Reflecting on Russell’s Religion and Science 3. Russell as a Skeptic, Even with Respect to Science

1. The present post is the third in a series of posts reflecting on the philosophical theses at work in Bertrand Russell’s Religion and Science.* In the series’ previous posts, I have directed attention to Russell’s “exclusivist epistemological scientism,” as I have dubbed it, the thesis that scientific knowledge is the only knowledge. I have also taken note that an adoption of that thesis requires the adoption of the further theses that there is no theological knowledge distinct from scientific knowledge, no philosophical knowledge distinct from scientific knowledge, and no mathematical knowledge distinct from scientific knowledge. In this post, I wish to direct attention to one of the at least two complications that any understanding of Russell’s exclusivist epistemological scientism has to recognize: for the Russell of Religion and Science, there is not even scientific knowledge. The other of the two complications will have to await its share of attention until the next post.

2. The most salient passage in which Russell denies that scientific theory counts in fact as knowledge begins with his saying (p. 14),

A religious creed differs from a scientific theory in claiming to embody eternal and absolutely certain truth, whereas science is always tentative, expecting that modifications in its present theories will sooner or later be found necessary, and aware that its method is one which is logically incapable of arriving at a complete and final demonstration.

Russell proceeds then to tell us that science achieves (1) not “absolute truth,” but rather “practical truth” or “‘technical’ truth” and (2) not “knowledge,” but “‘knowledge’.” He first (pp. 14-15) sets absolute truth aside.

But in an advanced science the changes are generally only such as serve to give slightly greater accuracy; the old theories remain serviceable where only rough approximations are concerned, but are found to fail when some new minuteness of observation becomes possible. Moreover, the technical inventions suggested by the old theories remain as evidence that they had a kind of practical truth up to a point. Science thus encourages abandonment of the search for absolute truth, and the substitution of what may be called “technical” truth, which belongs to any theory that can be successfully employed in inventions or in predicting the future. “Technical” truth is a matter of degree: a theory from which more successful inventions and predictions spring is truer than one which gives rise to fewer.

Russell proceeds next (p. 15) to set aside scientific knowledge, leaving us with but scientific “knowledge.”

“Knowledge” ceases to be a mental mirror of the universe, and becomes merely a practical tool in the manipulation of matter. But these implications of scientific method were not visible to the pioneers of science, who, though they practiced a new method of pursuing truth, still conceived truth itself as absolutely as did their theological opponents.

3. a. Two things may be said on Russell’s behalf here. The first is that he is, of course, absolutely right in pointing to the real progress that has been made in scientific knowledge. For example, it was once believed by most, including Aristotle and even Descartes, that light traveled instantaneously. As Professor Michael Fowler of the University of Virginia notes in his “The Speed of Light,” Galileo, in his Two New Sciences, has his character, Simplicio, “stating the Aristotelian position,”

SIMP. Everyday experience shows that the propagation of light is instantaneous; for when we see a piece of artillery fired at great distance, the flash reaches our eyes without lapse of time; but the sound reaches the ear only after a noticeable interval.

Now, of course, we know that, and I’ll put it cautiously, in at least some circumstances, light travels at a finite velocity, and so with a “lapse of time.”

3b. The second thing that may be said on Russell’s behalf is that the knowledge that we thought we had, that, say, in all circumstances,** light travels instantaneously, turns out to have been, not knowledge at all, let alone absolute knowledge, but merely, using Russell’s way of putting it, “knowledge.”

4. It remains the case. however, that, in at least some circumstances, light travels at a finite velocity, and so with a “lapse of time.”***

It is the case, moreover, that the proposition, “In at least some circumstances, light travels at a finite velocity, and so with a ‘lapse of time,’” is a true proposition and not at all a false proposition. It will not be displaced by a “truer” proposition at any point in the future, thereby becoming less true.

And it is the case, finally, that we know that, in at least some circumstances, light travels at a finite velocity, and so with a “lapse of time.” That knowledge is a genuine knowledge and not at all a case of non-knowledge or mere “knowledge.” It will not be displaced by an opinion that is more a knowledge at any point in the future, thereby becoming less a knowledge.

5. Let me add hastily that the piece of reasoning just concluded does not commit us to the view that, though “knowledge” may not “be a mental mirror of the universe,” knowledge is such “a mental mirror of the universe.” The relation in which a knowing mind stands to that which it knows is a topic that will have to await a post that will appear, if at all, sometime in a perhaps distant future.

