it obviously involves the faculties and processes by which we ordinarily do achieve knowledge…For science to be successful, therefore, there must be a match between our cognitive faculties and the world.[5]

Plantinga: How is Christian belief relevant here?
(1) The Christian belief that we were created in the image of God implies that we (like him) are able to know important things about our world and ourselves.[6] (This, according to Plantinga, is achieved via a sort of pre-established harmony that God has established between our cognitive faculties and the world, as well as ourselves, and God himself.)

Contrast this with naturalism.

Chomsky: It is just blind luck if the human science-forming capacity a particular component of the human biological endowment, happens to yield a result that conforms more or less to the truth about the world.[7]

Plantinga: How shall we understand this fit?

à One condition of this success is that perception for the most part, and under ordinary and favorable conditions, produces in us beliefs that are in fact true.[8]

Q2: What is Plantinga’s account of truth? What does it mean, according to Plantinga, to form a true belief?

Correspondence theory of truth

States that the truth or falsity of a statement is determined only by how it relates to the world and whether it accurately describes (i.e., corresponds [agrees] with) that world.[9]

Q3: Why accept the correspondence theory of truth? Particularly, given what we know now about how the corporeal features of different organisms (particularly their bodily orientation, survival conditions, perceptual machinery, etc.) influences the phenomenological reality in which they live, does the correspondence theory of truth even make any sense (e.g., what are the relevant terms that must “agree” – is it the term and the phenomenon, the term and the “thing in itself”, what Kant called the noumenon?)?

Q4: Even assuming it were possible to form beliefs that were true in the correspondence sense, i.e., beliefs that agreed with their object, in what ways would these beliefs be superior (practically, morally, or otherwise) to beliefs that were merely adaptive?

Q5: Why should the success of science depend on the capacity of our faculties, perceptual or otherwise, to produce true beliefs? Does Plantinga mean to suggest that science on some level entails the correspondence theory of truth?

Whether our epistemic faculties function (were designed?) to yield true beliefs or merely adaptive ones is to some extent an empirical question, and is therefore testable. The argument that they don’t function in this way can be developed as follows:

(1) On the correspondence theory of truth, what matters is material agreement between proposition and the world, such that a belief is a true if and only if it accurately describes the material nature of its object.
(2) There are certain situations in which a materially true belief would be less adaptive than the right kind of materially false one.
(3) Some of these situations are such that this is reliably the case (or is the case more often than not), i.e., most of the times that a situation of this type arises, the materially true belief would be less adaptive than the right kind of materially false belief.[10]
(4) Some of these situations are also such that the advantage derived from the materially false belief doesn’t owe to either (a) some non-standard feature of the situation (e.g., unfavorable viewing conditions) or (b) malfunctioning faculties (e.g., impairment or disease).
(5) There are possible biological mechanisms that reliably function to exploit the situations described in (2)-(4) that don’t interfere to too great an extent with the successful functioning of other mechanisms (e.g., those aimed at producing materially true beliefs in other situations, granted that these exist)
(6) Creating humans with such mechanisms as described in (5), however, is incompatible with the nature of God, insofar as (a) “it is impossible for God to lie,”[11] and (b) such design would constitute a “vicious determination to err,” thus undermining man’s capacity for free will.[12]
(7) Therefore, if theism is true, then there are no such biological mechanisms as described in (5).
(8) But there are such biological mechanisms such as described in (5).
(9) Therefore, theism isn’t true.[13]

Q6: What is your response to the argument above? Do you think that Plantinga is right to affirm premise (7) above, given that it entails the denial of premise (8)?

II. Reliability and Regularity

Plantinga: For science to be successful, the world must display a high degree of regularity and predictability…[This is because] intentional action requires a high degree of stability, predictability, and regularity. And of course the predictability in question has to be predictability by us. Furthermore, science requires more than regularity: it also requires our implicitly believing or assuming that the word is regular in this way.[14]

Whitehead: There can be no living science unless there is a widespread instinctive conviction in the existence of an Order of Things. And, in particular, of an Order of Nature…[This widespread conviction owes to the medieval insistence on the rationality of God.][15]

Q7: Do you agree with Whitehead’s analysis above? Does the widespread instinctive conviction in the existence of an Order of Nature owe to the medieval insistence on the rationality of God? What other explanations might there be for it?

