1. Operands and operators. The “operands” of arithmetic are 1, 0, etc., and the “operators” are +, -, *, /, etc. Algebra, then, which builds on top of arithmetic, introduces the “operands” x, y, etc.
2. The operands as distinguished into constants and variables. For example: 1 and 0 are “constants,” and x and y are “variables.” In arithmetic and algebra, the constants are numbers (e.g., 1, 0). The variables, then, are like blanks to be filled in with those constants (which, again, are numbers in the present context). x + 1 = 2 is like _ + 1 = 2. What constant/number, if put into that blank, would make a true proposition? The answer is of course 1. Thus, x = 1. That is: _ = 1. But why aren’t blanks actually used? The reason is that x is like a _ that must be filled in with the same constant/number everywhere—well, everywhere in the circumscribed sphere of that x’s usage. For example, consider: 2x + 3x = 10. That’s like 2_ + 3_ = 10 with the constraint that both _ must be filled in with the same constant/number. By contrast: 2x + 3y = 10 is like 2_ + 3_ without that constraint.
3. Relations. The “relations” of arithmetic and algebra are =, >, <, etc. Without the relations, no proposition can be made (a proposition being anything that’s either true or false). For example: 1 + 1 isn’t a proposition, for it can neither be true nor false. But both 1 + 1 = 2 and 1 + 1 = 3 are propositions (with the former happening to be true and the latter happening to be false).
4. x^2 + 6 = 5x is such that x = 2 or 3. Consider, though, that x + y = y + x is such that x can be any number and so can y. Thus: For some number(s) x, x^2 + 6 = 5x. And for all numbers x and y, x + y = y + x.
5. A pair of propositions in English analogous to the foregoing: (1) “For some American people x, x’s parents are from America.” (2) “For all Japanese people x, x’s parents are from Japan.”
6. Another pair: (1) “For some species of birds x, the prototypical x can fly.” (2) “For all species of fish x, the prototypical x can swim.”
7. I’ll also need to define the vocabulary 1, 2, 3, 4, 5, 6, 7, 8, 9, and 0, along with the grammatical system inherent in putting, say, 1 (⚫︎) before 2 (⚫︎⚫︎), and getting 12 (⚫︎⚫︎⚫︎⚫︎⚫︎⚫︎⚫︎⚫︎⚫︎⚫︎⚫︎⚫︎). That should come before bringing up the operands, the operators, and the relations, along with bringing up quantifiers etc.

In the logical language, the joint-attentional frame variant [establish], which is symbolized both linearly and diagrammatically as a square and is one of the four joint-attentional frame variants, will work as follows:

1. In “bicycle [establish] electric,” the joint-attentional frame is established on “bicycle” (whether referentially or categorically) and then “electric” is said about that frame. To translate that into English (if interpreted based on the extralinguistic context of the utterance as referentially definite and singular): “The bicycle is electric.”
2. In “electric [establish] bicycle,” the reverse is true. The joint-attentional frame is established on “electric (thing)” and then “bicycle” is said about that frame. To translate that into English in the foregoing way: “The electric (thing) is (a) bicycle.”
3. In “bicycle electric [establish]” or “electric bicycle [establish]”—those two phrases being logically identical to each other—the joint-attentional frame is established on what’s both a “bicycle” and “electric.”

To compare that to how English and Japanese work:

1. X口Y is like “X is Y” and XはY
2. Y口X is like “Y is X” and YはX
3. XY口 and YX口 are like “X Y is” and “Y X is,” XYは and YXは

For now, though, let’s analyze only X口Y and YX口. For example, in English and Japanese:

1. X口Y in English is like “X is Y,” e.g. “(the) cat is black”
2. X口Y in Japanese is like XはY, e.g. 日本人は時間を守る
3. YX口 in English is like “Y X is,” e.g. “(the) black cat is”
4. YX口 in Japanese is like YXは, e.g. 時間を守る日本人は

In both English and Japanese, then, the grammar uses the position of X and Y with respect to “is” or は (the reversal of the order of X and Y in the above examples being incidental for the present purpose) in order to differentiate between—to return to the camera analogy, although that analogy is, strictly or technically speaking, ideal only in the very limited scope of the speaker talking about something referential in the visual modality—”using a label in order to point the camera” and “labeling what the camera is pointing at.”