6. To sum things up temporarily: the Russell of Religion and Science, then, is committed on the one hand to the view that neither theology, nor philosophy, nor mathematics provides us with knowledge, though science does. On the other hand, he is also, and inconsistently, committed to the view that not even science provides us with knowledge, that is, to a thorough skepticism. I say, “temporarily,” because we have yet to take into account the second of the complications alluded to in the opening paragraph of this post. That we will do with the next post in the series.

7. I’ll conclude this post by recommending that you watch and listen to a comedic turning of Russell’s contrast between religion and science on its head, from the “Science is a liar…Sometimes” episode of the television series, It’s Always Sunny in Philadelphia.

Until next time.

Richard

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* Bertrand Russell, Religion and Science, with an introduction by Michael Ruse (Oxford and New York: Oxford University Press, 1997 [1935]). Religion and Science is readily available for purchase through Amazon.com. You need only click on the following image to be taken to the Amazon site:

** Though I’ve not researched the literature, I think it safe to assume that the vast majority of the statements of the view that light travels “instantaneously” left the “in all circumstances” clause unexpressed.

*** Our knowledge that, in at least some circumstances, light travels at a finite velocity, and so with a “lapse of time,” in no way rules out the at least logical possibility that we will at some point come to know that, in some other circumstances, light travels at an infinite velocity, and so with no “lapse of time.”

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Reflecting on Russell’s Religion and Science 2. Its Scientism Confirmed and Two Complications Raised

1. The present post is the second in a series of posts reflecting on the philosophical theses at work in Bertrand Russell’s Religion and Science.* In the series’ opening post, I did three things pertinent to the present one. First, I directed the readers’ attention to the opening paragraph of Russell’s essay, “The Art of Rational Conjecture, the first of the three essays that constitute the book, The Art of Philosophizing and Other Essays.** There (p. 1) Russell “gave expression … in a statement than which none more terse is possible” of the thesis of, as I dubbed it, “exclusivist epistemological scientism.” (If it is not immediately evident just what is meant by “exclusivist epistemological scientism,” a perusal of the previous post should help.). Russell’s statement reads:

Let us begin with a few words as to what philosophy is. It is not definite knowledge, for that is science. Nor is it groundless credulity, such as that of savages [sic]. It is something between those two extremes; perhaps it might be called the art of rational conjecture.

I took that identification of science with “definite” knowledge as a statement of the defining thesis of exclusivist epistemological scientism.

Second, over two or three steps, I expanded that statement of the defining thesis of exclusivist epistemological scientism into the fully explicit universal affirmative categorical proposition,

All instances of knowledge are instances of scientific knowledge.

and then converted that proposition into the logically equivalent,

Only instances of scientific knowledge are instances of knowledge.

Third, I set out as an historical task that of determining whether and, if so, to what extent Russell adheres to the doctrine of exclusivist epistemological scientism in Religion and Science. The aim of the present post is to complete that task.

2. The task is not that difficult to complete and will be quickly taken care of in the paragraphs to follow. There are, however, at least two complications; they will have to await a subsequent post or two.

Three texts demonstrate the presence of the doctrine of exclusivist epistemological scientism in Religion and Science. Its most full-throated expression is located at the end of the ninth chapter, “Science and Ethics.” There (p. 243) Russell tells us:

I conclude that, while it is true that science cannot decide questions of value, that is because they cannot be intellectually decided at all, and lie outside the realm of truth and falsehood. Whatever knowledge is attainable must be attained by scientific methods; and what science cannot discover, mankind [sic] cannot know.

There are two radical theses in the theory of ethics expressed here, the so-called emotivist theory of ethics. The one is that, as “questions of value” “lie outside the realm of truth and falsehood,”

No propositions of ethics are either true or false.

The other thesis is the thesis that as “questions of value” “cannot be intellectually decided at all,”

There is no ethical knowledge.

(The two theses are distinct the one from the other, for it is at least logically possible for a proposition to be true or false even though it knowing whether it is true or false may be beyond human capacity.)