Plantinga: What does this “rationality” of God consist in?

à [T]he medieval put it in terms of the question whether, in God, it is intellect or will that is primary. They thought that if intellect is primary in God, then God’s actions will be predictable, orderly, and conforming to a plan – a plan we can partially fathom.[16]

Q8: What are we to make of the tension between Plantinga’s claim that the belief that God operates in rational (i.e., predictable, reliable, constant) ways, which is thought to underwrite the development of science in the West, and James’ recognition that this same belief is what gives rise to the problem of evil, considered by many to be one of the most serious theological objections? How can the same belief be invoked to explain both contradictory data?[17]

In light of the debate between Aquinas and William of Ockham, it would seem that theism doesn’t unambiguously entail either the perfect regularity of the universe or its opposite. Perhaps, then, Plantinga is too charitable to credit theism for the success of science. The belief of an ordered universe seemingly is able to arise and persist without it.

Q9: What fact about God, with which the general populous was already sufficiently familiar, does Plantinga take to entail the regularity, predictability, and constancy of natural processes? If this entailment is as obvious or inevitable as Plantinga seems to imply, what are we to make of the disagreement between Aquinas and Ockham?

Q10: On a related note, which do you think is more likely: (a) that an ordered universe was inferred or deduced from people’s theistic beliefs; or (b) that these theistic beliefs were inferred from the observation that the universe seems to exhibit orderliness? We have clear instances (provided by natural theology) of people engaging in the latter process; but what would it look like for people to engage in the former?

III. Law

A. Law and Constancy

Plantinga: This constancy and predictability, this regularity, was often thought of in terms of law: God sets, prescribes laws for his creation, or creates in such a way that when he creates is subject to, conforms to, laws he institutes.[18]

William Whewell: But with regard to the material world, we can at least go so far as this – we can perceive that events are brought about not by insulated interpositions of Divine power, exerted in each particular case, but by the establishment of general laws.[19]

Plantinga: It is worth noting the connection here between moral law and natural law, or laws of nature…In each case…we have the setting forth or promulgation of divine rule for a certain domain of application. It is important to see that our notion of the laws of nature, crucial for contemporary science, has this origin in Christian theism (emphasis mine).[20]

Q11: Do you find Plantinga’s claim above plausible (see text in italics)? If not, what other explanations can you think of that might account for our notion of the laws of nature?

Plantinga: On this conception, part of the job of science is to discover the laws of nature; but then of course science will be successful only if it is possible for us human beings to do that. Science will be successful only if these laws are not too complex, or deep, or otherwise beyond us. Again, this thought fits well with theistic religion and its doctrine of the image of God; God not only sets laws for the universe, but sets laws we can (at least approximately) grasp.[21]

B. Law and Necessity

Plantinga: There is still another important way in which theism is hospitable to science: theism makes it much easier to understand what these laws are like. The main point has to do with the alleged necessity of natural law…[L]aws…are [true and universal in form,] but are not accidentally true.[22]

Plantinga: How shall we understand this non-accidentality?

à  They are nomologically necessary. This necessity is weaker than logical necessity (the laws of nature of not logically necessary), but still stronger than mere universal truth (not all true universal generalizations are necessary in this sense).[23]

Plantinga: Theism offers important resources here [for explaining what it is for something to be nomologically necessary]: we can think of the necessity of natural law as both a consequence and also as a sort of measure of divine power…From a theistic perspective, the reason [there are natural limits to our technological advancement] is that God has established and upholds this law for our cosmos, and no creature (actual or possible) has the power to act contrary to what God establishes and upholds…The sense in which the laws of nature are necessary, therefore, is that they are propositions God has established or decreed, and no creature – no finite power, we might say – has the power to act against these propositions, that is, to bring it about that they are false…We could say that they are finitely inviolable. Thought these laws are finitely inviolable, they are nonetheless contingent, in the sense that it is not necessary, not part of the divine nature, to institute or promulgate just these laws.[24]

Many philosophers – most notably, Leibniz – have proposed that our world, which God has created, is the best of all possible worlds. (In fact, Plantinga himself affirms this premise in his defense against the problem of evil.) This premise is meant to defend against certain objections to theism based on apparent non-ideal features of this world, e.g., the existence of evil.