That is, both English and Japanese use word order as a grammatical tool for the purpose of differentiating between (1) establishing a joint-attentional frame and (2) saying something about that frame.

But how should the logical language handle the non-口 cases, i.e. the other three joint-attentional frame variants? And how do English and Japanese handle those cases?

Consider for example:

1. “John slapped Jane.”

It’s possible to use emphasis in order to distinguish as follows:

1. “John slapped Jane.” (That is, it wasn’t a different person who slapped Jane.)
2. “John slapped Jane.” (That is, it wasn’t a different action that John took with regard to Jane.)
3. “John slapped Jane.” (That is, it wasn’t a different person who got slapped by John.)

For background: Whether we’re analyzing English, Japanese, or any other language possible to evolve naturally among human beings, there’s always the distinction—again, fundamental to all natural human language—between (1) how joint attention is established on X and (2) what’s said about X.

Interestingly: When using one of the copular verbs in English (e.g., “is,” “are”), there are only two places (or slots) for the arguments: before the copular verb and after the copular verb. That is—to bring up, appositionally, the traditional terminology—there’s the copular verb along with its “subject” and its “predicate.” And those two places/slots correspond to (1) how joint attention is established on X and (2) what’s said about X.

Consider for example:

1. “That man is the owner.”
2. “The owner is that man.”

When not using any of the copular verbs in English, however, and instead using one of the non-copular verbs: Even when there are, like with any of the copular verbs, the two places/slots of [before] and [after] for the arguments, with no other places/slots, those two places/slots don’t correspond to (1) how joint attention is established on X and (2) what’s said about X. Case in point: If we reverse “that man is the owner” to “the owner is that man,” that’s a different semantic change that if we reverse “John slapped Jane” to “Jane slapped John.” The question becomes, then: The semantic change that we get from the swapping of [before] and [after] with copular verbs in English, how do we get that same semantic change, again in English, with non-copular verbs?

As shown at the beginning of the present essay, emphasis is one of the tools that can help: “John slapped Jane” is different than “John slapped Jane.” There’s also another tool that can help (in a perhaps more logically rigorous way): “It was John who slapped Jane” is different than “it was Jane who was slapped by John.”

For copular verbs, then: There’s only one distinction that I’m concerned with in the present essay: that between (1) the place/slot/argument that establishes joint attention on X and (2) the place/slot/argument that says something about X. But for non-copular verbs: There are two distinctions: not only that between the foregoing, but also that between, e.g., the agent and the patient for the verb “slap.”

What pattern may there be of semantic difference between basic nouns and basic verbs? At first glance, relative permanence seems related. Consider for example: “The duck flew away.” The duck was almost definitely already in existence before it flew away, and it was almost definitely still in existence after it flew away. Only in a story with magic could it be otherwise. That is (again, unless there’s magic, e.g. a wizard casting a spell that causes a duck to appear in existence only long enough to fly away before then disappearing from existence): For any given thing in space that the basic noun “duck” is a true label or description of, the basic verb “fly” is a true label or description of that thing at fewer moments in time. Temporally speaking, there’s a whole-part relationship: The label/description “duck” is always true of that thing, meaning that being a duck is something true of every moment in time of its existence, and the label/description “fly” is sometimes true.

However, that proposed distinction doesn’t work because not only is the relationship between nouns like “duck” and verbs like “fly” a temporal whole-part relationship, but the relationship between nouns like “duck” and adjectives like “small” is also like that. That is: A duck is still a duck whether it starts or stops flying, whether it starts or stops being small. The nominal quality of being a duck is relatively permanent, and both the verbal and adjectival qualities of flying and being small are relatively impermanent.

