Aristotle for Everybody (Adler)

Adler, Mortimer J.  Aristotle for Everybody: Difficult Thought Made Easy.

Even with the advances in science, Aristotle’s shadow is unavoidable.  We still operate with concepts like “part,” “whole,” “motion,” “change,” etc.  Despite modern pedagogy in the university, we still use logic and assume it is valid.

“Great Divide”

First problem: What differentiates “all living organisms from inert bodies” (Adler 5)? From this we draw a line between some living organisms and others.  Aristotle keeps drawing these lines and classifying individuals.  In order to do this, he posits that each thing has a nature. He finally arrives at the conclusion that man is a rational animal.

On one side of the line are “bodies.”  On the other side are “attributes.” The key idea is that an attribute exists in a thing but not of itself.  A stone’s weight exists in the stone, but no one thinks that the weight of a stone exists on its own.  Moreover, a body changes; the attributes do not.  The attribute of hardness doesn’t become “smoothness.”  Rather, the stone becomes smooth.

We can best discuss man by seeing him in three different dimensions:

Man is:

Making (Beautiful).  This covers the metaphysical angle.

Doing (Good)

Knowing (True)

Man the Maker

A work of art is man-made. It is more accurate to say that man produces; he does not create.

Change and Permanence

The problem is how can something always be in a state of becoming, always in change, yet remain the same.  One type of change is motion (a change in place), alteration (a change in quality), and a change in quantity.  All of these changes take place in time.

The Four Causes

I can’t do any better than to quote Adler:

1. Material cause: that out of which something is made.
2. Efficient cause: that by which something is made.
3. Formal cause: that into which something is made.
4. Final cause: that for the sake of which something is made 

To Be or Not to Be

To understand Aristotle on being, we need a firm grasp of “matter,” “form,” “potentiality” and “actuality” (50).

Privation is a lack of a certain form. Potentiality is when you predicate the words “can be” of a thing.  A matter can lack a form but nonetheless have the potentiality for it. “Matter always has a limited potentiality for acquiring other forms” (53).

Man the Doer

Man usually acts towards a goal. This is practical thinking, thinking about means and ends. Means are the ways we achieve our goal or other means.  For Aristotle the end to which we aim is “living well.” However, when Aristotle says we are to aim for the right ultimate end, this isn’t relative.  There is an actual objective Good to which all seek to aim. People who do not aim for this objective end have disordered passions.

This is happiness.  It is important to note that ancient man didn’t consider those who were still living to be truly happy.

Man the Knower

“The senses are the doorway to the mind” (130). They are instruments, and in a nice turn of the phrase, the mind, too, is an instrument.  It is the “form of forms” (134). Thinking does more, as it also “relates the ideas it produces.”

The next chapter is on the laws of logic.  In some ways, that chapter alone is worthy of an entire review.  On the other hand, there isn’t much in it that isn’t also found in other logic texts. Some comments are appropriate, though.  For example, the term in both major and minor premises is the middle term. It functions to connect the major premise and the conclusion.

Moreover, if the major premise is negative, the conclusion must be negative.  A positive conclusion cannot follow from negative premises.

I recommend this book to any starter in philosophy.

Geisler’s Systematic Theology vol. 1

Geisler, Norman.  Systematic Theology: Introduction, Bible. Bethany House.

This book would be perfect if it were divided into two separate books.  The first half would be a book on prolegomena, foundations, and apologetic method.  Had I read such a book before I went to seminary, I would have been spared 8 years of wrong thinking (most of which would have been my fault).  The second half is a survey of issues relating to inerrancy, bible survey and introduction, and the like.

There is quite a bit of repetition in this book.  Numerous quotes by Albright, J. A. T. Robinson, and others appear over and over.  Moreover, much of this book can be found in The Big Book of Apologetics/Baker Encyclopedia of Apologetics.  It’s still good material, though.

Preconditions of theology:

  1. Mind capable of sending a message (encoder)
  2. Mind capable of receiving message (decoder)
  3. There is a common mode of communication shared by both persons.

God: The Metaphysical Precondition

Geisler defines metaphysics as the study of being.  

Theism posits an Infinite, Personal God that exists both beyond and in the universe. After surveying various forms of dualism and monism, Geisler posits a form of Thomism, noting that all finite beings are composed of act and potency in their very being.  Potentiality limits a finite being’s actuality, as opposed to God, who is Pure Act.

In a move somewhat rare among systematic theologies, Geisler actually defines being. It is that which is, either a mix of potency and act or a pure actuality. God is, other beings have.  From here Geisler moves to his arguments for the existence of this Pure Act.


Horizontal argument.

(1) Everything that had a beginning had a cause. 

(2) The universe had a beginning. 