That aside set aside, we can note that the proposition, “There is no ethical knowledge,” has to be accepted by one who, like Russell, accepts the theses that

All instances of knowledge are instances of scientific knowledge.

and

No instances of scientific knowledge are instances of ethical knowledge.

for together the two serve as the premises of the following patently valid argument (in Celarent; see the aforementioned immediately preceding post):

No instances of scientific knowledge are instances of ethical knowledge.
All instances of knowledge are instances of scientific knowledge.
Therefore, no instances of knowledge are instances of ethical knowledge.

3. Two further texts endorsing the doctrine of exclusivist epistemological scientism will catch the attention of readers of Religion and Science. In Chapter VI, “Determinism,” Russell tells us (pp. 144-145:

[T]here are three central doctrines—God, immortality, and freedom—which are felt to constitute what is of most importance to Christianity, insofar as it is not concerned with historical events. These doctrines belong to what is called “natural religion”, in the opinion of Thomas Aquinas and of many modern philosophers, they can be proved to be true without the help of revelation, by means of human reason alone. It is therefore important to inquire what science has to say as regards these three doctrines. My own belief is that science cannot either prove or disprove them at present, and that no method outside of science exists for proving or disproving anything.

And in Chapter VII, “Mysticism” (p. 189):

I cannot admit any method of arriving at truth except that of science….

4. In sum, the Russell Religion and Science does not accept as real any knowledge other than scientific knowledge. Insofar, therefore, as he remains consistent with the doctrine of exclusivist epistemological scientism, he will have to eliminate the other three, mathematics, philosophy, and theology, of the four major theoretical disciplines or magisteria, as I called them in the previous post, leaving only science. But there remain the complications I mentioned above. I will turn my attention to them in the next post or two.

Until next time.

Richard

* Bertrand Russell, Religion and Science, with an introduction by Michael Ruse (Oxford and New York: Oxford University Press, 1997 [1935]). Religion and Science is readily available for purchase through Amazon.com. You need only click on the following image to be taken to the Amazon site:

*** Bertrand Russell, The Art of Philosophizing and Other Essays (Totowa, New Jersey: Littlefield, Adams & Co., 1974 [1968]). I continue to be puzzled over the fact that, in a book bearing such a title, there is to be found no essay entitled “The Art of Philosophizing.”

The Art of Philosophizing and Other Essays too is readily available for purchase through Amazon.com. You need only click on the following image to be taken to the Amazon site:

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Reflecting on Russell’s Religion and Science 1. Scientism and the Four Purported Magisteria

1. One reason why I have not been posting over the past months is because I have been caught up in the teaching of courses new to me, in ethics, medical ethics, and environmental ethics. These having been courses for which I had not previously gone through the course preparation process, I have had to devote enough of my time in course preparation and management that I have had none left to devote to my blog.

It recently occurred to me, however, that I could and should combine my course preparation and my blogging, by posting to my blog, if sometimes in somewhat variant versions, the material that I am covering in the courses I teach. As it happens, I am scheduled to teach an introduction to philosophy course later this summer and it seems to me that that course is perfectly well fitted for the kind of integrated activity I have in mind. I intend, therefore, over the coming weeks and months, to offer in the form of posts to this blog some reflections on the material I plan to cover in this summer’s introduction to philosophy course (the courses in ethics, medical ethics, and environmental ethics can await their turn).

2. The primary text of the course will be Bertrand Russell’s Religion and Science,* published in 1935. This is not the book of Russell, it seems to me, that is most likely to show up in an introduction to philosophy course. That would be his The Problems of Philosophy. Indeed, I judge the latter to be the better book of the two. I have, however, used it, the latter, as the primary text in an introductory course in the past and quickly learned that my students found its first chapter’s extended focus on that which we can know of the author’s writing table to be, well, off-putting.

Religion and Science it is, then. Given, now, the title of the work, its readers can justly hope that the book will set forth at least some of Russell’s views on religion and science and on the relationship or relationships that exist between them. Given further that the book is being assigned in a course intending to introduce students and others to philosophy, those reading it with me can also justly hope that the book will set forth at least some of Russell’s philosophical views, so adding philosophy and the relationships it may have to religion and science into the mix of matters to be pondered. Given yet further that those reading Religion and Science with me might well notice that the back cover of the edition of the work at hand identifies Russell as an “English philosopher and mathematician,” they might well also hope that Russell’s understanding of mathematics and the relationships it may have to religion, science, and philosophy will be the object of some attention.

