Between False, Invalid, and Meaningless
Rand defined truth as “the recognition (i.e., identification) of the facts of reality” (ITOE 48; also Rand 1957, 1017
). She maintained: “Man identifies and integrates the facts of reality by means of concepts. He retains concepts in his mind by means of definitions. He organizes concepts into propositions—and the truth or falsehood of his propositions rests, not only on their relation to the facts he asserts, but also on the truth or falsehood of the definitions of the concepts he uses to assert them” (ITOE 48; see also Peikoff 1991, 137–39
Rand is here speaking of definitions of concepts not in whatever stipulative character they have, but in the assertion a definition makes for a concept’s relation to reality, in the full context of one’s knowledge. The hallmark of falsity for Rand is the contradictory. “Logic is the art of non-contradictory identification
. . . . No concept man forms is valid unless he integrates it without contradiction into the sum total of his knowledge” (Rand 1957, 1016
I noted in #2
that predications are conceptual identifications, that Edward Zalta takes the discipline of logic to be “the study of the forms and consequences of predication,” and that this fits well with Rand’s conception. Comportment between Rand’s conception of logic and prominent contemporary senses of logic,*
such as Zalta’s, is comportment in which we incorporate theirs into Rand’s with its distinctive general situation with existence. Contemporary logicians and philosophers of logic should see Rand’s conception of logic as including more of what they would call rationality beyond their formal logic.
Rand holds that “logic rests on the axiom that existence exists” (1957, 1016; further, Peikoff 1967, 112–13
). She holds that widest existence with its principle existence is identity
is the widest frame of knowledge. Nothing real is beyond existence with its fundamental principle. The elementary function of logic is to provide general constraints on concepts, definitions, propositions, and inferences for attaining and keeping: integrated truth, integrated in the widest context, ever in the widest frame, which is existence with its identity.
Rand holds also that all values (hence all problems, questions, solutions, games, wars, or victories) arise only for living existence, within wider existence. Consonant with that existential situation, we have that “It is value” logically presupposes “It is.” Widest existence with its fundamental principle frames the realm of value like any other. I say then for Rand, as for me, truth as recognition of reality is epistemologically more basic than functional correctness. (This does not entail that a sense of correctness is acquired later in development than a sense of truth.) In the functional system that is knowledge, the meaningless is epistemologically rooted in falsehoods.
The sense of truth of which I am speaking as epistemologically prior to a sense of correctness is only the sense of truth manifest in “It is.” The further, normative sense of truth manifest in “It is true that” presupposes not only “It is” but “Truth is to be pursued and can be missed.”
a form of organic functional correctness, and the latter is metaphysically prior to the former in that conceptual consciousness arises from non-conscious biological systems.*
Correctness is accordance with function. Meaningfulness is one success, one correctness in the functional system that is human thought.
To the extent that a concept’s definition is not assessable for contradiction, neither with other propositions warranted to be true, including other concepts’ definitions, nor more directly with reality,*
it will be most natural in Rand’s system to call the concept objectively meaningless. (Note that philosophic axioms are assessable.) A concept that has no definition—not ostensively, not expressly, not implicitly in a set of propositions using the concept—would also be meaningless. One important example of this latter sort of objectively meaningless concept would be one reifying the concept nothing
into anything more than not anything. The idea that I might have been conceived by parents other than the ones who actually conceived me is of that genre. Such a concept of I
relies on a reification of nothing. My tissue, in which development my mind arose, does not in any sense exist and bear possibilities before it existed. It is objectively meaningless to say I might have been conceived by parents wealthier, better educated, and so forth. The dense thicket of contingencies in such alternative personal histories leaves talk of such possibilities meaningless (cf. Boydstun 1996, 183–87
). The I
of such possibilities has no identity, no definition.