(3) Therefore, the universe had a Cause. 

The second premise needs defending, which those from Bonaventure to William Lane Craig have done:

1) An infinite number of moments cannot be traversed. 

(2) If there were an infinite number of moments before today, then today would never have come, since an infinite number of moments cannot be traversed. 

3) But today has come. 

(4) Hence, there were only a finite number of moments before today (i.e., a beginning of time). And everything with a beginning had a Beginner. Therefore, the temporal world had a Beginner (Cause).

Vertical Form of the argument:

This argument begins with “present contingent existence.” It argues from effect to Necessary Cause.

(1) If everything were contingent, then it would be possible that nothing existed. 

(2) But something does exist (e.g., I do), and its existence is undeniable, for I have to exist in order to be able to affirm that I do not exist. 

(3) Thus, if some contingent being now exists, a Necessary Being must now exist, otherwise there would be no ground for the existence of this contingent being.

But granting the arguments, would this even prove the Christian God?  It will get closer than you think.  Such a God would not be the one of finite godism, “since the cause of all finite things cannot be finite.”  Nor can it be the god of polytheism, since there can’t be more than one unlimited being.

Miracles: The Supernatural Precondition

The problem of definition: 

Weak sense: something that is not contrary to nature, only our knowledge of nature (Augustine). On this view an event doesn’t even have to be supernatural to be a miracle. This is obviously inadequate.

Strong sense: an event beyond nature’s power to produce (Aquinas, SCG 3).

A miracle doesn’t have to violate natural law. It is simply a new effect produced by a supernatural cause.

Answering objections

Spinoza: standard objection of “violating immutable natural laws.” Response: He begs the question on immutable laws.  He also operates in a closed system. 

Hume: Miracles are in-credible. Uniform experience is against miracles.  Response: He begs the question in advance by claiming to know uniform experience. He can’t know all possible sense experiences. Moreover, as Geisler notes, “he never weighs the evidence on miracles.  He simply adds evidence against them.”  Even worse, Hume’s method of “adding evidence” eliminates any unique experience in history, even natural ones.

Revelation: The Revelational Precondition

The possibility of divine revelation depends on the reality of God.  If God exists, which he does, then divine revelation is not only possible, but actual. The only real challenges today concern whether humans are capable of receiving this revelation (postmodernism) and whether the medium is reliable.

Geisler correctly notes that “In order for an infinite Mind to communicate with finite minds, certain things must be possible. To begin, there must be a common  principle of reason that both possess.” Language and being are analogical.

Geisler’s charts are really good.

While some like to say that man’s thought sinfully distorts general revelation, and at one level that is true, general revelation is still essential to human thought. And while it is true that “Scripture determines what we believe on general revelation,” we still use general revelation (e.g., laws of logic) to make that statement.

That doesn’t fully answer the existential question: when our understanding of general revelation and our understanding of special revelation clash, who wins?  Geisler says the interpretation with more certainty. Sometimes this is general revelation, sometimes special.

Logic: The Rational Precondition

Geisler summarizes here his other writings on logic.  At their most basic they are:

1) Law of non-contradiction
2) Law of identity
3) Law of excluded middle.

In order to help us think better, Geisler has given a nice summary of categorical propositions:These should be written on the inside of all study bibles.

(1) There must be only three terms. 

(2) The middle term must be distributed at least once. 

(3)Terms Distributed in the conclusion must be distributed in the premises. 

(4) The conclusion always follows the weaker premises(i.e., negative and particular ones). 

(5) No conclusion follows from two negative premises. 

(6) No conclusion follows from two particular premises.

 (7) No negative conclusion follows from two affirmative premises.

Most evangelicals will go with him this far, but what is the relationship between Logic and God? According to Geisler, Logic is subject to God ontologically. “God is prior to logic in the order of being.”  Nevertheless, God is rational by his very nature. On the other hand, logic is prior to God epistemologically.  As Geisler notes, the statement “God is God’ makes no sense unless the law of identity holds (A is A).”  The statement “God exists” isn’t true unless the law of noncontradiction is true.

Meaning: The Semantical Precondition

Thesis: all true statements must be meaningful.  Geisler identifies three different types of schools: conventionalism (Wittgenstein), essentialism (Plato), and realism.  Conventionalism is self-falsifying, for when it says all linguistic meaning is conventional, it, too, is relative.

Truth: The Epistemological Precondition

Thesis:  Truth is that which corresponds to its object.

Exclusivism: The Oppositional Precondition

Thesis: Christianity’s truth claims entails that other religious oppositions are wrong (or at least cannot be correct at the same time as Christianity’s).  Much of this is standard fare in evangelical apologetics, but Geisler hones in one of John Hick’s questionable presuppositions.  Hick says an undifferentiated Real is known in all faiths.  The problem is that an undifferentiated Real doesn’t have any definable characteristics, which means it can’t be identified. It can’t be known in any faith!  Even worse, if it is undifferentiated, then no symbol can represent it.