Now imagine the following scenario:
(1) Assume there exist two alternative ways of ordering the cosmos, either by establishing set A of natural laws or set B. Then,
(2) Given the pragmatic principle that “there is no difference that doesn’t make a difference somehow, somewhere, somewhen,”[25] the cosmos governed by set A would yield a different set of outcomes than the cosmos governed by set B.
(3) Once all of these outcomes were taken into account, it seems that one of the two cosmoses would be qualitatively superior to the other (e.g., contain less evil, provide for more expressions of virtue, etc.). But then,
(4) If God were morally perfect, it seems he would be compelled to choose to instantiate the cosmos that allowed for the superior outcomes. Furthermore,
(5) Insofar as choosing the best of two possible alternatives is logically entailed by being morally perfect, this choice would not be contingent but necessary – indeed, logically necessary. But then,
(6) It would not be true that the laws of nature are contingent either, since God was necessitated by his nature to instantiate them.

Q12: Can Plantinga consistently affirm both premises, i.e., both (a) that God has created the best of all possible worlds (or that there is such a thing as a best of all possible worlds); as well as (b) the natural laws that God has established are contingent? If so, how might we resolve the apparent conflict between them?

IV. Mathematics

A. Efficacy

Plantinga: Why should the world be significantly describable by these mathematical structures? Why should these complex and deep structures be applicable in interesting and useful ways?[26]

Objection: No matter how the world had been, it would have been describable by mathematics of some kind or other.[27]

à Plantinga: Perhaps so; but what is unreasonable, in Wigner’s terms, is that the sort of mathematics effective in science is extremely challenging mathematics, though still such that we human beings can grasp and use it (if only after considerable effort)…That mathematics of this sort [i.e., exhibiting deep simplicity] should be applicable to the world is indeed astounding. It is also properly thought of as unreasonable, in the sense that from a naturalistic perspective it would be wholly unreasonable to expect this sort of mathematics to be useful in describing our world.[28]

B. Accessibility

Plantinga: Just as it is unreasonable, from a naturalistic perspective, to expect mathematics of this sort to be efficacious, so it is unreasonable, from that perspective, to expect human beings to be able to grasp and practice the kind of mathematics employed in contemporary science.[29]

Plantinga again defers to the objection that such abilities as are exhibited by theoretical physicists and mathematicians are unnecessary for survival and reproduction, and actually constitute a positive hindrance.

Q13: Do you buy this argument? Do you agree with Plantinga that the efficacy and accessibility of mathematics is unreasonable on the assumption of naturalism? If not, what other (naturalistic) explanation might there be for these features?

C. The Nature of Mathematics

Plantinga: Theism provides a better explanation for certain properties of numbers and sets, namely,
(1) Their abstractness
(2) Their ontological necessity, i.e., that they exist necessarily
(3) Their ontological dependence on thinkers or mind[30]

Plantinga: The most natural way to think about abstract objects, including numbers, is as divine thoughts.[31]

D. Mathematical Objects as Abstract

Plantinga: The objects of mathematics…are abstract objects. Abstract objects, so we think, differ from concrete objects in that they do not occupy space and do not enter into causal relations…But this creates a puzzle. It seems sensible to think that the objects we can know about can causally affect us in some way, or at least stand in causal relationship with us…[I]t seems sensible to think that a necessary condition of our knowing about an object or kind of object is our standing in some kind of causal relation to that object or kind of object. If this is so, however, and if, furthermore, numbers and their kin are abstract objects, then it looks as though we couldn’t know anything about them.[32]

So, Plantinga claims, since we stand in causal relationship to God, and God in causal relationship to abstract entities (by thinking them), we also stand in causal relationship to abstract objects via the mediation of God.

Q14: Are you satisfied with Plantinga’s (realist) analysis of abstract objects? If not, what alternative analysis might be preferable?

