On Peikoff's ‘Fact and Value’

I wrote the following 28 years ago. At that time I gave copies to a few people, but did not publish it. The forthcoming book referred to in the last paragraph is Objectivism: The Philosophy of Ayn Rand. 'Fact and Value' had the lead role in the Objectivist schism of 1989. Most other comments about the schism have been about whether Objectivism is closed or open, or about sanctioning. I considered that a mere "turf war" then, and still do.

ON PEIKOFF’S ‘FACT AND VALUE’

by Merlin Jetton        July 27, 1989

The series of articles by Peter Schwartz, David Kelley, and Leonard Peikoff was both interesting and disappointing to read. It amazes me that such a heated exchange could arise from the mere event of David Kelley making a speech.

I have come to expect such behavior from Schwartz. He has a history of making straw men and burning them. He sometimes makes bizarre judgments. He did that in this instance, operating under the principle that one should judge a speech by its audience and its content is irrelevant. But to me Peikoff’s article ‘Fact and Value’ was the most disturbing part of the exchange. It was not just that he put words in Kelley’s mouth and was unfair in judging him. There are probably many people who would agree with that. There will probably be much said and written about it, so I shall, for the most part, leave that subject for others. The most disturbing part of Mr. Peikoff’s article was the illogical statements. He is the most prominent living spokesman for Objectivism, a philosophy which is committed to reason and logic. As such, I would expect from him a more acute attention to logic.

I considered calling this article “The All or Nothing Syndrome”, which is an affliction of Mr. Peikoff’s. It refers to the tendency to obliterate the distinction between “some” and “all” (or between “none” and “some”), which is an extremely important one in logic. There are several instances of it in Peikoff’s article.

He says, “In my judgment, Kelley’s paper is a repudiation of the fundamental principles of Objectivism.” Kelley and Peikoff clearly have different views about the relationship between fact and value. But did Kelley repudiate “A is A”? Does disagreement on just one principle imply disagreement on all of them?

He argues for the principle: Every “is” implies an “ought”. Note that the first word is “every”, not “some”. The word “every” makes it an overstatement. It baffles me to hear that any trivial, irrelevant fact implies an “ought.” There is the always applicable one that I ought to regard it as a fact, but that is far from the principle’s intended meaning.

He claims that the good is a species of the true and that evil is a species of the false. This is an apparently profound idea, so I did not take it lightly. Consider the logic of this statement. It says if X has the attribute “good”, then X necessarily also has the attribute “true”, and that if X has the attribute “evil”, then X necessarily also has the attribute “false”. I have a few comments:

Some X being both good and true does not imply that any X which is good is also true; similarly for both evil and false.

Hitler was evil. Would Peikoff also say he was “false”? If so, that is bizarre.

It implies there is no such thing as an evil truth. Is the fact that Hitler and the Nazis murdered millions of people not an evil truth? And Peikoff later gives examples of bad truths, such as too much exposure to the sun is bad and getting caught in a tidal wave is bad, which are inconsistent with the claim.

Similarly, it implies there is no such thing as a good falsehood, for which a counterexample easily comes to mind. Suppose A tells a lie to B to protect C, where B has malicious intent and C is innocent of wrongdoing.

It is muddled. There are truths about what is good for us and about what is bad for us. It is good for us to know these truths. There are falsehoods about what is good for us and what is bad for us. It may be or is (the right verb depends on the case) bad for us if we believe these falsehoods. This makes sense, but it is far from what he wrote.

I checked Ayn Rand’s writing for an idea having any resemblance to it and found nothing. And Peikoff exhorts the reader to not rewrite Objectivism!

He correctly paraphrases Kelley as saying: Truth and falsity apply primarily to ideas, and good and evil primarily to actions. Note that Kelley uses the word “primarily”, not “exclusively” or “only”. Yet Peikoff launches an extended polemic as if Kelley had said one of the latter. Admittedly Kelley gave a couple of poor examples in discussing the subject. Kelley also failed to make it clear that no dichotomy can be drawn between a man’s ideas and his actions. But did Peikoff deliberately misrepresent Kelley to set up his polemic? Or did he fail to note the logical import of the word “primarily” means there are exceptions? Either way, it does not speak well for Mr. Peikoff.

He devotes a substantial part of his article to his ideas about the connection between fact and value, between cognition and evaluation. He summarizes his view in a single principle -- cognition implies evaluation -- which he says is the main point of his article. In my opinion, when he was writing this, he was so eager to railroad Kelley that he let his emotions interfere with his reasoning and clear communication. (Does this mean that his evaluation implied his cognition?) This is a topic on which I have not spent sufficient time to articulate well my own ideas, but I shall not let that stop me from making a few comments:

I found it difficult understanding clearly what he said and I attribute it to his lack of clarification of key concepts. For example, “evaluation” may mean a judgment about true/false or about good/bad. Ayn Rand more than once said that to properly evaluate what someone says or writes, look for the definitions. Well, I found none in Peikoff’s exposition.