Language: The Linguistic Precondition

Thesis: How do our concepts relate to God?  They can’t be equivocal, for that would be self-defeating.  They can’t be univocal, since God is infinite.   Analogy makes the most sense. It allows for both similarity and differentiation.  Similar to Parmenides’ dilemma, Geisler notes: “Either one’s principle of differentiation is inside of being or it is outside of being. If outside, then things do not differ in being; they are identical in being, and monism is true. The only way to maintain a pluralism essential to theism is to insist that things differ in their very being. Yet how can they differ by what they have in common? The answer is that they cannot, if being is univocal. But it isn’t.”

We’re not done yet, though.  We can say that we have univocal concepts but analogical predication. The definition is the same between God and creatures, but the application is different.

Interpretation: The Hermeneutical Precondition

Contra Heidegger, Geisler asks how he can say Being is unintelligible. How could he know this about Being unless he understood it?  Moreover, Heidegger’s denial of correspondence assumes that his denial corresponds to the way things are.

Heidegger correctly notes that man is a contingent being, yet he draws back from affirming the logical conclusion: there is a Necessary Being.

Contra Derrida, his statement that all meaning is limited by language tries to get outside those limits in order to establish them.  (The rest of the criticisms flow from this critique).

Savage Burn: “it is fruitless to turn to poetry to avoid metaphysics. Metaphysical questions still exist, and they cannot be answered in anything but metaphysical language. Any so-called poetical protest is nothing more than an exercise in ventilating one’s tonsils.”

The Alternative

Can we know things objectively? Yes.  The metaphysical precondition, God, has made it possible.  Geisler: “The objective basis for meaning is found in the mind of God.” Much of this chapter is standard fare in grammatical-historical hermeneutics.  The following is a long quote, for which I indulge the reader’s forgiveness, but it is worth noting:

Applying the six causes to meaning will help explain the point. Following Aristotle, scholastic philosophers distinguished six different causes: 

(1) efficient cause—that by which something comes to be;

 (2) final cause—that for which something comes to be; 

(3) formal cause—that of which something comes to be; 

(4) material cause—that out of which something comes to be; 

(5) exemplar cause—that after which something comes to be; 

(6) instrumental cause—that through which something comes to be.

 Remember the example of the chair? A wooden chair has a carpenter as its efficient cause, to provide something to sit on as its final cause, its structure as a chair as its formal cause, wood as its material cause, the blueprint as its exemplar cause, and the carpenter’s tools as its instrumental cause. As we have seen, applying these six causes to meaning yields the following analysis: 

(1) The writer is the efficient cause of the meaning of a text. 

(2) The writer’s purpose is the final cause of its meaning. 

(3) The writing is the formal cause of its meaning. 

(4) The words are the material cause of its meaning. 

(5) The writer’s ideas are the exemplar cause of its meaning. 

(6) The laws of thought are the instrumental cause of its meaning. 

In conclusion, we use the laws of logic in biblical hermeneutics.  Anything else makes rational meaning impossible.

Historiography: The Historical Precondition

Method: The Methodological Precondition

The Evangelical method begins with an inductive basis in Scripture, which involves an abductive step.  It will also deduce truths from Scripture and make use of analogies.  He puts them all together into what he calls a Retroductive Method, worth quoting in full:

1. The Inductive Basis: 

(a) God cannot err. 

(b) The Bible is God’s Word. 

2. The Deductive Conclusion: 

(c) The Bible cannot err. 

3. The Use of Analogies: 

(d) Just as Christ was divine and human yet without sin, even so the Bible is divine and human yet without error. 

(e) Just as nature (God’s general revelation) presents difficulties with possessing errors, so does the Bible (God’s special revelation). 

4. The Use of General Revelation: 

(f) The earth is not square. 

(g) The sun does not move around the earth.

 5. The Retroductive Method: 

(h) The biblical teaching is fleshed out in view of facts known from general revelation and the data (phenomena) of Scripture.

 (i) There are errors in the manuscript copies.

 (j) The Bible uses figures of speech and other literary devices, round numbers, everyday (nontechnical) language, paraphrases, etc.

 (k) The deductive conclusion (point c) is understood in the light of the retroductive enhancement. For example: (1) The Bible is without error only in the original text, not in all the copies. (2) Round numbers, observational language, figures of speech, and paraphrased citations are not errors.

The rest of the book is a summary and defense of inerrancy, inspiration, and the like.  Some things to note, like Geisler’s chart between accommodation to error and adaption to finitude.