For those not familiar with the debate, here is a brief overview of the most popular alternatives:[33]

The deepest question about [abstract objects] is whether there are any. Textbooks feature a triumvirate of answers: realism, nominalism, and conceptualism. There are many species of each view, but the rough distinctions come to this. Realists hold that there are [abstract objects], understood as mind-independent entities. Nominalists deny this (though some hold that there are tropes). And conceptualists urge that words (like ‘honesty’) which might seem to refer to [abstract objects] really refer to concepts, understood as mind-dependent entities. Nominalism and conceptualism often come together and often are assimilated to the extent that they both involve a non-realist stance about universals. Such a stance is typically coupled with an attempt to reduce universals to other entities such as sets or classes of their instances or, as Lewis (1986) has proposed, to sets of all their possible instances.[34]

V. Induction and Learning from Experience

Plantinga: Another and less obvious condition for the success of science has to do with our ways of learning from experience. We human beings take it utterly for granted that the future will resemble the past…and this expectation is crucial to our being able to learn from experience [and engage in science]...We human beings, including those among us with properly functioning cognitive faculties, are inevitably addicted to inductive reasoning. And this is another example of fit between our cognitive faculties and the world in which we find ourselves. Like the others, this fit is to be expected given theism.[35]

VI. Simplicity and Other Theoretical Virtues

Plantinga: Scientific theories…are underdetermined by the evidence…[For example,] for any finite set of observation of the path of a comet, infinitely many different curves can be found to fit…[36]

Plantinga: [W]hy do we choose certain hypotheses to endorse, when there are infinitely many compatible with our evidence?

à Because these hypotheses, as opposed to others, display the so-called theoretical virtues. Among these virtues the following have been proposed: simplicity, parsimony (which may be a form of simplicity), elegance or beauty, consilience (fit with other favored or established hypotheses), and fruitfulness.[37]

Plantinga: Naturalism gives us no reason at all to expect the world to conform to our preference for simplicity. From that perspective, surely, the world could just as well have been such that unlovely, miserably complex theories are more likely to be true. Theism with its doctrine of the Imago Dei, on the other hand, is relevant in two quite distinct respects. First, insofar as we have been created in God’s image, it is reasonable to think our intellectual preferences resemble his…Second, what we have here is another example of God’s having created us and our world in such a way that there is that adequatio intellectus ad rem.[38]

Many of Plantinga’s arguments in this chapter seem to loosely follow this structure:
(1) The world has certain improbable features (regularity, predictability, constancy; laws that are simple, parsimonious, accessible, beautiful perhaps; etc.)
(2) Human beings have certain improbable features (natural tendency to believe in the regularity, predictability, and constancy of the world; natural instincts for mathematical and inductive reasoning; natural preferences for simple, parsimonious, beautiful theories; etc.)
(3) The match we find between the world’s features and the features of human beings is also unusual or improbable.

Q15: But doesn’t the truth of premise (1) significantly diminish the force of premises (2) and (3), particular since evolutionary theory predicts that (2) and (3) will follow from (1)? Do you think Plantinga intends for his argument to be cumulative, i.e., to acquire additional force from each additional premise, or is he rather just meaning to drive home the same basic point from several possible angles? If the former, do you think his attempt is successful? Why or why not?

Q16: Do you share Plantinga’s doubts that, on naturalism, we should find a fit between our cognitive faculties and the world we live in? Do any of Plantinga’s specific examples provide any special difficulty for you? If so, which ones and why? If not, why not?

VII. Contingency and Science as Empirical

Plantinga: [This link to the empirical that we call testability] is an essential part of modern science. Here there is another crucial connection between theistic belief and modern science. According to theism, God has created the world; but divine creation is contingent…God is not obliged, by his nature, or anything else, to create the world; there are plenty of possible worlds in which he doesn’t create a world outside himself. Instead, creation is a free action on his part. Furthermore, given that he does create, he isn’t obliged to do so in any particular way. It is this doctrine of the contingency of divine creation that both underlies and underwrites the empirical character of modern Western science. This relationship between the contingency of creation and the importance of the empirical, in science, was recognized very early; indeed, the former is the source of the latter (emphasis mine).[39]