The last hope, that Russell will have interesting things to say about mathematics in Religion and Science, may yield in the course of its reading to disappointment. But hoping that the book will have interesting and important, if not therefore always also true, things to say about religion, science, philosophy, and the relationships between and among them will, I can guarantee, not have been in vain. And I, on the other hand, hope that I will be able to make up for the lacunae in the treatment in Religion and Science of mathematics by bringing in on occasion what Russell has to say on the subject elsewhere, what others have had to say, and, passing, to be sure, from the more significant to the less, what I have to say.

3. And so one of the major themes of the introductory course at hand and of the accompanying series of posts will be the respective natures of the four purported magisteria of science, mathematics, philosophy, and religion. I owe, of course, the use of the term, “magisteria,” to Stephen Jay Gould and his theory of the “nonoverlapping magisteria,” typically abbreviated as “NOMA.” According to Gould’s “Nonoverlapping Magisteria,”** the “NOMA principle” holds that:

Science tries to document the factual character of the natural world, and to develop theories that coordinate and explain these facts. Religion, on the other hand, operates in the equally important, but utterly different, realm of human purposes, meanings, and values—subjects that the factual domain of science might illuminate, but can never resolve.

I should perhaps, and in the not too distant future, devote a post to a comparison of Gould’s views on the nature of science, that of religion, and the relationship or relationships between them, with Russell’s. For the purposes of the present post, however, I will let the opportunity for that comparison pass and content myself with the observation that there are not just the two purported magisteria that Gould had in mind, but four, existing in the following hierarchy very evident in, at least, classical Western thought:

4. Theology
3. Philosophy
2. Mathematics
1. Science

I have placed theology at the top of the hierarchy, instead of religion, because it is theology, as the theoretical component of the religions Russell and classical Western thought have had most in mind, that most appropriately stands in correspondence with the theoretical disciplines of science, mathematics, and philosophy.

4. Returning to Russell, I will propose to my students and fellow readers that our first focus be on his “exclusivist epistemological scientism” (as I will dub it; I will clarify the “exclusivist” and the “epistemological” presently). Russell gave expression to this view of the place of science in a statement, than which none more terse is possible, in the opening paragraph of the essay, “The Art of Rational Conjecture, the first of the three essays that constitute the book, The Art of Philosophizing and Other Essays.*** There (p. 1), in the course of telling us what he thinks philosophy is and is not, Russell also tells us what he thinks science is.

Let us begin with a few words as to what philosophy is. It is not definite knowledge, for that is science. Nor is it groundless credulity, such as that of savages [sic]. It is something between those two extremes; perhaps it might be called the art of rational conjecture.

The defining thesis of exclusivist epistemological scientism is, then, the thesis,

Knowledge is science.

or, expanding its statement a bit,

All knowledge is scientific knowledge.

or, expanding the statement yet further so that we have before us a fully explicit universal affirmative categorical proposition, as logicians are wont to identify it,

All instances of knowledge are instances of scientific knowledge.

or, equivalently, thus making more fully explicit the reason for the “exclusivist” of the “exclusivist epistemological scientism” tag,

Only instances of scientific knowledge are instances of knowledge.

5. This thesis is, of course, an epistemological thesis, in the jargon of philosophy; in a somewhat more ordinary language, it is a thesis in the philosophical theory of knowledge. It is moreover, to put it mildly, a radical thesis in the philosophical theory of knowledge. If, indeed, it is true that, to revert to its last-but-one formulation, all instances of knowledge are instances of scientific knowledge, then we are faced with a set of arguments, surely disconcerting at least to some or even to many, but also nonetheless absolutely valid arguments.

First,

No instances of scientific knowledge are instances of theological knowledge.
All instances of knowledge are instances of scientific knowledge.
Therefore, no instances of knowledge are instances of theological knowledge.

That is, in brief, there is no, as some have purported there to be, theological knowledge.

Then,

No instances of scientific knowledge are instances of philosophical knowledge.
All instances of knowledge are instances of scientific knowledge.
Therefore, no instances of knowledge are instances of philosophical knowledge.

That is, in brief, there is no, as some have purported there to be, philosophical knowledge.

And, finally,

No instances of scientific knowledge are instances of mathematical knowledge.
All instances of knowledge are instances of scientific knowledge.
Therefore, no instances of knowledge are instances of mathematical knowledge.