Note: To the everlasting embarrassment of Bible critics, at least those who claim to be followers of Christ, Jesus affirmed exactly the opposite of what much of negative “higher criticism” teaches.

Short History of Modern Philosophy (Scruton)

Scruton, Roger.  A Short History of Modern Philosophy. New York: Routledge, 2002.

This was a joy to read.  Scruton communicates depth with a certain type of elegance rarely matched in academic writers.  Bertrand Russell is probably the closest equivalent.

There are several angles from which we can view Scruton’s work.  An exhaustive review of each figure and movement would be beyond the scope of this review.  Several key themes emerge in Scruton’s narrative.  Substance never disappears as a concept, pace modern nominalists.  On the other hand, it cannot stand simply in its Aristotelian form.  Developments in mathematics, logic, and language require a sharper focus on substance.

First, some comments on Aristotle’s logic. Every proposition contains both subject and predicate, which corresponds to substance and attribute (Scruton 16). Since a substance can have, or perhaps lose, different attributes, a substance is something that survives change.  One problem raised is whether substances can cease to exist and what is meant by the term “exist.”

Distinction between stuff and things.  Stuff can be measured.  Things can be counted.  This made the idea of substance rather fuzzy.

The Port Royal Logic

 The Jansenist critics of Descartes anticipated several key breakthroughs in logical analysis. They noted the distinction between the intension and extension of a term.  The former denotes what a thing is.  The latter applies to the set of things: man vs. the class of men.


Gottfried Leibniz emerges as a true champion in this narrative. Spinoza had previously said there was only one substance and an infinity of modes.  Leibniz, by contrast, saw reality as reducible to individuals known as “monads,” which Scruton highlights as (68):

1 Monads are not extended in space. 

2 Monads are distinguished from one another by their properties (their ‘predicates’). 

3 No monad can come into being or pass away in the natural course of things; a monad is created or annihilated only by a ‘miracle’. 

4 The predicates of a monad are ‘perceptions’—i.e. mental states—and the objects of these mental states are ideas. Inanimate entities are in fact the appearances of animated things: aggregates of monads, each endowed with perceptions.

 5 Not all perceptions are conscious. The conscious perceptions, or apperceptions, are characteristic of rational souls, but not of lesser beings. And even rational souls have perceptions of which they are not conscious. 

6 ‘Monads have no windows’—that is, nothing is passed to them from outside; each of their states is generated from their own inner nature.

To be sure, not every organic thing is an individual monad. Most aren’t. Humans, for example, would be aggregates of monads.


Scruton’s analysis of Hegel’s logic put the brakes on any Hegelian speculations I might have had.   The main difficulty with Hegel, apart from his impenetrable prose, is that his use of terms doesn’t mirror the way the world normally uses such terms.  In normal usage, logic is a tool.  For Hegel it is almost an active, living entity.

Scruton summarizes the problem in reading Hegel in one elegant, witty passage:

“It is not to be expected that such a logic can readily be made intelligible, or that a philosophy which is able cold-bloodedly to announce (for example) that ‘Limit is the mediation through which Something and Other is and also is not’ should be altogether different from arrant nonsense” (175).

Scruton interrupts his survey after Nietzsche to make a few comments on political philosophy.

For John Locke, when I mix my labor with an object, I make it my own. It becomes my property (206).   Locke’s arguments on natural rights are interesting and quite important.  Contract theory, however, is built on a much shakier foundation.  Scruton identifies several problems. 1) On what grounds do we infer the existence of such a contract?  It is almost always an implied contract, if it exists at all.  Claims of “tacit consent” are vacuous, as Hume noted.  It’s not clear how anyone born in such a society gave “tacit consent.”

Marx takes Hegel’s concept of alienation and comes up with “false consciousness.”  Scruton notes that Marx didn’t use alienation all that much later on in life.  What is “alienation?” As Scruton observes, 

“Under capitalism it is not only objects, but also men, who are bought and sold. And in this buying and selling, under the regime of which one party has nothing to dispose of but his labour power, we reach the ultimate point in the treatment of men as means. Men have become objects for each other, and whatever remnants of their human (social) life remain will be dissipated” (225).

Although such a view is not entirely coherent (and Marx would trade it in for “false-consciousness” later on), it did have imaginative power.  A false consciousness, on the other hand, is a universal error one makes in examining the social world. This unhappy consciousness emerges from Marx’s analysis of “base” and “superstructure.”

Following this chapter Scruton examines utilitarianism and British idealism.  More pertinent for this review will be Scruton’s analysis of Gottlob Frege’s logical revolution.  