Q17: Again, why think that this is true? Many have argued, for the reasons previously provided, that libertarian free will and moral perfection are logically incompatible properties.[40]

Summary

Plantinga: With respect to the laws of nature, therefore, there are at least three ways in which theism is hospitable to science and its success, three ways in which there is deep concord between theistic religion and science. First, science requires regularity, predictability, and constancy; it requires that our world conform to laws of nature…Second, not only must our world in fact manifest regularity and law-like behavior: for science to flourish, scientists and other must believe that it does…Third, theism enables us to understand the necessity of inevitableness or inviolability of natural law: this necessity is to be explained in terms of the difference between divine power and the power of finite creatures.[41]

Of course, by the end of the chapter, Plantinga has offered far more examples than those mentioned above. Below I have compiled the more complete list:

What sorts of conditions would be required for the success of science?

(1)     There must be a match between our cognitive faculties and the world.[42] More specifically, humans must have faculties adequate to the task of discovering and/or apprehending the laws that govern the orderliness of nature
(2)     Conversely, the natural laws must not be too complex, or deep, or otherwise beyond us
(3)     The world must display a high degree of regularity and predictability[43]
(4)     Humans must also be disposed to believe that the world is regular in this way
(5)     Math has to be efficacious and accessible (the world must be describable by mathematics that are accessible by us)[44]
(6)     The future has to sufficiently resemble the past (to allow for induction)
(7)     We must have an instinct for inductive reasoning[45]
(8)     Nature has to abide by laws that satisfy the virtues of theories, or we have to have the tendency to prefer those virtues that the actual laws actually possess (simplicity, parsimony, beauty, etc.)[46]
(9)     Nature has to has to have a relation to the empirical so as to enable testability[47]

How is Christian belief relevant here?

(1)     We are created in the image of God, and like him, are capable of knowing things about the world[48]
(2)     God providentially governs the world in such a way as to provide the requisite stability and regularity[49]
(3)     Theism enables us to understand the necessity or inevitableness or inviolability of natural law: this necessity is to be explained in terms of the difference between divine power and the power of finite creatures.[50]
(4)     Theism, by providing the conceptual framework of laws, helps us understand what it is in virtue of which nature is stable, regular, and constant
(5)     Theism makes it much easier to understand what these laws are like, namely as nomologically necessary. Theism offers important resources here [for explaining what it is for something to be nomologically necessary]: we can think of the necessity of natural law as both a consequence and also as a sort of measure of divine power
(6)     Theism explains why mathematics exhibits the efficacy and accessibility that it does[51]
(7)     Theism provides a natural way to understand what mathematical objects are (thoughts in the mind of God), and also how they causally affect us (namely, through the mediation of God, who stands in causal relation to both numbers as well as us)[52]
(8)     Theism explains why the past resembles the future, namely because
(9)     Theism explains why human beings have an instinct for inductive reasoning, namely that God has designed our faculties to be adequate to this task, because of his interest in our having knowledge of the world[53]
(10)  Theism explains why nature abides by laws that feature the theoretical virtues, and/or why we have a preference in our theoretical reasoning for the virtues that the natural laws actually possess[54]
(11)  Theism provides a natural way to understand what it is for something to be empirical and contingent, namely in terms of what God did out of his radical freedom.[55]

Plantinga actually makes the stronger claim that the conditions necessary for science to succeed are unexpected on naturalism, “an enigma,” “a piece of enormous cosmic luck,” “a not-to-be-expected bit of serendipity.” Ultimately, in Plantinga’s assessment, “Naturalism stands mute before such questions.”[56]

Q18: Is Plantinga right that naturalism has no ready explanation for the fact that the conditions necessary for the success of science obtain in our world? If not, what explanations might naturalism offer?

Q19: Any final thoughts with regard to the points/argument listed above? Do you find any of them particularly strong or particularly weak? If so, which ones?

The primary objective of this chapter is to demonstrate that there is deep concord between faith and science, which Plantinga hopes to establish by arguing that certain theistic beliefs are actually required in order for science to arise and flourish. 

Q20: Do you think Plantinga's argument that the success of science in the West owes to their theistic (Christian) beliefs was ultimately successful? What other unique features of the West during this time might plausibly have contributed to the emergence and subsequent flourishing of science?