I will presume that he meant by his principle something like this: one should properly understand the phenomena or idea (Objectivist epistemology), then decide whether it is good or bad based on one’s understanding (and act accordingly). If this is even close, then I believe he made a poor choice of words by using “imply”. This is a term of logic and generally means the consequence follows necessarily from the premise(s). But cognition and evaluation are volitional, so evaluation is not a necessary, automatic consequence of cognition. Cognition and evaluation can only be connected logically by thinking, which is volitional.

Mr. Peikoff said “every cognition implies an evaluation”, using “evaluation” in the sense of good/bad. If he really believes that, then I say his belief is seriously flawed. It would be a gross overstatement. If the instance of cognition were one of learning a new subject or idea and the knowledge gained were not instantaneously integrated, it would be a gross mistake to make such an evaluation. Facing reality and making good judgments also requires proper recognition of one’s state of knowledge.

Now imagine a person who believes that every cognition demands moral evaluation and who is afflicted with the all-or-nothing syndrome. That person would be overzealous to pass moral judgment and would do so on a fragment of evidence, evading any evidence which would indicate a different judgment.

Mr. Peikoff may have impressed a few readers by pointing out the contrapositive of his principle, i.e. that non-evaluation implies non-cognition, but I saw it as a misuse of logic. One of my previous comments was about the use of “imply” in this context. Another pointed out an obvious counterexample to ‘all cognition implies evaluation’. His contrapositive applied to that counterexample is: If the person did not pass moral judgment, then the person learned nothing!

Mr. Peikoff tries to posit a much more extensive connection between true/false and good/evil, between “is” and “ought”, and between fact and value than can be reasonably substantiated. It was both innovative and revolutionary for Ayn Rand to hold that there was such a connection, considering that Hume and many later philosophers held that there was absolutely no connection. However, the negation of “none” is “some”, not “all”.

Peikoff says “Kelley’s viewpoint is an explicit defense of a dichotomy between fact and value, or between cognition and evaluation, and thus between mind and body.” Here is misrepresentation and a non sequitor in the same sentence! Kelley defended a difference or distinction between fact and value, but hardly a dichotomy. Even if Kelley had defended a dichotomy between cognition and evaluation, it would be a dichotomy between two functions of mind, which clearly would not imply a dichotomy between mind and body.

Mr. Peikoff says, “a proper philosophy is an integrated whole, any change in any element of which would destroy the entire system.” I have two comments:

It implies no one philosophical principle is stronger than any other. In other words, every philosophical principle is equally important. I find this notion totally contrary to Peikoff’s often repeated claim that knowledge is hierarchical.

It seems to say you either have it all right or none of it right. It is another instance of the all-or-nothing syndrome.

He did not discuss the Libertarians like Schwartz did, but he did say he completely agreed with Schwartz, who is also much afflicted with the all-or-nothing syndrome. An example is: Some Libertarians are anarchist-subjectivists. They are morally reprehensible. Therefore, any Libertarian is morally reprehensible.

Mr. Peikoff’s all-or-nothing syndrome appears again in his closing paragraphs. He tells readers, in effect, to agree with him totally or disassociate themselves with Objectivism. This article makes me wonder how Objectivism will flourish with him carrying the torch. Logical flaws and the all-or-nothing syndrome make poor impressions. The all-or-nothing syndrome may come in handy in polemics and politics, but it is anti-logic and anti-reason. I believe it is inappropriate for anyone who considers himself/herself to be objective.

I have made some strong criticisms of Mr. Peikoff here, so it seems appropriate that my closing be tolerant, and I shall not pass judgment on him solely on the basis of ‘Fact and Value’ and be guilty of the all-or-nothing syndrome. I did agree with parts of his description of Objectivism. I have appreciated his past lectures. I shall probably be tolerant enough to buy his forthcoming book.

How We Know #14: Overview

In Chapter 11 Binswanger presents an overview of the history of philosophy. It is a striking contract of two perspectives on percepts, concepts, and knowledge. The major characters for one perspective are Aristotle and Ayn Rand. The major characters for the other are Plato, Descartes, and Kant.

“The root of the clash between Aristotle and Plato lies in their opposed views on a fundamental.”

“Aristotelians uphold the primacy of perception over conception: perceptual awareness precedes, and supplies the base for conceptual awareness; concepts are abstractions from perceptual material.”

“Platonists assert the opposite position – i.e., the primacy of concepts over perception. Platonists claim that some or all concepts are grasped by some unspecifiable, ineffable form of awareness of ”universals” dwelling in another “higher” reality.”