That is, in brief, there is no, as some have purported there to be, mathematical knowledge.

We should note that the three arguments all exhibit the same logical structure, the one to which medieval logicians attached the name, “Celarent” (you’ll have to google it; this post is already too long). The arguments are, as already noted, all valid: that is, if, that is, if, their premises are true, the conclusions must also be true. I’ll leave unanswered, for now, the further question of whether any or all of the arguments are sound, that is, of whether, in addition to their being sound, they are such that, in each case, both of their premises are true.

6. Now, according to the “Publisher’s Preface” to The Art of Philosophizing and Other Essays, the three essays contained in “this little volume” and thus too the “The Art of Rational Conjecture,” “were written by Bertrand Russell during the second World War” and so at least several years, if not nearly a decade, after Religion and Science. We should set for ourselves the historical task, then, of determining whether and, if so, to what extent Russell adheres in the earlier work to the several theses just set forth. This we will do in the coming series of posts. More importantly, we should set for ourselves the further, philosophical, task of reflecting with and/or against Russell, and others, and determining for oneself which of the several theses, if any, might be true. This too we will do.

Until next time.

Richard

* Bertrand Russell, Religion and Science, with an introduction by Michael Ruse (Oxford and New York: Oxford University Press, 1997 [1935]). Religion and Science is readily available for purchase through Amazon.com. You need only click on the following image to be taken to the Amazon site:

** As of this writing, Gould’s “Nonoverlapping Magisteria,” can be read online at The Unofficial Stephen Jay Gould Archive, http://www.stephenjaygould.org/library/gould_noma.html.

*** Bertrand Russell, The Art of Philosophizing and Other Essays (Totowa, New Jersey: Littlefield, Adams & Co., 1974 [1968]). I admit to being puzzled over the fact that, in a book bearing such a title, there is to be found no essay entitled “The Art of Philosophizing.”

The Art of Philosophizing and Other Essays too is readily available for purchase through Amazon.com. You need only click on the following image to be taken to the Amazon site:

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Non-contradiction, Divine Omnipresence, and Dual Citizenship

1. Good Aristotelian that I am, or at least neo-Aristotelian, I introduce and make use of the principle of non-contradiction, that

No being can both be and not be, in the same respect and at the same time.

in virtually every course I teach. One immediate application of that principle is the thesis that

No being can both be in any one place and not be in that same place, in the same respect and at the same time.

2. I have found that students sometimes have difficulty understanding the difference between that thesis and the thesis that

No being can both be in one place and be in another place, in the same respect and at the same time.

My attempts at getting them to see the difference have seldom gone much beyond (1) repeating the two theses slowly and (2) and then pointing out that the thesis of divine omnipresence of classical theology, that

At least one being, God, can both be in one place and be in another place, in fact, in all other places, in the same respect and at the same time.

is not the same as the thesis, contradicting the principle of non-contradiction, that

At least one being, God, can both be in one place and not be in that same place, in the same respect and at the same time.

One can, that is, consistently uphold both the principle of non-contradiction and the thesis of divine omnipresence.

3. I believe I have found a more helpful, because more concrete, first exemplification of the difference at hand, for another immediate application of the principle of non-contradiction is the thesis that

No person can both be a citizen of any one nation and not be a citizen of that same nation, in the same respect and at the same time.

I have found that students have little difficulty in understanding the difference between that thesis and the thesis that

No person can both be a citizen of any one nation and be a citizen of another nation, in the same respect and at the same time.

or its equivalent

At least one person can both be a citizen of any one nation and be a citizen of another nation, in the same respect and at the same time.

for they can see that, in fact, not just one person, but many persons are citizens of two nations; they hold dual citizenships.

In my efforts to make clear that the principle of non-contradiction does not rule out a being’s being in one place and in another, I will in the future bring in the possibility of dual citizenship before that of divine omnipresence.

Until next time.

Richard

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Michael Anton on Behalf of the Thesis That Religion Is the Basis of Republican Government

1. No doubt because of the political circumstances in which the United States currently finds itself, I have in turn found myself wanting to know more about and better understand the political theory and philosophy of the nation’s founders, the “founding fathers.” So, coming upon Michael Anton’s “Founding philosophy. A review of The Political Theory of the American Founding by Thomas G. West” in The New Criterion and noting that Anton had served as Deputy Assistant to President [Trump] for Strategic Communications, I thought that the review might well be worth the reading.