What did Frege do?  He overthrew Aristotelian logic.  He began by examining J. S. Mill’s claim that arithmetic was abstracted from experience, as in 2+3 = 5. Numbers are empirical aggregates from experience.  Frege responded that Mill could give no account of the number zero.  Moreover, while I cannot with my senses apprehend a 1,000 sided figure, I am easily prepared to acknowledge such a figure exists.  And in the final coup de grace on Mill, Frege notes that induction assumes probability, but probability presupposes arithmetical laws (250).

Frege then asks, “What is a number?” They can’t be a property, since if I say “Socrates is one,” I do not attribute the property of one-ness to Socrates. Nor are they abstractions. If numbers are objects, then we need to be able to locate them, and that entails a host of philosophical headaches. 

A more immediate problem, and one for which Frege is ultimately famous, concerns existential quantification.  If I say “Unicorns are horned animals,” am I saying that unicorns exist?  Frege made it clear that identity and prediction are different.

I don’t feel smart enough to explain what Frege meant by sense and reference, so we will go on to Heidegger, particularly, Scruton’s wonderful rhetorical comments on Heidegger.  

“It is impossible to summarise Heidegger’s work, which no one has claimed to understand completely. In the next chapter I shall give reasons for thinking that it may be unintelligible” (268).

“the reader has the impression that never before have so many words been invented and tormented in the attempt to express the inexpressible” (268).

“All these are more or less pompous ways of distinguishing things from persons” (269).

“Heidegger notices and applauds the result, but does not, as he perhaps should, feel threatened by it” (269).

“One thing is clear, which is that Heidegger’s conclusions, where intelligible, are clearly intended as universal truths, not merely about the human condition, but about the world as such” (272).

“Heidegger does not give any arguments for the truth of what he says. Most of Being and Time consists of compounded assertions, with hardly a ‘thus’, ‘therefore’, ‘possibly’, or ‘it might follow that’, to indicate the relations which are supposed to hold between them” (272).

This book was a sheer pleasure to read and absorb.  It is easily my favorite text and first recommendation on the history of modern philosophy.

Review: Aristotle’s Organon

Included within this larger work are several major treatises.  Every critical thinker would do well to study “Categories,” “On Interpretation” and the first and last parts of “Topics.”  Posterior Analytics is interesting while Prior Analytics is highly technical.

Categories is the intro text to Aristotle’s Metaphysics, or so said some essay from Plato.Stanford.Edu said.  Good enough for me.  It is short and clear.  It also gives us the grammar for later Christian theology.

Some things are predicable of a subject but never in a subject.  By “being present in a subject” Aristotle means “incapable of existence apart from a subject” (2, 1a).

Substance is that which is neither predicable of a subject nor present in a subject.  

  • Primary: The individual man or horse. (this-ness)
  • Secondary: the species man; the genus animal.

Key point: everything except primary substances is either predicable of a primary substance or present in a primary substance.  The proposition “the man is an animal” is necessarily true, but not the reverse.  Further, the species is to the genus as the subject is to predicate.

A primary substance has no contrary, for what can be the contrary to an individual man? Yet, while remaining numerically one it can admit contrary qualities.

Chapter 6: What is Quantity?

It is either discrete or continuous.  Time, for example, is a continuous quantity.

Chapter 10: Opposites

Things are opposed in four ways:

  1. Correlatives
  2. Contraries
  3. Privatives to positives
  4. Affirmatives to negatives

Chapter 12: Being “prior’

There are four senses in which a thing can be “prior:”

  1. Time.
  2. Numerical sequence
  3. Order in a list
  4. Natural priority

On Interpretation

Every proposition must contain a subject and a verb.  

Contradictories: the opposite denial of an affirmation. The affirmation is of a universal character.  The denial is not. One must be true and the other must be false.

Universal: that which is of such a nature that can be predicated of many subjects

Contrary: the positive/negative proposition of a universal character.

Prior Analytics

Goal: state the moods and nature of the syllogism made from possible premises.

A perfect syllogism: when the last term is contained in the middle premise as a whole, and the middle is either contained in, or excluded from, the first as in or from a whole, the extrames must be related (24a 34).

Major term: the term in which the middle is contained.

All premises in the mode of possibility are convertible to each other (32a 24). “It is not possible” = “it is impossible” = “it is necessary not to belong.”

Posterior Analytics

This is a more readable treatise than the previous one.  His thesis is that not all knowledge is demonstrative.  Our knowledge of immediate (i.e., not mediate) premises is independent of demonstration (72b).  Logical demonstration is an inference from necessary premises.

From there Aristotle moves to some comments on essences.

Essential attribute: it belongs to its subject as an essential element (like a line in a triangle).  They “inhere” in the subject.  This gets tricky. When Aristotle says “inherence,” does he mean they exist “within” the subject?  