In the functional system that is knowledge, another important example of the meaningless by way of having no definition would be concepts whose entire ambit of propositions in which they are logical subjects are propositions stating what the referents of the concept are not. No positive definition, no identification of existence, is thereby attained. The subject that is center and base for negative-way, beyond-being theology*
is objectively meaningless (cf. Rand 1957* and Kant KrV B149; B308–9; A254–56 B310–12; A780–82 B808–10; Westfal 2004, 64–66
The subject of a purely negative theology has not even the limits of Pegasus or of a partial mathematical function such as 5 minus 7 among the natural numbers (positive, counting numbers). There is logic appropriate to characters like Pegasus and to 5 minus 7 among the naturals, which logic has its relations to logic for the concrete world (Epstein 2006, 413–36
). There is no such logic for the absolute non-identity of the subject of purely negative theology. On the positive side, concerning the putative personality that is God, in the full context of present human knowledge, we may put personality-God in the same region as Pegasus (cf. ITOE Appendix, 148
What is objectively meaningless in the context of knowledge attained in a culture is not necessarily objectively meaningless also in the more restricted context of knowledge of a less advanced culture. The meaninglessness of purely negative theology can be seen at our culture’s stage of knowledge. It could also have been seen in the eras of the Middle Platonists and the Neo-Platonists who embraced negative theology. Was my first example of the meaningless by way of having no definition—the example of me before my tissue began—objectively meaningless in the culture of Plato and Aristotle? I do not know. My judgments, in present study, of what is objectively meaningless are with respect to the higher knowledge-stage of our world today. And they are for individuals old enough to be reading books such as Atlas Shrugged
Shortly, I shall craft a niche for cases of the objectively meaningless in defined concepts and in propositions, looking to implications of Rand’s epistemology. That is, I shall expose a way, in Rand’s framework, in which propositions, including definitions, can fail to be assessable for contradiction. The objectivity of which I speak in the objectively meaningful is, all together, Rand’s recognition sense of the objective
with its metaphysical and epistemological faces as well as her sense of the objective
in her partition intrinsic-subjective-objective.*
Rand was cognizant of Aristotle’s principles of definition according to genus and species and according to essentials.*
In Introduction to Objectivist Epistemology
), she integrates the former of those Aristotelian principles with her analysis of concepts in terms of measurement omission. She recasts the Aristotelian virtue of definitions according to essentials by dropping his conception of essence as intellectual, universal form joined to and ontologically separable from matter it informs and by dropping the Aristotelian information of our minds by such forms in perceptual, memorial experience. Rather, she upholds definitions of concepts reflecting reality by taking for essence of the class under the concept the shared distinguishing characteristic that explains, within present extent of knowledge, the greatest number of other characteristics distinctive of members of the class. Essential characteristics are constructively discerned by actively thinking over the differences, similarities, thematic relations,*
and causal relationships discerned in particulars.
Notice that what was properly the essential characteristic of a concept at an earlier stage of human knowledge could become improper with the advance of knowledge. Holding onto the old form of the concept could become irrational, a defiance of reality, an obfuscating embrace of false for true (e.g.
). The old concept could be sub-optimum in truth and sub-optimum in the strength of objective meaning possible in the more advanced context of knowledge.
Rand was also aware of the controversy among contemporary philosophers concerning the soundness of the modern division of propositions into analytic or synthetic (a, b, c
).This controversy had been prominent in academic print*
and in semi-popular works such as A. J. Ayers’ Language, Truth, and Logic
(1952; quoted in Peikoff 1967, 94
) and the writings on philosophy of science by Hans Reichenbach and Philipp Frank (who was quoted in Basic Principles of Objectivism lectures in the nineteen-sixties; Branden 2009, 22–23
) in the four decades before Rand’s ITOE
. Immediately after completing the ITOE-
series in The Objectivist
, she issued therein Leonard Peikoff’s “The Synthetic-Analytic Dichotomy,” which came down on the side of those who had argued variously against the distinction. In ITOE
Rand rejected the distinction in the course of laying out her theory of right definition (cf. White 1952, 318–30; Peikoff 1967, 94–97, 100–106, 115; Browne 2007, starting here
). “The nominalists of modern philosophy, particularly the logical positivists and linguistic analysts, claim that the alternative of true or false is not applicable to definitions, only to ‘factual’ propositions. Since words, they claim, represent arbitrary human (social) conventions, and concepts have no objective referents in reality, a definition can be neither true nor false” (ITOE 47–48
Rand’s theory of concepts is not nominalist, but objectivist (and mensural). Proper concepts are aimed to reflect realities and those realities’ places in and relationships to wider realities. Proper definition of a concept enables us to keep concepts straight in mind and ever-tuned to reality in our ever-growing grasp of it. Writing,
I should mention, is a tremendous tool for stabilizing and sharpening expressly defined concepts, for better remembering them, and for drawing them together to discern contradictions and implications. I should mention, too, as I frequently do mention, with reason: when a mathematician or scientist speaks out the equation she is writing on the board for class, she is speaking the concepts and relationships in purely natural language. Neither she nor the class will need to have facility in concepts of artificial, formal languages, meta-language, and logics within formal languages to solve a partial differential equation or to prove that every group is a subgroup of the permutation group on some set.