“Only extreme Platonists hold that the existence of percepts depends on concepts. E.g., Kant claims that perception is shaped by “categories of the intuition,” and in contemporary jargon, perception is theory-laden.” The result in either case is viewing perception as distorted, biased, “merely relative to us,” or not of “things as they are in themselves.”

“The primacy of perception leads to a wider point: knowledge is essentially “bottom-up,” not “top-down.” Conceptual knowledge is acquired by building up from perceptual data.”

A later section, The Kantian Reversal, critiques the ideas of Immanuel Kant. “Kant reversed a crucial distinction, between the what and the how – between what one knows and how one knows it. Kant turns the means of awareness into the only objects of awareness” (385).

Chapter 11 is the last chapter, so this probably is my last post on How We Know.

How We Know #13: Free Will

Chapter 10 is about free will or volition.

Free will has traditionally been thought of as the ability to choose among alternative physical actions. This is not false, but it is quite superficial. The actual primary is the rationality or irrationality of one's mental processes. It is this that is under one's direct volitional control. It is fundamentally an epistemological issue. "Man's free will consists in his sovereign control over how he uses his mind." But sovereign control is not omnipotence. Determinism denies this sovereign control. It claims that one's sense of control is illusory.

One's power to take hold of the mental reins is present as a choice. In Ayn Rand's terms, it is the choice between thinking or not. "Mental focus is wider and deeper than thinking; it is the precondition of thinking." Epistemologically, focus mean rationality.

"Perceptual processes are automatically in contact with the world; conceptual processes are not. Conceptual processes performed out of focus result in mental content that is invalid, subjective, out of touch with reality.

The basic choice of focus is independent of any specific motive.

"Fundamentally, consciousness is navigational: it is identification used to guide action. A prime example is the process of deliberating on alternative courses of actions." It is both intellectual and practical.

Man can reflect on and evaluate his own decision making process, including among others I am too tired now to decide or I need more information, or I'm uncertain but must choose.

A man's character is the net product of all of his choices. Every choice leaves its trace.

Volition is axiomatic. "Volition is not only self-evident -- directly introspectible -- it is fundamental to conceptual cognition" (355, my italics).

How We Know #12: Principles

Chapter 9 is about principles. He defines a "fundamental" as a causal factor on which a multi-level, branching series of effects depends, analogous to a tree. Examples given are the division of labor in economics and natural selection in biology. The only things that are fundamental simplicitur are the axioms of existence, identity, and consciousness. Knowing fundamentals is a source of immense cognitive power and unit-economy. Examples given are the heliocentric model and the decimal number system.

A "principle" is a fundamental generalization that serves as a standard of judgment in a given domain. Principles are needed for an economical long-range view of consequences. Similar to concepts, principles are integrations. They are formed by abstraction by observing similarities and differences. They are contextual and should be treated as absolutes within a context. An example he elaborates is individual rights. They are frames of reference as a to guide a diagnosis of concretes, and should not be imposed mechanically on unexamined concretes. 

How We Know #11: Proof and Certainty

Chapter 8 is about proof and certainty. To prove an idea, one needs to link it back to perceived fact. The Objectivist term for this process of going back down the hierarchy to prove an idea is reduction. Contrary to contemporary notions, there is only one logic, not both one of discovery and one of proof. Instead, there are two different directions of motion along the same logical, hierarchical structure – derivation moves "up" from the perceptually given, while proof moves back "down" to the perceptually given.

"New knowledge can contradict old mistaken beliefs, but not old knowledge." He gives the example of when black swans were discovered in Australia. "The generalization "Swans are white" could not logically have warranted making the assertion: "There are no black swans anywhere in the world." That is not what was known at the earlier stage. The new knowledge is: "Swans are white, except in Australia where some are black." Thus, the end result is more knowledge, not less."

The three sources of cognitive errors are illogic, false premises, and incomplete information.

Knowledge and certainty are distinguishable concepts. Knowledge is differentiated from ignorance; certainty is differentiated from states that are less so. "Certainty" refers to cognitive status. Knowledge has both a metaphysical and epistemological component. "Fact" is purely metaphysical. Certainty is contextual.

Binswanger's formulation of the Law of Rationality is: In reaching conclusions, consider all the evidence and only the evidence.

There are sections on arbitrary ideas, the ad ignorantiam fallacy, and the burden of proof principle. He presents Ayn Rand's concept of objectivity. The final section is on the intrinsic-subjective-objective trichotomy. He illustrates it in regard to concepts. Most of that is covered in Chapter 3, on which I commented in #3 and #4 of this series. 

How We Know #10: Logic

Chapters 6 and 7 are about logic -- theory and practice, respectively.

The three laws of logic are the law of identity, the law of non-contradiction, and the law of excluded middle. His more economical formulations of these in the same order are: Everything is something. A thing can’t be everything. A thing can’t be nothing.