[1] P. 276.
[2] P. 276-277.
[3] P. 277.
[4] P. 280.
[5] P. 280.
[6] Plantinga says that this feature, while perhaps not being the chief part of the image of God, is at least a crucial one (see p. 279).
[7] P. 279-280.
[8] P. 281.
[10] In other words, these situations represent sufficiently stable features of the environment as to allow for the evolution of mechanisms that exploit them.
[11] Heb. 6:18.
[12] Descartes writes in the Meditations, “When we say...with respect to the body suffering from dropsy, that it has a disordered nature because it has a dry throat and yet does not need drink, the term 'nature' is here used merely as an extraneous label. However, with respect to the composite, that is, the mind united with this body, what is involved is not a mere label, but a true error of nature, namely that it is thirsty at a time when drink is going to cause it harm. It thus remains to inquire how it is that the goodness of God does not prevent nature, in this sense, from deceiving us” (CSM II, 59). He continues later, “[Notwithstanding] the immense goodness of God, the nature of man as a combination of mind and body is such that it is bound to mislead him from time to time...Yet it is much better that it should mislead him [on the occasion of some sickness] than that it should always mislead when the body is in good health” (CSM II, 61). He continues further with suggestions toward how we may even learn to cope with and correct such errors: “[In] matters regarding the well-being of the body, all of my senses report the truth much more frequently than not. Also, I can almost always make use of more than one sense to investigate the same thing; and in addition, I can use both my memory, which connects present experiences with preceding ones, and my intellect, which has by now examined all the causes of error”  (CSM II, 61). “In the case of our clearest and most careful judgments, however, this kind of explanation would not be possible, for if such judgments were false they could not be corrected by any clearer judgments or by means of any natural faculty. In such cases I simply assert that it is impossible for us to be deceived. Since God is the supreme being, he must also be supremely good and true, and it would therefore be a contradiction that anything should be created by him which positively tends towards falsehood...Hence this faculty must tend towards the truth, at least when we use it correctly (that is, by assenting only to what we clearly and distinctly perceive...)” (CSM II, 102-103).
[13] It should be noted that certain theistic premises can also allow for such exceptions under special circumstances. For an example of an argument employing such premises, see Descartes’ Meditations, .
[14] P. 281-282.
[15] P. 282.
[16] P. 283.
[17] James prescribes pluralism as the way out of this dilemma: in other words, the admission of some element of chance or irregularity into our metaphysic. See A Pluralistic Universe, .
[18] p. 284-285.
[19] P. 285.
[20] P. 286.
[21] P. 287.
[22] P. 288.
[23] P. 289.
[24] P. 290-291.
[25] Pragmatism, .
[27] p. 294.
[28] P. 294.
[29] P. 296.
[30] P. 297-298.
[31] P. 299. For a more in-depth discussion of Plantinga’s metaphysics, including those concerning abstract objects, see http://rocket.csusb.edu/~mld/The%20Metaphysics%20of%20Alvin%20Plantinga.pdf. See also sect. 5e of “Platonism and Theism” in IEP at http://www.iep.utm.edu/pla-thei/#SH5e.
[32] P. 301-302.
[33] See section 1.1.5: Realism, Nominalism, and Conceptualism of “Properties” in SEP at http://plato.stanford.edu/entries/properties/.
[35] P. 302-303.
[36] P. 306-307.
[37] P. 307-308.
[38] P. 309.
[39] P. 311-313.
[40] E.g., see Sect. 5: Is Necessary Perfect Goodness Possible of “Perfect Goodness” in SEP at http://plato.stanford.edu/entries/perfect-goodness/#DivFre.
[41] P. 292-293.
[42] P. 280.
[43] P. 281.
[44] P. 294-296.
[45] P. 302-303.
[46] P. 309.
[47] P. 311-313.
[48] P. 280.
[49] p. 282.
[50] P. 292-293.
[51] P. 294-296.
[52] P. 294-296.
[53] P. 302-303.
[54] P. 309.
[55] P. 311-313.
[56] P. 293.
[57] Recall chapter .