2. It was, and for one reason because it contains a relatively explicit argument on behalf of the thesis that religion is the basis of republican government, a thesis that has considerable currency these days. Anton’s expression of the argument is concise, stated almost in passing.

In reality, West shows that Jefferson—like all the founders—well understood that republican government is impossible absent a strong moral foundation in the people, which in turn depends on religion, which government therefore has a duty to promote.

3. Before, however, entering upon the task of “regimenting” the argument, i.e., of so restating it that its logic is more fully explicit, it is worth noting that Anton, in stating that Jefferson “well understood” the sequence of thoughts expressed in the sentence just quoted, is both saying that that sequence of thoughts represents Jefferson’s view and that he, Anton, himself is in agreement with Jefferson on the matter.

That said, let’s observe that the one sentence quoted above actually gives expression to two arguments, the second of which is represented solely by the “which government therefore has a duty to promote,” i.e., the conclusion that:

Republican government has a duty to promote religion.

I’ll return to that argument below, if only briefly.

4. The first of the one sentence’s two arguments is expressed in the passage’s “republican government is impossible absent a strong moral foundation in the people, which in turn depends on religion.” Anton’s statement can be so reformulated that the argument’s validity is patently obvious.

As a first step, the “republican government is impossible absent a strong moral foundation in the people” can be restated as:

Only peoples having a strong moral foundation are peoples [capable of] having a republican government.

Similarly, the “which [strong moral foundation in the people] in turn depends on religion” can be restated as:

Only peoples having religion are peoples having a strong moral foundation.

Together the two propositions serve as the premises of the following argument:

Only peoples having a strong moral foundation are peoples [capable of] having a republican government.
Only peoples having religion are peoples having a strong moral foundation.
Therefore, only peoples having religion are peoples [capable of] having a republican government.

5. It is evident that the argument is perfectly valid, in that, if its two premises are true, then its conclusion is also, and necessarily, true. Perhaps, however, it will be worth taking the few simple steps needed to make its validity even more evident. First, then, the latter of the two propositions just spelled out is logically equivalent to the universal categorical proposition that:

All peoples having a strong moral foundation are peoples having religion.

The former of the two propositions just spelled out is logically equivalent to the universal categorical proposition that:

All peoples [capable of] having a republican government are peoples having a strong moral foundation.

Together the two propositions serve as the premises of the following argument:

All peoples having a strong moral foundation are peoples having religion.
All peoples [capable of] having a republican government are peoples having a strong moral foundation.
Therefore, all peoples [capable of] having a republican government are peoples having religion.

Students of traditional logic will recognize that this argument is a categorial syllogism of the form known as Barbara, all instances of which are valid.

6. Anton’s argument on behalf of the thesis that religion is the basis of republican government, i.e., that all peoples [capable of] having a republican government are peoples having religion, is, as I said above, a valid argument. That, however, tells us only that, if the two premises are true, the conclusion is also true; it does not tell us that the conclusion is true, tout court. The argument can tell us that the conclusion is true only if it, the argument, is sound, only, that is, if both the argument is valid and its premises are true.

7. Our question, then, is that of whether the premises of Anton’s argument are both true. Now, of course, they are not “self-evident,” as, say, “all bachelors are unmarried males” is self-evident. They therefore can only be known to be true if they are conclusions of sound arguments.

The argument on behalf of the conclusion that

All peoples having a strong moral foundation are peoples having religion.

would have to be an argument similar in form to Anton’s argument and so read like this:

All peoples [having some requisite characteristic] are peoples having religion.
All peoples having a strong moral foundation are peoples [having some requisite characteristic].
Therefore, all peoples having a strong moral foundation are peoples having religion.

8. I have invited, or perhaps challenged,** Mr. Anton to provide such an argument. I also invite any reader to provide one. And, while I was and am at it, I further invited him and now also invite the reader to provide the premises that would, in a valid argument, conclude to the aforenoted thesis that:

Republican government has a duty to promote religion.

The thesis that “all peoples having a strong moral foundation are peoples having religion” will undoubtedly be a premise of the argument, but not the only premise.

Until next time.