With all of that said, my proposed distinction is as follows (without using the terms “verb,” “noun,” and “adjective”):

1. There are the always-true labels (e.g., “duck”).
2. There are the sometimes-true labels that go back and forth between being true and false more freely (e.g., “fly”).
3. And there are the sometimes-true labels that go back and forth between being true and false less freely (e.g., “small”).

1. The order of English, as an internal categorizational system, is mapped onto both the phonological order of English and the orthographical order. That is: The internal categorizational system is externalized into both its spoken and written counterparts.
2. Analogously, the order of the physical world is mapped onto the auditory sensory order, the visual sensory order, and the tactile sensory order, along with the orders of the rest of the sensory modalities. In fact, epistemologically speaking we should, and do, actually go in the opposite direction: We compare the sensory orders of all of the different sensory modalities, looking for where there’s isomorphism.
3. The thymological order, generalized into a (human-)universal description and explanation of the (human) mind; here we find another order, and we can theorize that order (i.e., the human-universal-generalized thymological order) to be in part isomorphic with the human-universal-generalized physical order of “the” brain and nervous system. That is, we can theorize that the mental patterns inherent to being human can be in part mapped onto certain physical patterns.
4. George Boole in The Laws of Thought (1854) showed that the order of the symbolic system of arithmetic and algebra, including the order of its rote manipulation, is isomorphic not only to arithmetic and algebra but also to part of logic.

In The Sensory Order (1952), it was as if Hayek was saying: “You want a (physical) science of human behavior, which would necessarily go along with a (physical) science of the human brain and nervous system? That is, you want a physical science to replace the traditional way of thinking about human action and the human mind? A physical science to replace economics, linguistics, and the rest of the praxeological and thymological sciences? Well, here you go. Good luck.” In other words: Hayek, being famously diplomatic, didn’t just turn his back on the mainstream and go his own way. Instead, he worked together with the mainstream: He took the mainstream’s approach as seriously as possible, and in fact did (some of) their work for them—he steelmanned the mainstream in the most heroic way possible—but in doing so he showed, indirectly, the fool’s errand that it really is.

Physics builds the physical order out of the sensory order. Psychology, in turn, conceived of as a physical science, must then go in the opposite direction. It must build the sensory order out of the physical order. That is: We build a model of (1) what’s physically happening out in the world, along with a model of (2) what’s physically happening in the brain and nervous system, as a reflection of (3) what’s physically happening out in the world; and with all of that, we go far from the sensory order only to just circle right back.

Economics, along with the rest of the social sciences, as traditionally done (e.g., in Smith, in Mill) take for granted the direct sensory order. Those sciences, though, if made into physical sciences, in order to conform to the zeitgeist of modernity, would no longer be able to take that for granted. They’d need to instead be founded on the indirect sensory order. Thus: In taking the mainstream’s own project seriously, and putting it on a better footing than ever before, Hayek showed, indirectly, the futility of the project—well, at least in the short term.

To be fair, though: Hayek’s work on the subject wasn’t just a reductio ad absurdum. It wasn’t just him taking the mainstream premises to their logical conclusions as a way of showing, diplomatically and indirectly, the impracticalities of those premises in the social sciences. Distractingly, perhaps, Hayek was also genuinely interested in the physiology of consciousness for its own sake, including the pre-conscious factors in the development of conscious experience of one kind vs. another, those pre-conscious factors being both organism- and species-level. However, that interest wouldn’t have carried him so far back into the subject, after he had shelved it for 30+ years, if not for the profound significance to the questions of (1) how to do natural science properly, (2) how to do social science properly, and (3) how to keep natural science in its proper place.