Proper concepts and their definitions have objective bases in the world and in the nature of consciousness, including the nature of thought. The concepts triangle, seven, hand,
are not arbitrary, purely conventional constructs. They have meaning, truth, and utility, whatever the natural language in which they are expressed. Objective meaning is structured after properly integrated truth. Objective meaning, like an objective concept and its definition, has validity by reality as it stands in the fullest present human knowledge of reality. Meaning in the system that is knowledge is not an arbitrary free invention. For meaning, I say, as Rand says for definition, “objective validity is determined by reference to the facts of reality” (ITOE 46
Rand reserves the term arbitrary
for cases of the arbitrary entailing dissonance with reality rationally differentiated and integrated. In the negative sense of the subjective, as spoiling objectivity, we can say more briefly that Rand reserves the term arbitrary
for cases of subjective arbitrariness (e.g. ITOE 42–43
). Such is Rand’s use when she writes against arbitrariness in modern empiricism, rationalism, and philosophy of science: “Its exponents dismissed philosophical problems by declaring that fundamental concepts—such as existence, entity, identity, reality—are meaningless; they declared that concepts are arbitrary social conventions . . .” (Rand 1970, 83
). Notice Rand concurs that if
concepts were arbitrary conventions they would be meaningless.
Where we might say something was arbitrary in a sense not subversive of objectivity, Rand uses the term optional
. “After the first stage of learning certain fundamentals, there is no particular order in which a child learns new concepts; there is for a while, a broad area of the optional, where he may learn simple, primary concepts and complex, derivative ones almost concurrently, depending on . . .” (ITOE 20, also 70, 72, and Appendix, 180
). Where we might say, to indicate universality, “consider an arbitrary scalene triangle” or “consider an arbitrary body having angular velocity omega,” we mean nothing more than any
when we say arbitrary,
and Rand has no complaint about the arbitrary in that sense. Further, she should have no issue with objectivity-comporting arbitrariness in choices of coordinate system, number base, or natural language. But when she
she means the subjectively arbitrary, the one necessarily objectively meaningless.
We saw earlier Rand’s awareness of logical positivism with its attachments to nominalism and to sharp division of propositions into either synthetic or analytic. Logical positivism is also known as logical empiricism.*
Rudolf Carnap was a principal in that philosophical movement. He held that metaphysical statements such as Heidegger’s “the Nothing nothings” are meaningless (Carnap 1959, 69–73
). Carnap defended a divide between synthetic and analytic statements. Furthermore, statements that are neither one of those are meaningless. We have seen above the different reason that Rand too would regard the famous statement of Heidegger as objectively meaningless.
Validity within propositional and predicate logic is generally taken to mean: that merit of argument in which the conclusion cannot be false if the premises are true.*
We speak also of validity in property titles and in contracts. Kant had much work for a sense of validity in epistemology joining those two senses. He announces in the Preface to the first edition of the Critique of Pure Reason
that a central component of that work “refers to the objects of pure understanding and is intended to make comprehensible the objective validity of understanding’s a priori
concepts” (xvi; see Pippin 1982, 154–58
That general epistemological sense of objective validity in concepts is useful in application to concepts and propositions in philosophical systems besides Kant’s. In his mature, pragmatic philosophy, Dewey writes: “According to experimental inquiry, the validity of the object of thought depends upon the consequences of the operations which define the object of thought” (1929, 103
). Speaking of experiment, Dewey refers to the process “by which the conclusion is reached that such and such a judgment of an object is valid” (ibid., 230
). Logical positivist Ayer writes: “In saying that we propose to show ‘how propositions are validated’, we do not of course mean to suggest that all propositions are validated in the same way. On the contrary we lay stress on the fact that the criterion by which we determine the validity of an a priori
or analytic proposition is not sufficient to determine the validity of an empirical or synthetic proposition. For it is characteristic of empirical propositions that their validity is not purely formal” (Ayer 1952, 90
). For Ayer one can validate a proposition either by finding it to be analytic or by finding it to be empirically verified.