Richard

* Michael Anton’s “Founding philosophy. A review of The Political Theory of the American Founding by Thomas G. West” (The New Criterion, Vol. 36, No. 10, June 2018).

** Or tried to invite or challenge; finding a working email address for people as much in the public eye as Mr. Anton is difficult.

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Logical Errors in a Logic Textbook, Alas!

1. Early on in his Socratic Logic, Peter Kreeft offers what I’ll take to be two arguments in favor of a thesis that traditional, or Aristotelian, logic is superior to modern, or symbolic or mathematical, logic, that, indeed, modern logic is, as I’ll put it for him, a defective logic. The matter is of some importance in logical theory, for, if he is right, the past century and a half or so of progress in logic has been an illusion.

2. I will critique the first of the two arguments in the present post, leaving the second for a post to come. The first argument can be formulated as:

Any logic accepting an invalid argument as a valid argument is a defective logic.
Modern symbolic/mathematical logic is a logic accepting an invalid argument as a valid argument.
Therefore, modern symbolic/mathematical logic is a defective logic.

Kreeft and I can easily agree that the argument is a perfectly valid argument, in that, if its two premises are true (or were true), then the conclusion must be true (or would have to be true). But then the question arises of whether the argument is more than just a valid argument, but a sound argument, having both of its premises true. Now, though Kreeft leaves the first premise unexpressed, I am fully confident that he would take it as true, without any “ifs,” “ands,” or “buts.” We disagree, however, about the second premise, for while Kreeft holds that it is true, I hold that it is simply false.

3. To see that this is the case, let’s turn, then, to Kreeft’s formulation of the argument in question. It starts out well enough (p. 24).

A logically valid argument is one in which the conclusion necessarily follows from its premises. In a logically valid argument, if the premises are true, then the conclusion must be true. In an invalid argument this is not so. “All men are mortal, and Socrates is a man, therefore Socrates is mortal” is a valid argument. “Dogs have four legs, and Lassie has four legs, therefore Lassie is a dog” is not a valid argument. The conclusion (“Lassie is a dog”) may be true, but it has not been proved by this argument. It does not “follow” from the premises.

So far, so good.

Kreeft continues (Ibid.).

Now in Aristotelian logic, a true conclusion logically follows from, or is proved by, or is “implied” by, or is validly inferred from, only some premises and not others. The above argument about Lassie is not a valid argument according to Aristotelian logic. Its premises do not prove its conclusion. And common sense, or our innate logical sense, agrees.

Still, so far, so good.

But then the argument goes off the rails, for Kreeft goes on to claim in the next sentence:

However, modern symbolic logic disagrees.

That is, according to Kreeft, while Aristotelian logic and common sense agree that the argument about Lassie is not valid and that its premises do not prove its conclusion, “modern symbolic logic disagrees.” The disagreement is not over whether the argument about Lassie is an argument, but over whether it is valid. Kreeft is therefore committed to saying modern logic holds that the argument about Lassie is a valid argument and therefore that modern logic holds that some invalid argument about Lassie is a valid argument.

4. Kreeft could not be more wrong. In no way would the so-called “predicate calculus,” that branch of modern logic by which the argument at hand would be assessed, pronounce it valid. On the question of whether or not the argument about Lassie is a valid argument traditional logic and modern logic in full agreement.

5. Let me set the argument forth both as it would be presented in traditional logic and as it would be presented in the “predicate calculus.” In traditional logic, stating the argument even a bit more carefully than Kreeft does, the argument would read:

All dogs are animals having four legs.
Lassie is an animal having four legs.
Therefore, Lassie is a dog.

As, as we have seen, Kreeft has said:

The conclusion (“Lassie is a dog”) may be true, but it has not been proved by this argument. It does not “follow” from the premises.

And no logician will or even can come up with a sequence of inferences acceptable to traditional logic that would begin from the two premises and those two premises alone and logically arrive at the proffered conclusion. For, if all that we are given to know is what we know through the argument’s premises, it may well be, for all we know, that Lassie is, not a dog, but a turtle.

On the other hand, of course, we could introduce the premise that Lassie is a dog into the argument. The argument would then read:

All dogs are animals having four legs.
Lassie is an animal having four legs.
Lassie is a dog.
Therefore, Lassie is a dog.

Then, however, we would have a different argument, one in which the conclusion that Lassie is a dog would certainly follow from the premises. But this argument is precisely that, a different argument.