In building a model of the grammar of a natural language, we often find that (1) two different linguistic forms have the same logical substance and (2) the same linguistic form has two different logical substances. For example: (1) The two words “have” and “has,” as in “I have a cold” and “he has the flu,” differ only in linguistic form; their logical substance is the same. (2) And the one word “have,” as in “I have a cold” and “he could have gotten the flu” differ not in linguistic form but in logical substance. The former meaning of “have” is obvious. If you “have” a cold, then you’re in that state. The latter meaning, by contrast, isn’t so obvious. It’s that of the past tense. Compare “could” and “could have,” “would” and “would have.”

Imagine building a system of logical notation that has a way of symbolically representing the past tense, the present tense, and the future tense, along with many of the other logical distinctions underlying the grammatical system of natural language. In effect, you’d be building a differently aligned language, in its connections between the surface form of its symbols and the deep substance of its meaning. You’d be realigning, reclassifying; you’d be building a different order.

What we do in physics is analogous. In doing physics, or (in other words) in building a physics model of sensation, we often find that (1) two different sensory forms are caused by the same physical substance and (2) two different physical substances cause the same sensory form. Physics, then, in an analogous way to logic, is an artificial realignment for a philosophical or scientific purpose. Physics replaces the “natural language of sensation” (metaphorically speaking) with an “artificial language of sensation.” In that way: Linguistics is to logic as the introspective psychology of sensation is to physics. Just as linguistics and logic study two separate but interconnected orders, one being more natural than the other, the introspective psychology of sensation studies the “sensory order,” as Hayek calls it, and physics studies the “physical order.”

The natural science of the psychology of sensation, then, studies the “neural order,” which is the interconnection between the sensory order and the physical order. According to Hayek, something in (the physical structure of) the brain, along with the rest of the nervous system, must be isomorphic to (the mental structure of) of the mind. What that “something” is, which can be theorized right from the start of the inquiry as necessarily existing, is left as an open question for me (and not a very highly prioritized one)—though Hayek does make some interesting guesses—for the philosophical significance of Hayek’s starting point in theoretical psychology to the question of the epistemology of the sciences of human action and the human mind doesn’t depend on the answer to that question, i.e. the question of what that “something” is.

The significance is simply that building a properly founded natural science of human behavior and the human nervous system, without sneaking in through the back door anything that’s just directly taken from introspective psychology, would be extraordinarily roundabout (not to mention of dubious utility to economics, linguistics, and the other praxeological and thymological sciences).

That is: We’d have to go from the sensory order, as we experience it naturally, to the physical order, and then we’d have to turn back, going from the physical order, through the neural order, all the way back to the sensory order, but no longer as we experience it naturally: We’d have to build a sufficiently accurate and detailed (physical) model of the brain, along with the rest of the nervous system, that’s in some way isomorphic to a correspondingly sufficiently accurate and detailed (mental) model of the mind. And then we’d just be right back where we started!

It’s the spirit of the Scottish Enlightenment that’s closest to the spirit of my work. Francis Hutcheson (1694-1746) was one of the founding fathers of the Scottish Enlightenment, and soon after Hutcheson came several giants, David Hume (1711-1776) the greatest among them.

In the 19th century, though, Alexander Bain (1818-1903) was one of the most important of the Scots still working as part of the tradition of the Scottish Enlightenment, and (according to The Stanford Encyclopedia of Philosophy here) Bain stood on the cusp: He argued for the replacement of “the philosophy of mind” with “empirical psychology,” which in doing so he helped bring about—though of course the zeitgeist of the 19th century surely made that transition inevitable. In short: The kind of thinking that Hutcheson, Hume, and others did was no longer considered to shed light on metaphysics (i.e., on questions about the ultimate fundamentals of reality). It was demoted to being about the mind and the mind only. It became nothing more than the systematic introspection into the system of the mind, with the mind taken in that new paradigm as a thing apart from reality.

The killing blow, then, to the weakened tradition of the Scottish Enlightenment, was the tabooing of introspection. The “philosophy of mind” (the term “philosophy” at that time being equivalent to the term “science” nowadays) became “empirical psychology,” and then in turn what was admitted as “empirical” eventually shifted: The mind was no longer admitted as a proper object of empirical observation. In psychology, from then on, only models of the brain (along with anything else physical, e.g. the eye, the ear) were taken as properly scientific.