In Rand’s philosophy, Peikoff takes validation to be “any process of establishing an idea’s relationship to reality, whether deductive reasoning, inductive reasoning, or perceptual self-evidence” (1991, 8
As Peikoff had expressed it in his 1976 lecture series The Philosophy of Objectivism,
in the broad sense includes any process of relating mental contents to the facts of reality. Direct perception . . . is one such process. Proof
designates another type of validation. Proof is the process of deriving a conclusion logically from antecedent knowledge” (see further, Peikoff 1991, 118–20, 137–38
Rand observes “there are such things as invalid concepts, i.e., words that represent attempts to integrate errors, contradictions or false propositions, . . . or words without specific definitions, without referents, which can mean anything to anyone . . . . An invalid concept invalidates every proposition or process of thought in which it is used as a cognitive assertion” (ITOE 49
That is a big umbrella. I think of objectively meaningless concepts as a type of invalid concept. They are a subdivision of that type of error; not every invalid concept is objectively meaningless. Rand constructs an invalid concept man
in which his ability to run is taken for his essential characteristic and running entities
is taken as genus of the concept (ITOE 71
). To better absorb this example, one should imagine that one does not have the other conception and definition of man rational animal
, not even implicitly. Try to imagine that for basic adult definition of man one has only the definition running animal,
alongside running water
and so forth as species of running entities
That would be a misidentification of the essential trait of man. It would be an objectively invalid concept, but not an objectively meaningless concept. Such a concept is assessable for validity. For one thing, it is assessable for contradiction with reality, including contradiction with other concepts warranted by reality in the present context of knowledge. That is to say, such a concept is objectively meaningful though it is objectively invalid.
Earlier I examined invalid concepts objectively meaningless by way of having no definition. There are defined concepts empty of distinctive positive identity. Such a concept will yield propositions incorporating specifically it
: not assessable for contradiction. Such a concept and such propositions composed distinctively by them are objectively meaningless. Consider a concept super-knowledge
(which is what some concepts of faith or intuition come to) that is stipulated to be nothing other than imageless and wordless apprehension higher than knowledge resulting from perceptual and logical means. This would be an invalid concept that is objectively meaningless. Keeping to the stipulated sense of the subject term, in saying “Super-knowledge is beautiful,” the subject is without positive identity beyond its genus apprehension
. There is nothing objectively meaningful being said beyond “Some apprehension is beautiful.” No assessments of this
proposition for contradiction by particular or specific identities are by test of the proposed species super-knowledge
. Similarly it goes with susceptibility to assessment for contradictions in “Beauty is super-knowable.” That beauty is apprehensible is all the objective meaning.* References
Ayer, A. J. 1952 [1936, 1946]. Language, Truth and Logic
Boydstun, S. 1996. Volitional Synapses. Objectivity
Branden, N. 2009. The Vision of Ayn Rand
Carnap, R. 1959 . The Elimination of Metaphysics through Logical Analysis of Language. A. Pap, translator. In Logical Positivism
. A. J. Ayer, editor. Free Press.
Dewey, J. 1929. The Quest for Certainty
. J. A. Boydston, editor. 1984. Southern Illinois.
Epstein, R. L. 2006. Classical Mathematical Logic
Kant, I. 1781. Critique of Pure Reason
. W. J. Pluhar, translator. 1996. Hackett.
Peikoff, L. The Analytic-Synthetic Dichotomy. In Rand 1966–67.
——. 1991. Objectivism: The Philosophy of Ayn Rand
Pippin, R. B. 1982. Kant’s Theory of Form
Rand, A. 1957. Atlas Shrugged
. Random House.
——. 1966–67. Introduction to Objectivist Epistemology
ed. H. Binswanger and L. Peikoff, editors. 1990. Meridian.
——. 1970. Kant versus Sullivan. In Philosophy: Who Needs It
. 1982. Signet.
Westfal, K. R. 2004. Kant’s Transcendental Proof of Realism
White, M. G. 1952. The Analytic and the Synthetic: An Untenable Dualism. In Semantics and the Philosophy of Language
. L. Linsky, editor. Illinois. *
A different response to Rand’s epistemology in areas treated in the present study can be found here
~~~~~~~~~~~~~~~~ With Measurement
Measurement is the identification of a relationship in numerical terms—and the complexity of the science of measurement indicates the complexity of the relationships which exist in the universe and which man has barely begun to investigate. They exist, even if the appropriate standards and methods of measurement are not always . . . easily available . . . . If anything were actually “immeasurable,” it would bear no relationship of any kind to the rest of the universe, it would not affect nor be affected by anything else in any manner whatever, it would enact no causes and bear no consequences.[cf. Note 3]
The motive of the anti-measurement attitude is obvious: it is . . . the desire, epistemologically, to escape from the responsibility of cognitive precision and wide-scale integration; and metaphysically, the desire to escape from the absolutism of existence, of facts, of reality and, above all, of identity. (ITOE 39)
I have proposed that in Rand’s philosophy objective meaningfulness requires the setting of identity by definition. Objective meaning is given an additional level of strength by Rand’s epistemology and its metaphysical presuppositions, by the principles: (i) All concretes, whether physical or mental, stand in measurable relations to other concretes. (ii) Cognitive systems are measurement systems.*
Best and most meaningful concepts are those given mathematical, measure-theoretic analysis. After one has defined a concept, one can further amplify meaning by specifying the concept’s dimensions of the subsumed items and the measurement scale(s) those dimensions afford. This specification is an objective issue, a matter of discerning what is the magnitude character of the dimensions shared by the items covered by the species in the definition (see Note 27
In my dictionary, solid
is defined as “a substance that is neither liquid nor gaseous.” Yes, that much is necessary for understanding the meaning of solid. A little reflection yields “a substance that is neither liquid nor gaseous, that is, a substance that does not flow” (presuming a context of common durations and precisions of observation). With advances in our network of mechanical concepts, including their mathematical characterization, we can say further
. . .