6. Now, in the modern logic, the argument would be stated as:

For any existent x, if x is a dog, then x is an animal having four legs.
Lassie is an animal having four legs.
Therefore, Lassie is a dog.

The judgment that Kreeft advanced about the Aristotelian formulation applies equally well here.:

The conclusion (“Lassie is a dog”) may be true, but it has not been proved by this argument. It does not “follow” from the premises.

And no logician will or even can come up with a sequence of inferences acceptable to modern, symbolic or mathematical logic, that would begin from the two premises and those two premises alone and logically arrive at the proffered conclusion. For, if all that we are given to know is what we know through the argument’s premises, it may well be, for all we know, that Lassie is, not a dog, but a turtle.

On the other hand, of course, we could introduce the premise that Lassie is a dog into the argument. The argument would then read:

For any existent x, if x is a dog, then x is an animal having four legs.
Lassie is an animal having four legs.
Lassie is a dog.
Therefore, Lassie is a dog.

Then, however, we would have a different argument, one in which the conclusion that Lassie is a dog would certainly follow from the premises. But this argument is precisely that, a different argument.

7. If the foregoing holds up, I have shown that the first of the two arguments that Kreeft has offered on behalf of the thesis that modern symbolic/mathematical logic is a defective logic, fails, in that he has not shown that that argument’s premise, that:

Modern symbolic/mathematical logic is a logic accepting an invalid argument as a valid argument.

is true.

In a post to come, I will offer a critique of the second of the two arguments Kreeft advances on behalf of the thesis that modern symbolic/mathematical logic is a defective logic.

Until next time.

Richard

* Peter Kreeft, Socratic Logic. A Logic Text Using Socratic Method, Platonic Questions, and Aristotelian Principles. Edited by Trent Dougherty (Edition 3.1; South Bend, Indiana: St Augustine’s Press, 2014 [2004])

If you wish, you may purchase a copy of Socratic Logic through Amazon.com by simply clicking on the following:

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Countering the Philosophical Skepticism of Former Secretary of the Treasury Robert Rubin

In an April 30, 2018, New York Times Opinion page article, “Philosophy Prepared Me for a Career in Finance and Government,” former Secretary of the Treasury Robert Rubin singled out his undergraduate Harvard University Professor Raphael Demos for special praise, telling us:

Professor Demos would use Plato and other great philosophers to demonstrate that proving any proposition to be true in the final and ultimate sense was impossible. His approach to critical thinking planted a seed in me that grew during my years at Harvard and throughout my life. The approach appealed to what was probably my natural but latent tendency toward questioning and skepticism.

Rubin then went on to say:

I concluded that you can’t prove anything in absolute terms, from which I extrapolated that all significant decisions are about probabilities. Internalizing the core tenet of Professor Demos’s teaching — weighing risk and analyzing odds and trade-offs — was central to everything I did professionally in the decades ahead in finance and government.

I myself have to admit to having a “tendency toward questioning and skepticism,” if, though natural, hardly latent. Here and now, for example, I cannot help doubting that Professor Demos was able to “use Plato and other great philosophers to demonstrate that proving any proposition to be true in the final and ultimate sense was impossible,” at least in “the final and ultimate sense.” Or, I’ll put it directly: There is no way to prove in absolute terms that it is impossible to prove anything in absolute terms.

On the other hand, one can prove that one can prove that at least some propositions are true in “the final and ultimate sense” by presenting the actual proofs that they are true, for whatever is actual must be possible. I have in fact presented such very genuine philosophical proofs or demonstrations in the pages of this very blog. I invite you to peruse the:

A Proof That at Least One Thing Can Be Proven in Philosophy,” of March 6, 2018;

Sathya Sai Baba. The Man Who Was God,” of February 20, 2018; and

A Diagram of the Trinity,” of February 8, 2018.

There are also some earlier posts related to the Trinity, links to which can be found in the three posts listed.

I’ll close by repeating the claim I made in the last of the aforementioned posts:

My arguments, I submit, are valid, in that their conclusions must be true if their premises are true. Moreover, they are not only valid, but sound, in that their premises, and therefore their conclusions, are true. Moreover still, they are not only sound, but apodictic or demonstrative, in that their premises, and therefore their conclusions, are not just true but necessarily true.

Until next time.

Richard

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