In summary: The “philosophy of mind” in the 18th century became a kind of “empirical psychology” founded on introspection in the early 19th century, which in turn became a different kind of “empirical psychology” by the late 19th century. The analysis of the mental mechanisms of human action and the human mind was pushed aside, and the analysis of the physical mechanisms thereof took over.

With all of that said, however: I’d like to argue that, actually, the tradition of the Scottish Enlightenment didn’t just degenerate first into introspective psychology (with Bain) and then into non-introspective psychology (post-Bain); it actually split off at the root, growing not only into psychology, on one hand, but also logic, on the other hand. Hume introspected in order to understand (the fundamentals of) the system of the mind in its understanding of (the fundamentals of) the system of reality. Post-Bain, the new field of psychology specialized in the former part of that, viz. in the goal of understanding the mind in a fundamental and systematic way, and the new field of logic specialized in the latter part of that, viz. in the reality-related considerations. And mirroring the further degeneration into non-introspective psychology, logic too degenerated: It lost its substance as it transformed into formal logic. John Stuart Mill’s treatise A System of Logic (1843), which Mill thought of as a contribution to the “science of science itself,” soon went out of fashion—it was almost entirely prose. Boole in The Laws of Thought (1854) adapted algebraic notation to logic, and from then on it was formal (or mathematical) logic that inspired the intellectual world—a project that (to no fault of Boole’s) became increasingly unmoored from the Scottish tradition (along with the broader British tradition, e.g. in Locke, in Berkeley) of checking whether there’s actual substance underneath the pretty surface form of eloquent words and other symbols.

And finally, in the 21st century: Introspection is taboo in science, the physical is taken much more seriously than the mental in psychology and elsewhere (in keeping with introspection as taboo in science), a substance-unchecked mathematics has all but swallowed up logic, and there are few thinkers left in philosophy of science.

Imagine that you’re talking to a police officer about a suspicious person reported to have had a knife. You say: “The man who had the knife also had a gun.” But what if the same suspicious person, doing the same thing, was instead reported as having had a gun? You may have instead said: “The man who had the gun also had a knife.” Both facts are true from your subjective perspective. The man had both a knife and a gun. But what you say to the police officer—assuming, of course, that you want him to know both facts—depends on what you know about what he knows about.

Interestingly, though: If we take out of the analysis the speaker and the listener, along with their differing subjective perspectives (e.g., the speaker knowing X but the listener not), and we just imagine the scene itself (of the man with the knife and the gun) from an omniscient, objective perspective, then there’s no possible distinction between what we’d imagine between the original sentence and its flipped-around counterpart. Whether “the man who had the knife also had a gun,” or “the man who had the gun also had a knife”—whether the speaker is making one assumption about the listener or another—the two omnisciently, objectively imagined scenes are identical: There was a man of a certain kind. He had both a knife and a gun, both of them of a certain kind. And he was doing certain things, e.g. walking in a certain way.

Imagine that you’re at a cafe with a friend. You see three men walk in, one of them young and the other two old. Imagine also that you (believe that you) know something that (you believe that) your friend doesn’t, viz. that the young man is a famous chess player. You may point in the direction of the three men and say: “The young man is a famous chess player.” Pointing in that direction narrows down the possible referent(s) of the subject of the utterance to just those three men, and the category “young man” narrows down the possible referent(s) further: The only possible referent is now just that one man.

In saying that “the young man is a famous chess player,” first you (1) establish joint attention on the referent, in this case “the young man,” and then you (2) say something about that referent, in this case “is a famous chess player.”

But it’s also possible to flip it around. Instead of saying that “the young man is a famous chess player,” which uses the fact that he’s a young man as (perhaps) nothing more than just a way of establishing joint attention on him, you can say that “the famous chess player is a young man,” which makes the fact that he’s a young man into the point that you’re making about him.