Solids are distinguished from fluids in virtue of the fact that they have moduli of rigidity that are not (too close to) zero; any solid is capable of withstanding shearing forces up to some particular measure. The particular modulus of rigidity of a particular solid object is part of what constitutes its individual identity, and the fact that its particular modulus is not zero is what qualifies it for the class solid.
. . .
Meaning that is strengthened by measure-theoretic analysis expands the possibilities for uncovering contradictions with reality together with contradictions among one’s concepts as cohorts reflecting the unity that is existence with identity. Consider the ways in which explicitly specifying quantitative dimensions of mechanical concepts perfected their meaning and helped to weed out their contradictions in the progression from Descartes to Leibniz to Newton. Made quantitative and free of contradiction, those concepts have powered invention and engineering in the modern world. Consider also:
. . .
From those percepts, general causal principles (from “Pushed balls roll” to “Applied torque causes onset of rolling”) are formed after the general pattern of how universal concepts are formed from percepts. Harriman’s book is an attempt to spell out more specifically the abstraction process from elementary causal principles such as “pushed balls roll” to general scientific principles—the tremendous abstraction process that is ampliative induction—illustrated by episodes in the history of science. . . .
I remarked previously, taking issue with Rand, as follows:
. . .
There are indeed some indispensable concepts we should not expect to be susceptible to being cast under a measurement-omission form of concepts. Among these would be the logical constants such as negation, conjunction, or disjunction. The different occasions of these concepts are substitution units under them, but the occasions under these concepts are not with any measure values along dimensions, not with any measure values on any measure scale having the structure of ordinal scale or above. Similarly, it would seem that logical concepts on which the fundamental concepts of set theory and mathematical category theory rely have substitution units, but not measure-value units at ordinal or above. The membership concept, back of substitution units and sets, hence back of concepts, is also a concept whose units are only substitution units. Indeed, all of the logical concepts required as presupposition of arithmetic and measurement have only substitution units. Still, to claim that all concretes can be subsumed under some concept(s) other than those, said concept(s) having not only substitution units, but measure values at ordinal or above, is a very substantial claim about all concrete particulars.
. . .
(See also here.
I said earlier in this addendum that in Rand’s philosophy objective meaningfulness requires the setting of identity by definition. I say further: Some logical and set-theoretic concepts—not, or, and, all, some, set
—are defined by implicit definitions, a specification of their roles supporting meaning and truth of propositions, displayed most essentially in the propositions of logic and mathematics themselves. To be sure, these concepts are rooted in structures of action and situation learned in child development. (Notice also that some functions of these concepts can be implemented in machines.) Later they are rarified for use in language and abstract thought. (On action origins, see a, b. On Piaget’s perspective, see the contributions of Smith, Boom, and Campbell here. On acquisition of logical notions in language acquisition, see a, b, c, c´.
The concept collection
is not the very same as the concept set
as the latter is used in logic or mathematics. Then too, logical class membership, which is used in Rand’s explication of conceptual class, is not the very same as natural-species membership such as Silver’s belonging to the horse species. Validity of the concept natural-species membership
is not the full warrant for the concept class membership
Perfecting the meaning and warrant of the concept class membership
will not rely on a measure-value omission. Substitution units are not to be analyzed in terms of measure-value units. The concepts from logic and mathematics that are required for an analysis of measurement, thence measurement omission, are not to be analyzed in terms of the latter. That is why I have held, contrary to Rand, that certain logical and set-theoretic concepts are not to be analyzed in terms of measure-value omission, which is the explanatory structure distinctive of Rand’s analysis of concepts. It remains that the proposal to analyze all other concepts in terms of measurement omission (at least to the level of ordinal measurement) is a substantial, definite, meaningful, and meaning-giving proposal.