The nature of man’s consciousness include two facts central to logic: (1) Perception is the base of all conceptual cognition. (2) Only a few distinguishable units can be held in one frame of awareness.

Context is important. “The contextual nature of knowledge reflects a metaphysical fact and as epistemological one.” Metaphysical: reality is an interconnected whole. Epistemological: human consciousness works by detecting similarities and differences (198).

Hierarchy pertains to a number of ways in which things exist in an order of dependency. There is a hierarchy of learning and one of inference. Regarding the latter, Quine is sharply criticized for his flippant dismissal of hierarchy.

The section The Spiral Process of Knowledge echoes Leonard Peikoff.

Logic is not concerned only with inference or the manipulation of symbols as often presented. It is the means of keeping conceptual cognition connected to reality. On to logical practice, it is often assumed that logic is only about inference, but logic exists for all conceptual functions subject to volitional control (213).

About logic and concepts, he gives rules for definitions, reformulating traditional negative ones in positive terms. The traditional one of stating the essential attributes of the concept’s referents becomes the rule of fundamentality.

He addresses several things to avoid such as misclassifying. “Carving nature at the joints – i.e. on the basis of fundamentals – provides the most unit-economical system of classification.”  As an example of misclassifying would be to divide all living organisms between "stripes" and "solids." Besides excluding organisms that are neither, it is non-essential and explains nothing else. He comments on Rand's Razor: concepts are not to be multiplied beyond necessity or integrated in disregard of necessity (230- 232). 

A proposition is “a grammatically structured combination of concepts to identify a subject by a process of measurement-inclusion.” Concepts are not properly described as true or false, but as valid or invalid. (239). 

Venturing beyond Ayn Rand he addresses non-referential propositions and the “fallacy of pure self-reference” (248-51).

How We Know #8: Higher Level Concepts

“The intensity of seeing varies in regard to: clarity, acuity, time, attention, and purpose” (HWK, 164).

"Considering the wealth of conceptual subdivisions of "seeing" that have been formed to capture sub-ranges within the above axes of measurement. Here are some, listed in alphabetical order: descry, espy, gawk, glance, glimpse, look, ogle, peak, scan, stare, watch" (165).

Huh? What axes of measurements? There are some measurable differences, e.g. time, between these subdivisions. On the other hand, they are not fully sorted by time. Moreover, there are qualitative differences as well that Binswanger does not acknowledge as qualitative, for example, different purposes. Also, regarding these alleged measurements, what standard unit analogous to an inch and what measurement instrument analogous to a ruler or tape measure apply? For the sake of argument hypothesize such a standard unit. How is it that gawk is N₁ of said units, glance is N₂ of said units, scan is N₃ of said units, and so forth, where the N's are non-ordinal numbers? To echo a frequent comment Ayn Rand made: Blank out. Am I using a different meaning of "measurement" than Binswanger? Yes, one that is more rigorous, objective, and based in perception, which is the ultimate base of all knowledge. It is not some fuzzy or corrupted meaning.

Binswanger does not say what measurements are "omitted” for the concept motion. He only mentions "measurement ranges that were left open in forming" the concept (154). Regardless, the concept motion highlights qualitative differences even more. Varieties of motion include walking, running, crawling, flying, riding, swimming, jumping, rolling, swinging, and dancing. Non-human motions would add many more varieties. Are the differences between all these subdivisions of motion solely a matter of measurements? Clearly not; they differ qualitatively. For example, swimming is in water and the others are not. Riding in a car is different in multiple ways from the others. Running, walking, crawling, jumping and dancing use the legs in qualitatively different ways.

It also follows that, contra Binswanger (p. 166-7) and Rand, teleological measurement is a flimsy metaphor. It is teleological ranking. The differences between authentic measurement as I described above and ranking overwhelm their similarity.

How We Know #7: Higher Level Concepts

Chapter 4 is about higher-level concepts. First level concepts are formed directly from perception. Following Rand, higher-level concepts are formed by "abstraction from abstractions." For example, furniture is formed from the prior first-level concepts table, bed, chair, etc. The higher-level concept is a wider integration.

Binswanger contrasts his and Rand's view from that of Realists. The Realist "model implies that wider concepts have less cognitive content than the narrower ones from which they were formed. For the Realists, "table" abstracts the "universal" from individual tables by mentally subtracting away and discarding everything that differs among tables. Then, "furniture" discards even more" (141). In contrast "Rand's theory recognizes that concept-formation is integrative, which means that the wider concept contains more cognitive content than any of the narrower ones from which it was formed" (141).

His portrayal of the Realist view seems biased. He uses "subtract" and "discard" rather than "ignore" or "neglect." "For Realists, reaching a more abstract level means having a narrower "insight" into a universal embedded inside a given universal -- the "furniturehood" lurking inside of "tableness" and "bedness." For Realists, the wider concept, the emptier of cognitive content" (141). 