With this knowledge Aristotle explores how a middle term in a syllogism, one that is necessary, leads to universal knowledge (75b).

Every syllogism is affected by means of three terms.  For example, A inheres in C by means of A’s inhering in B and B’s inhering in C.

More on substance-language.  Predicates which signify substance signify that the subject is identical with the predicate or a species of the predicate.  For example, if A is a quality of B, then B cannot be a quality of A.  You can’t have a quality of a quality.

The Heart of the Matter is the Middle Term

“Quick wit is the faculty of hitting upon the middle term instantaneously” (89b). The middle term in a syllogism can sometimes be seen as the “Cause.”

Sophistical Refutations

This is a guidebook on how to refute Hellenic sophists.  Very technical.

Signs of an apostle, a logical hypothetical

The signs of a true apostle were performed among you with utmost patience, with signs and wonders and mighty works (2 Cor 12:12).

Does this mean that only apostles can do signs and wonders?  In logical form, the argument is this:

If an apostle, then you will see signs and wonders.

It’s a good modus ponens argument (which are the best of arguments).  It looks like this

P: x is an apostle
q: x does miracles

P –> q
Therefore, q.

Simple enough.  The reverse, however doesn’t hold.  You can’t logically say,

If anyone does signs and wonders, then he must be an apostle.

That is the fallacy of asserting the consequence.  It looks like this:

1. P –> q
2. q
3. Ergo, p
4. You, however, are not p [~3].
5. Ergo, ~q.

Do you see where the fallacy was?  It was in step 2.  The argument in normal prose looks like this:

1. If someone is an apostle, then he will do miracles.
2. Someone does miracles.
3. ergo, he is (or would be) an apostle.
4. You, however, are not an apostle.
5. Therefore, signs and wonders aren’t happening.

You can’t assert “q” in a p –> q argument.

Conclusion: whether signs and wonders happen today, the point is they weren’t limited to the apostles, as is evident in Acts.


A problem in classical logic

This is from my friend, Dominic Foo.

In Aristotelian logic, if you said that “All roses are red.” the “contrary” of this is “No roses are red”, and since the contradictory of “no roses are red” is “some roses are red”, there is a straight forward inference from “All roses are red” to “some roses are red”. Statements of the form “All x is P” implies that “Some x are P”.

Now you might think this is “common sense”, but this is actually fallacious on modern symbolic and mathematical logic. Consider the following proposition: “All unicorns have horns” and “Some unicorns have horns.” In symbolic logic the latter statement is *not* entailed by the former unlike Aristotelian logic. “All unicorns have horns” is translated in symbolic logic as “For all x, if x is a unicorn x has a horn” and for “Some unicorns have horns” this is translated as “There is some x such that x is a unicorn and x has a horn.” However it is a logical fallacy to infer that there is some unicorn from the universal statement that all unicorns have horns. In symbolic logic you have to be able to make true statements about empty sets. For example, “For all x, if x is the largest prime number then x is divisible only by itself and 1.” Of course the set of largest prime numbers is zero, there is no largest prime number, but in mathematics you have to be able to make statements like these on empty sets without implying that there is a member of the set in order to perform reductio ad absurdum proofs.

It is this “Aristotelian logic” thinking which caused some of the objectors to think “No female nature is assumed” which is equivalent to “All female natures are not assumed” implies or entails, “There are female natures”. Whereas on symbolic or mathematical logic, which I am a lot more used to, it seems pretty obvious to me that one can make universal statements on a set without implying that the set is non-empty.

Book Review: The Word of God and the Mind of Man (Nash)

Nash, Ronald.  The Word of God and the Mind of Man. Zondervan: 1982. Reprint by Presbyterian and Reformed.RonNash

The possibility of our having cognitive knowledge about God was denied on three grounds:  God is too transcendent; 2) human knowledge is de jure problematic; 3) human language was de jure problematic.

Question of the book: Can the human logos know the Logos of God (Nash 14)?

Hume’s Gap: our pivotal beliefs must rest on something besides knowledge.

Kant’s wall: there is a wall between the world as it is and the sense world.

For the Neo-Orthodox, revelation is always an event.  It is never cognitive knowledge about God.

Defense of Propositional Revelation

(A)  All S is P                                             (E) No  S is P

(I)  Some S is P                                         (O) Some S is not P.

(A) All revelation is propositional       (E) No revelation is propositional

(I) Some revelation is propositional    (O) Some rev. Is not propositional

We can rule out O as irrelevant to the discussion.  The Neo-Orthodox thinks that all evangelicals hold to A, but that’s false.  We hold to I.  Further, holding to I doesn’t entail the claim that all revelation is propositional.

