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.