He says Rand's theory attributes more cognitive content to higher-level concepts. However, "more cognitive content" is ambiguous. Does it mean more units subsumed or a wider range of attributes? He says little or nothing about the former and sides with the latter. Clearly furniture subsumes more units (things or referents) than does chair. Based on more units subsumed, the Realist view adds rather than subtracts or discards. Of course, the criteria of inclusion into the higher level concept is less strict for the Realist view, and it is likewise for Rand's theory. For example, the criteria of inclusion for furniture is less strict than for chair. One criteria for chair, but not furniture, is that its purpose is for sitting, a criteria not met by table, dresser, etc., which have other purposes. 

While I agree with his portraying the Realist view as pursuing an "elusive phantom", I regard it as somewhat less mystical than he. What is elusive in the Realist view is the pursuit of something which is precisely identical in each instance or unit of the concept. In his and Rand's view the pursuit is of similarity. The ramifications of that difference are monumental. I give a hat tip to Peter Abelard. 

Is the Realist view that there is something precisely identical in each instance amiss for all concepts? I don't believe so. I believe numbers qualify, for example, the number 2 abstracted from all instances of pairs.

Some sort of "intuition" or "insight" is required for the pursuit of similarity of higher-level concepts. In his final chapter Binswanger writes about the concepts inertia, natural selection, and germ. In my view the developers of these concepts had some sort of extraordinary capacity, which for lack of a better term I call "intuition" or "insight." They grasped the similarity that other people had not.

Returning to his text, the second type of higher-level concept consists of subdivisions or "narrowings" of existing concepts. "Narrowings have virtually never been discussed in the history of epistemology" (142).  That agrees with my experience. 

"There are two ways of subdividing an earlier concept: 1) by narrowing the earlier concept's measuring range, or 2) by adding a new characteristic, a characteristic not used in forming the earlier concept" (142). 

How We Know #6: Concept-Formation

Binswanger says, "Things that are similar differ quantitatively" (HWK, 110). Then noting that a young child may not see a pig and a collie as similar, he says in all cases similar concretes possess varying degrees of the distinguishing characteristic, and those degrees fall within “specified categories of measurement” – which is why they appear as similar. Ayn Rand called this “measurement omission.” (HWK, 115).

In effect he denies that similar things or attributes can have only qualitative differences. Similarly, in the Appendix of ITOE2 Rand assented to “establish the similarity by showing the characteristic is the same and only [emphasis mine] the measurements vary” (ITOE2, p. 221).

Is it true that all differences between units that fall under the same concept are only quantitative? Both Rand and Binswanger say yes. I say absolutely not. There are many, many exceptions. It takes only one to disprove their claim, but I will offer more anyway.

Consider boats. Having some means of locomotion is essential to being a boat. There are oars, sails, outboard motors, water jets, paddle-wheels, air fans, and inboard engines of various kinds – steam, gas, diesel, nuclear, electric, coal. These are qualitative differences, not quantitative ones. One attribute – speed – of locomotion and even other differences being measurable does not imply that every attribute is measurable.

Consider animals. Some live on land, some in water, some both. Some are carnivores, some herbivores, some omnivores. For some respiration uses lungs, others gills, still others skin. Some have fur, some have scales, and some have feathers. I could go with many other kinds, not simply degrees, of differences. These are qualitative differences, not quantitative ones.

Consider different tools -- hammer, screwdriver, wrench, pliers, file, saw, etc. Each has a different purpose, which is qualitative, not quantitative.

I will defer qualitative, non-quantitative, differences of motion to a future post.

Binswanger says nothing about it, but later in ITOE Rand undercut her prior claim of omitting only measurements when she addressed concepts of consciousness.

“For instance, the concept “thought” is formed by retaining the distinguishing characteristics of the psychological action (a purposely directed process of cognition) and by omitting the particular contents as well as the degree of the intellectual effort’s intensity. The concept “emotion” is formed by retaining the distinguishing characteristics of the psychological action (an automatic response proceeding from an evaluation of an existent) and by omitting the particular contents (the existents) as well as the degree of emotional intensity” (ITOE, 32).

“These concepts [knowledge, science, idea, etc.] are formed by retaining their distinguishing characteristics and omitting their content. For instance, the concept “knowledge” is formed by retaining its distinguishing characteristics (a mental grasp of a fact(s) of reality, reached either by perceptual observation or by a process of reason based on perceptual observation) and omitting the particular fact(s) involved” (ibid., 35).

Why did she say omitting particular “contents” and “facts”? What happened to omitting only measurements?