In short God reveals knowledge to his creation and some of this knowledge about himself is contained in the form of propositions (45). And even if one wants to claim that revelation is personal, saving faith still presupposes saving faith about something.

The Christian Logos

This is the heart of Nash’s project. Key idea: “Jesus Christ, the eternal Logos of god, mediates all divine revelation and grounds the correspondence between the divine and human minds” (59).

The Christian Rationalism of St Augustine

Augustine has some sort of interplay between the uncreated Light of God and the mutable light of the human mind (81). How can the human mind understand the eternal Forms within God’s mind?  Nash suggests three ways:

(1) The human intellect is both passive and active with respect to the forms (85). It is passive, pace Kant, in that it doesn’t create the conditions for knowledge. It is active in the sense that it judges and receives.

(2) The forms are and are not separate from the divine mind.

(3) The human mind is and is not a light that makes knowledge possible.

While Nash had a fine discussion on how Augustine modified Plato’s essentialism, and I don’t necessarily disagree, the chapter just feels “short.” I know he wrote a book on the topic and it is worth pursuing there.

In Defense of Logic

When Nash wrote this book, the Dooyeweerdian school in Toronto was a force to be reckoned with (one sees something similar in John Frame’s works).  Nash gives a fine rebuttal to the Dooyeweerdians: if human reason is valid only one one side of the cosmonomic boundary, “then any inference that God is transcendent must be an illegitimate application of human reason” (99). In other words, if God is transcendent, you are in error for saying he is transcendent!


The Logos of God has created the logos of the human mind in such a way that that it can receive cognitive, propositional knowledge about a transcendent God.


Review: Logic-A God Centered Approach (Poythress)

This isn’t a logic textbook, yet it isn’t quite a worldview approach to logic.  It is something of both, yet completely neither.  I still liked it, though.

Image result for logic poythress

He begins with a theological “grounding” of logic, which amounts to a summary of his and Frame’s approach to worldview.  It’s good, but it lasts about 200 pages before you get into the “nuts and bolts” of logic.

He then gives a primer on deductive syllogisms, propositional logic, quantification, functions, sets, modal logic, and much else. I did enjoy the fact that he pointed out how pure systems like Russell’s and others are so formal as to have little content.  This is analogous to the desire for “pure being.”

64: Logic is an aspect of God’s mind.  It reveals God’s attributes.

89: Logic is God’s self-consistency

Key argument: Logic is personal, but it doesn’t depend on any one human person, since if all humans perished, logic would still be true. It is transcendent, displays his attributes, and is part of God’s speech (80).

This next part is important, as it provides another foundation for the rest of the book’s argument:

Axioms of Propositional Logic

Principle of Tautology: (p V p) ⊃ p 

You might need to learn this one.  Poythress’s work is unique in the sense that he puts every single axiom through a truth table.

Principle of Addition

⊃ (p V q)  “If it is dark, then (either it is raining or it is dark)”

The Principle of Permutation

(p V q) ⊃ (q V p)

If (either it is raining or it is dark), then (either it is dark or it is raining)

The Associative Principle

(p V (q V r)) ⊃ (q V (p V r))

If (either it is raining or (it is dark or it is cold)), then (either it is dark or (it is raining or it is cold))

The Principle of Summation

(q ⊃ r) ⊃ ((p V q) ⊃ (p V r))

If (it is dark implies it is cold), then (the assumption that (it is raining or it is dark) implies the conclusion that (it is raining or it is cold)).

While it might not seem like it, these are powerful tools and the reader is encouraged to work through a few of them in truth tables in the appendices.  The book has some severe drawbacks, in that it isn’t a logic textbook, and some important concepts are woefully underdeveloped (like modal logic).  But I did enjoy it and parts of it should be read.

Frame Paper, Part 1

This is a paper, or rather part of an exercise, we had to do in seminary.  It was 12 years ago.  The italicized is the issue under discussion

1. Implication is something that pervades our experience.

Men are rational creatures (but much more than that!). While some men are not logically consistent, they cannot escape the demands that logic and rationality make on their lives. Even if men are not able to formulate symbolic arguments, they see the implications of such arguments everyday and act (or refuse to act!) accordingly. It is indirectly tied to the determinative nature that presuppositions (or ultimate) commitments play in our experience. Men may not fully understand (or rather, articulate) an issue, but they can act accordingly.

2. Logic is a hermeneutical tool.

Logic, like hermeneutics, seeks to unpack the meaning of a sentence (or structure of thought). Building off implication, which doesn’t give new meaning to the statement, but rather rearranges the meaning in new ways. Similarly, logic in theology doesn’t give “new meaning” to the text, but unpacks and rearranges meaning already there.

