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).

JARS 17.1

The Journal of Ayn Rand Studies 17.1 is now available. I received my paper copy very recently. It contains my article “The Beneficiary Statement and Beyond.” A link to the abstracts for it and the other articles is here. It also contains my reply to Roger Bissell’s article about volition in an earlier issue. If you are not a subscriber and don't want to pay, then you will need to see a payer’s copy or wait about 5 years when it becomes freely available on JSTOR.

How We Know #9: Propositions

Chapter 5 is about propositions. Binswanger ventures beyond Ayn Rand, who said little about propositions. He divides propositions into classificatory and descriptive. Regarding the first he says, "Concept-formation operates by measurement-omission (to establish a range) and conceptual identification operates by measurement-inclusion (inclusion in an established range)." Descriptive propositions also work by measurement-inclusion.

The section Negative Propositions is interesting. He writes: "Negative propositions are those having the form "S is not P" -- e.g., "Lassie is not a beagle" or "Lassie is not small." Negative propositions are differentiations. Negative classificatory propositions assert that the subject is different from the existents subsumed by the predicate, and thus is to excluded from the predicate-class (Lassie is excluded from the class of beagles). ... Negative propositions work by measurement-exclusion" (179).

"Thus, negative propositions do not refer to some supposed "negative facts." Everything that exists is something. To be non-P is to have a positive identity, but one that is different than P" (179).

Interesting cases are ones about imaginary subjects. "A proposition about God, unicorns, or the integer square root of 17 is not differentiating an existent from other existents, but a valid idea from an invalid one" (180). Ayn Rand wrote some about invalid concepts in ITOE.

There is a section The Analytic-Synthetic Dichotomy. For the most part Binswanger refers to the same-named article by Leonard Peikoff in ITOE and ITOE2. Along with the analytic-synthetic distinction, Immanuel Kant made a distinction between a priori and a posteriori propositions. He said an a priori proposition is logically necessary and an a posteriori proposition is logically contingent. Peikoff is very critical of  contrasting "contingent facts" with necessary facts. Somehow "contingent" regarding propositions about the future doesn't seem to occur to him. (For example, I might have an 80th birthday.) Maybe it is not only him, but philosophers generally. Anyway, it does to yours truly. Actuaries consider future contingencies a lot.

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.

Experience and a Smartphone

I interrupt my series of posts about How We Know because (a) I referred to John Locke in HWN #4 and HWN #5 and (b) I bought my first smartphone recently.

The great British philosopher John Locke said that the only knowledge humans can have is based upon experience. While trying to learn how my new smartphone works, what Locke said came to mind forcefully.

It is my first smartphone. My past experience with touch-screen devices and smartphones is scanty. There was and remains a lot to learn about where and how to do what I want or need to do. Trial and error has been frequent. Merely activating the phone to being able to make a call took a meandering path. I spent much time online in chat mode. I was instructed to take the battery out and restart the phone 2 or 3 times before succeeding. I didn't change carriers, so I thought activating the phone would be enough to access voicemail again. It wasn't near that simple. Also, my old phone didn't require a password to access my voicemail; my new one does.

Where to go and what to do has not been very intuitive. I even failed to answer my first incoming call in time. To make a call I had tapped the phone icon. So when the phone icon appeared for the incoming call, I tapped it to answer. That didn't work. I tapped harder to no avail. Then I read in the manual that I need to slide the icon to answer a call. Silly me!

In summary, my new phone has required a significant amount of experience, and it will take a lot more, before I know enough to use it proficiently.

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.