Binswanger also confuses counting, e.g. the number of sides of a polygon and atomic numbers, with measurement. “An interesting case of measurement is that of measuring materials qua materials, such as wood, copper, water. Obviously, one can measure the attributes of the objects formed out of various materials, but in what sense is the difference between copper and lead a difference in measurement? On the sensory level, one uses difference in perceptible qualities—the colors differ, the densities differ, the hardness differs, etc. … Modern chemistry, however, goes to a deeper level: copper and lead differ in “atomic number.” Atomic number is a measurement. It refers to the number of protons in the nucleus of the atom: copper has 29 protons, lead has 82” (p. 121).

However, counting and measurement are quite different. Both use numbers, but counting uses only integers and measuring uses both integers and fractions. Authentic measuring as done by scientists, engineers, and others uses a measuring instrument – a ruler, weight scale, thermometer, voltmeter, pressure gauge, etc. Counting does not rely on such instruments.

By the way, what is the atomic number of wood? 😊

Note: Some of the above is repeated from my article 'Omissions and Measurement' in The Journal of Ayn Rand Studies, Vol. 7, No. 2 (Spring 2006). Link. Another related article is my 'The Sim-Dif Model and Comparison' that appeared in The Journal of Ayn Rand Studies, Vol. 11, No. 2 in December, 2011. Link. Either can be read on-line for no money with a free JSTOR account.

How We Know #5: Concept-Formation

Binswanger contrasts the Objectivist concept of triangle with what he alleges is Locke's concept of triangle. (HWK, 118).

Objectivist: The concept of a triangle includes those that are either equilateral, or isosceles, or scalene.

According to Binswanger: "The Realist theory of concepts says just the opposite. Locke, for example, says that "triangle" is a concept of what is neither equilateral nor scalene "but all and none of these at once" [Locke, IV, VII, 9].  (Binswanger skipped Locke including "equicrural", a synonym of isosceles.)

I admit that Locke is vague and even apparently contradictory here. How can the concept triangle be both all and none of these sub-kinds at once? But I think Binswanger interprets Locke uncharitably. Locke's phrase can be interpreted as "but all and none of these singly." That dissolves the apparent contradiction. And isn't that what the general idea triangle is -- a flat shape that has three straight sides and three angles? The units of the general idea include equilateral and isosceles and scalene triangles, but the general idea triangle itself is not limited to any one of these sub-kinds.

Neither Locke nor Binswanger present a visual model that captures the general idea of triangle, but I offer the following. Imagine a manipulable triangle on a computer screen that allows one to grab any vertex where two lines intersect and move the vertex anywhere desired with such two intersecting lines remaining straight and unbroken. It would be like the one on this page with two revisions. The stationary vertex would be movable, and the movable vertexes could be moved off the x-axis.

Bishop George Berkeley cited Locke's passage about the abstract idea triangle and then, plainly with ridicule, said, "All I desire is that the reader would fully and certainly inform himself whether he has such an idea or no" (The Principles of Human Knowledge, Introduction, paragraph 13). I hereby reply, "Yes, I do!"

How We Know #4: Concept-Formation

I think Binswanger misrepresents John Locke and misclassifies him as a Moderate Realist. "Locke's version of Moderate Realism tries to avoid positing non-specific universals, but implies them nonetheless. ... Here, "whiteness" is the universal. It has some non-specific attribute, such as is found in the slightly different shades of white characterizing chalk, snow, and milk. ... On any Moderate Realist Theory, we grasp the non-specific attribute by abstraction, which is conceived as a subtractive process, as a process of disregarding differences. Locke, for instance, writes that "the mind, to make general ideas comprehending several particulars, leaves out ... those qualities that distinguish them " [Locke, III, VI, 32 (my emphasis)]" (p. 103-4).

I disagree with Binswanger's interpretation. Locke neither implied nor posited imperceptible and precisely identical fragments (essences) that exist within every particular regarded as a unit of the same concept. Locke is usually classified as a Conceptualist. Regarding him as a Moderate Realist is bizarre, considering his remarks about real essence in Essay Concerning Human Understanding (ECHU). He contrasted real essences (metaphysical) to nominal essences (epistemological). For Locke the real essence of physical objects is the imperceptible micro-structure that causes the observable qualities of the object. Nominal essences are formed by abstraction, are "the workmanship of the understanding", and are based on similarity (e.g. ECHU, Bk III, Chap III, 14-15). Also, see sections 1 and 2 here.

See ECHU, II, XI, 9 and ECHU, III, IV, 15 where Locke writes about whiteness. Contrary to Binswanger's claim, Locke did not posit a metaphysical universal of whiteness that is identical in each instance. Indeed, the second paragraph denies the existence of a known real essence of whiteness. "There is neither ... nor a supposed, but an unknown, real essence, with properties ... But, on the contrary, in simple ideas the whole signification of the name is known at once, and consists not of parts, whereof more or less being put in, the idea may be varied, and so the signification of name be obscure, or uncertain."