3. Define the nature of a logical must.

Logical musts are both analytic and moral. Those who know the truths of several premises know the conclusion, whether they act on it or not. Secondly, logical musts are moral in nature. Men are created imago Dei and since logic and rationality is a part of God’s character, to be logical is to be faithful to God.

4. Logic is dependent on ethical values.

If logical musts pervade men’s experience, then there is some ethical foundation for why this is so. However, logic itself does not provide the foundation for ethics. There must be some transcendent standard which gives meaning to logic. This standard, I suggest, is Christian theism.

5. What is the nature of logical certainty?

Logical axioms appear certain because on one level they are “obvious” to the world. Scripture teaches us that we must live wisely and by implication we are to live according to these facts insofar as they line up with Scripture. However, logic is not the normative perspective and so will at times need to be modified by Scriptural reflection. We are certain because God has revealed facts in nature (which do not contradict his word), commands us to live wisely and to judge all things by his word which at times will cause us to modify a previous system.

6. Is it biblically legitimate to use logic in theology? Does such use of logic conflict with sola scriptura?

Yes. Logic is a characteristic of God and while not the normative standard for the believer, it will not contradict God’s word provided logic is put in its proper category. Logic no more violates sola Scriptura  any more than the practice of hermeneutics does. Logic, like hermeneutics, unpacks meaning already in the text.

7. If you cannot handle the implications of formal logic, what is the next best thing to do? Why? Discuss.

If one is not ready for formal logic then he ought to become more self-critical and anticipate objections. Doing this implicitly involves the obedience/learning paradox. The more self-critical one becomes, the more logical he comes (that is, assuming that he seeks out logical instruction from more mature and perhaps, philosophically trained believers).

8. Discuss some limitations of logic.

Logic, for one, cannot provide its own epistemological justification. There must be a worldview present to provide the preconditions for intelligibility. Secondly, human logic is fallible. Or rather, human application of logical principles is fallible. While not necessarily a fault with logic, often logic fails to provide “the persuasive power” that more situational perspectives might have.

9. We cannot learn all we know all we know from logical proofs. Discuss, evaluate.

Proofs are tools of logic and while useful and indispensable, they are only secondary. More importantly, proofs themselves do not constitute the premises. In short, premises are often suggested by an extra-logical source (divine revelation, sense-experience, etc.). Therefore, logic often has no more authority than the source of its premises. This is quite useful for the Christian apologist. Logic presupposes God (of course, this argument can and needs to be developed elsewhere in Reformed studies).

10. Apparent contradiction is insufficient ground for rejecting a premise. Discuss.

A chief example of this truth is the Christian doctrine of the Trinity. But more to the point of what Frame is discussing: we may not have all the facts that present with us. Granted the support of a premise that the author left unstated, the contradiction disappears. The author might have a perspective on the issue from which there is no contradiction. Of course, upon further evaluation the author might just be wrong and the contradiction stands regardless. But this issue should keep young theologians from jumping to premature conclusions.

11. Human logic is never a final test for truth. Why? Discuss.

Human logic is subject to human finitude. It does not escape the fact that humans do not know all the facts, their imperfect use of the right facts, and the fallibility of their own logical systems. In other words, it does not have all the perspectives on a given situation.

12. “Logical order” is an ambiguous expression.

Logical order is an umbrella phrase for different kinds of orders. Among other things, it is unclear as to whether one is speaking of temporal orders, varying degrees of conditionality, causality, and priority, among other things. The difficulty of such an expression becomes obvious when one looks at the decrees of God and the ordo saludis.

13. Analyze the controversy between the supra- and infralapsarianism.

The supra- wanted to see everything in the context of God’s electing love. The infra- wanted to see it in terms of God’s unfolding drama. Within the context of “logical order” the supra- saw everything in presuppositional priority whereas the infra- saw everything in anticipated temporality.

14. Theological doctrines have a tendency to become analytic. Explain, evaluate using examples.

Analytic doctrines imply the truth of the inclusion within the premise. Seen this way, many doctrines imply one another rather than counteract one another. Human freedom is intelligible only within the context of a sovereign God who gives meaning to human actions. God is good because his attributes are inseparable from him and good becomes part of the definition of God. This allows the believer a sense of certainty that the analytic doctrines can index.

15. Give some examples of theological discussion in which the burden of proof is an important issue. Show why.

Whenever one sets forth a new doctrine he has the responsibility to show that he is correct. The Baptist must show that God no longer deals covenantally with families with respect to covenant membership. The pro-choice advocate must show that the fetus is not alive and so may be killed without moral qualm. Traditionally, the Christian theist has had the burden of proof for God’s existence, but if he redefines his position as an a-atheist with the understanding that all men know God, then the atheist has the burden of proof to show that God does not exist!