"Abstract ideas are the workmanship of the understanding, but have their foundation in the similitude of things. I would not here be thought to forget, much less to deny, that Nature, in the production of things, makes several of them alike: there is nothing more obvious, especially in the race of animals, and all things propagated by seed. But yet I think we may say, the sorting of them under names is the workmanship of the understanding, taking occasion, from the similitude it observes amongst them, to make abstract general ideas, and set them up in the mind, with names annexed to them, as patterns or forms, (for, in that sense, the word form has a very proper signification,) to which as particular things existing are found to agree, so they come to be of that species, have that denomination, or are put into that classis. For when we say this is a man, that a horse; this justice, that cruelty; this a watch, that a jack; what do we else but rank things under different specific names, as agreeing to those abstract ideas, of which we have made those names the signs? And what are the essences of those species set out and marked by names, but those abstract ideas in the mind; which are, as it were, the bonds between particular things that exist, and the names they are to be ranked under?" (ECHU, III, III, 13).

Locke scholar Michael Ayers (1991) wrote:

"Locke really believed that nothing on earth could possibly perform the function that the Aristotelians ascribed to their specific essences or forms. Although the Aristotelian essence and Locke's nominal essence both define the boundaries of a species, the former does so ontologically.  ...  But the Lockean nominal essence is intrinsically an epistemological essence and nothing more, a criterion by reference to which we mark off the members of the species. The boundary marked is a precise one which owes its existence to our drawing it: reality itself simply could not, in Locke's view, supply such a boundary. Reality can supply resemblances, but resemblances do not constitute natural boundaries. Resemblances do not draw lines" (Locke: Epistemology and Ontology, Vol. 2, 67-68, my bold).

About Binswanger's quote from Locke (first paragraph above), how is Locke saying "leave out" (neglect or ignore) specific qualities of particulars so different from Ayn Rand's "omitting measurements"? How is Ayn Rand's "omitting measurements" not “disregarding differences” (Locke's phrase), at least different measurements or numbers? How is "omitting measurements" not subtractive? Omit means "leave out," despite Binswanger (and Rand) insisting that it doesn't. "[O]mitting measurements is not a process of deletion or excision" (p. 115).

Locke recognized how little men knew about real essence or the substratum of substances in his time. Binswanger is off-base when he says: "The Realists' separation of existence and identity reaches its clearest expression in Locke. His concept of "substratum" in which a thing's qualities supposedly inhere is a "something I know not what" -- i.e. an existent without any identity (since the identity pertains to the qualities not in the substratum)" (p. 105).

I disagree with his interpretation. Corpuscularianism was a physical theory that supposes all matter to be composed of minute particles, similar to atomism. The theory became important in the seventeenth century. Among the leading corpuscularians were John Locke and his scientist-friend Robert Boyle. Locke lived before scientists discovered sound empirical evidence of atoms, molecules, elements, and chemistry. Ergo, he did not know then-unknown details about the "substratum" underlying objects that we can perceive. Locke can be read as saying nothing stronger than that, via perception, we can receive no clear, distinct, positive idea of substratum; that the only concept of substratum of which our experience affords us is an obscure one. If Ayn Rand had said she knew nothing about subatomic particles and the nature of chemical bonding and how those things relate to everyday perception, would Binswanger have turned Ayn Rand into a Moderate Realist? I highly doubt it.

My essay Pursuing Similarity is here. 

How We Know #3: Concept-Formation

Chapter 3 is devoted to the nature of concepts. Binswanger says there are four main theories -- Realism (e.g. Plato), Moderate Realism (e.g. Aristotle), Nominalism (e.g. Wittgenstein), and Objectivist (Ayn Rand).

"According to Realism, a concept is a term that designates a metaphysical universal: a special kind of non-specific element present in all the members of a class, an element that is grasped directly by some sort of non-sensory "intuition" or "insight"" (p.101).

"Moderate Realists count as realists because they hold that abstraction refers to metaphysical universals; the theory is "moderate" in holding that these universals exist as aspects of perceptual concretes, not as separate entities dwelling in another world. In effect, Moderate Realism shatters the Platonic Form and puts a fragment of it inside each concrete" (p.102).

Binswanger elaborates his version of Objectivist epistemology. 

Binswanger says more about measurement omission than Ayn Rand did. He quotes Rand: "If a child considers a match, a pencil, and a stick, he observes that length is the attribute they have in common, but their specific lengths differ. The difference is one of measurement. In order to form the concept "length," the child's mind retains the attribute and omits the measurements. Or, more precisely, if the process were identified in words, it would consist of the following: Length must exist in some quantity, but may exist in any quantity. I shall identify 'length' as that attribute of any existent possessing it which can be quantitatively related to a unit of length, without specifying the quantity." [ITOE, 11]

Rand seems to say that "omitting measurements" is only omitting specific numbers -- of inches or centimeters or whatnot -- not omitting the attribute length. The match, pencil, and stick each have a length in reality, even if the child knows nothing about authentic measurement. In other words, there is length (metaphysical, ontological) and measured length (epistemological). The former can be simply perceived; the latter requires a special effort. The former doesn't require numbers; the latter does. The former is not a comparison; the latter is a comparison of two lengths, one from a measuring instrument (ruler or tape measure or whatnot).

Binswanger does not say what I just did, but he portrays the child's understanding of length somewhat differently than Rand did. He writes: "In speaking of "measurements" I am referring to the subconscious mechanics of the concept-forming process, not to any consciously performed, explicit, process of measuring. A child beginning to conceptualize things is, of course, incapable of explicit measurement. On the conscious level, he is only aware of similarities and differences. But the objective basis of those similarities and differences is the quantitative variation of a commensurable characteristic" (p.118). He does not claim the child implicitly measures.

Binswanger tries to explain that humans don't really omit measurements. More exactly they recognize that measurements vary. He says that things that are similar differ quantitatively. "Similarity is measurement proximity. "Proximity" is a relative term, depending on a contrast with something that is more distant, which can be called "the foil." Similarity is thus contextual, a matter of relative proximity of measurements in contrast to the relatively distant measurement of a foil. In such a set-up, the bigger difference swamps the smaller difference, making the smaller difference appear as similarity. What is experienced as similarity is, at root, lesser difference" (p. 112).

Here at least the smaller differences among similar things are swamped rather than omitted. 

There are also sections of Chapter 3 on integration and unit-economy.

How We Know #2: Perception

Chapter 2 is about perception. I rank it as the best chapter in the book. His treatment is more elaborate than Ayn Rand's, but very coherent with it and there is little disagreement. They differ slightly on how sensations or sensory input are integrated into perceptions.

Some key points follow.
- Perception is axiomatic. It is our primary, basic contact with the world.
- Perception is inerrant and the foundation of all knowledge. Any errors are conceptual.
- We are aware of existence as a unified whole, not involving our consciously constructing things to be aware of existence. 
- Perceptual content is automated, a biological given, not subject to volitional control. We have some control over attention but not content. 
- He appeals to the direct realism of J. J. Gibson.

A rather unique feature is his distinction form vs. object. He traces it back to Thomas Aquinas. Leonard Peikoff made the same distinction in OPAR, but not as strongly as Binswanger does. 

My aside: this use of form is very different from Aristotle's. Aristotle famously held that every physical object is a compound of matter and form. Binswanger uses form to mean the nature of perceptual awareness.

He tackles many of the topics often discussed by philosophers regarding perception: hallucination, naïve realism, representationalism, and appearance versus reality. 

How We Know #1: Foundations

How We Know is the title of a recent book by Harry Binswanger. He presents his theory of knowledge based on Ayn Rand's Objectivist philosophy. He was a friend and associate of her for many years.

The book is well-written in my opinion and well worth reading. I agree with most of it. I will devote several blogposts to it.

Chapter 1 is titled Foundations. His foundations are the same as Ayn Rand's. I refer the reader to the Table of Contents using the Look Inside feature at the above Amazon link for what the fundamentals are.

He emphasizes consciousness being a biological faculty more so than Rand did.

"Conscious activities, whether sensory or conceptual, have, like the heartbeat, a biological function. Man has eyes for the same reason he has a heart: to sustain his life; vision is an adaptive, biological, life-sustaining capacity. The same is true of the other sense modalities: each provides man with life-sustaining information about the world.
     And the same is true of the faculty of reason. The mind, the reasoning intellect is a vital organ. A biologist could not understand the heart if he did not know its biological function, and a philosopher cannot understand reason, or any other faculty of consciousness, if he ignores the biological function of that faculty" (p. 37).

He addresses what consciousness does for animals to prepare the stage for what it does for man.

Rand was rather skeptical about evolution. Binswanger is not. He defers some of his discussion of evolutionary biology until later in the book, but biology is prominent in Chapter 1.

He gives a different meaning to "self-evident" than most people. Self-evident means "available to direct awareness. "Self-evident" is not a synonym for "obvious." To one who has learned arithmetic, it is obvious that two plus two is four, but that truth is not self-evident; it is inferred by a process of comparison and counting. But that the page you are reading exists is not an inference; it is self-evident. The data of sensory perception are self-evident (23).

Ayn Rand said the last thing, too, but it seems unusual in philosophy. Neither The Encyclopedia of Philosophy (Colliers-Macmillan 1967) nor the on-line Standford Encyclopedia of Philosophy have "self-evident" as a separate entry.