By Jimmy (Jimbo) Wales
Date: Thu, 1 Sep 1994 09:25:05 EST
From: Jimmy -Jimbo- Wales firstname.lastname@example.org
To: Multiple recipients of list AYN-RAND email@example.com
Subject: Opening essay
What follows is the current version of my own notes on the theory of propositions. Since these are notes written for my own consumption, they assume a particular context of knowledge: mine. This means that I use the terminology I'm personally comfortable with, but without explaining that terminology very much. As far as I am aware, though, this terminology is the same as that in common use in Objectivist circles, so hopefully quibbles about what concept is identified by what word will be kept to a minimum.
There is a certain sense in which this essay should be published at the *end* of our discussion of Introduction to Objectivist Epistemology. But I publish it now to indicate in part where I think we should be headed. This is my own current answer to what I think are the most pressing questions in Objectivist epistemology.
0. Preface"The organization of concepts into propositions, and the wider principles of language -- as well as the further problems of epistemology -- are outside the scope of this work, which is concerned only with the nature of concepts." (Rand, ITOE, p.75.)
This short essay contains my current working thoughts on the theory of propositions.
1. Propositions and SentencesJust as words are not concepts, sentences are not propositions. A word is a visual-auditory symbol that serves to transform a concept into a concrete mental entity. The sentence is one fundamental unit of language, made so by the fact that the sentence is the means by which we concretize our ideas at the next higher level of organization above concepts, i.e., propositions.
A proposition is a mental entity composed of two or more valid concepts or proper names in the particular fashion demanded by man's means of cognition (reason). The principles of language are determined by this overriding psycho-epistemological function: to concretize by converting into perceptual form various mental entities. Words designate and concretize concepts; sentences designate and concretize propositions.
A proposition serves the function of applying conceptual abstractions to a specific problem. In order to serve that function properly, it must be made up from precisely meaningful concepts and/or proper names.
The meaning of a proposition is whatever it asserts about reality. A proposition is meaningful (and thus a valid proposition) when two basic conditions are satisfied. First, the proposition must be composed of meaningful elements in the form of valid concepts and proper names. Second, the proposition must be composed in accordance with the necessities of human cognition; a random collection of concepts is not a proposition. When these two conditions are not met, we do not have a meaningful proposition. We have an invalid proposition, an arbitrary assertion, or worse.
Sentences refer to propositions contextually. The same sentence vocalized by two different speakers may have completely different meanings.
"2+2=4" as uttered by a parrot does not express a proposition. The bird has memorized the sounds, and can generate the perceptual symbols that we understand as referring to a commonly known proposition, but nothing further. It would be absurd to claim that the bird knows math.
Another example is "E=MC^2," Einstein's famous formula. When this mathematical sentence is written by a layman, it does not express a proposition. It is a set of symbols that the layman cannot decode. He does not have the necessary knowledge of the meanings of the constituent symbols, and may not even be able to ascertain if the utterance is grammatical!
Consider a person with a different context: a beginning physics student. This student has learned the meanings of the different terms involved. He knows what facts of reality are identified by "E," "M," etc. He knows the rules of mathematics governing the formation of equations. He therefore fully understands the meaning of the claim.
What he may not know, of course, is whether the claim is an identification of reality. It might contain a contradiction whose presence cannot be detected without more information. An important point to remember here is that in order to know the *meaning* of a concept, one need not know all of the characteristics of the entities subsumed under that concept. Similarly, in order to know the *meaning* of a proposition, one need not know whether the proposition is true or false.
Now consider a person with yet another context: the experienced physicist who has undertaken an investigation of Einstein's theory of relativity. For this physicist, the claim is more than just meaningful. It is *known to be true*. That is, this physicist has validated the proposition; he has proved it.
An important thing to remember about sentences is that they do not always state the full context of the proposition. Sentences serve a particular psycho-epistemological function in reducing cognitive complexity by concretizing propositions. That purpose would not be served if every sentence had to include all of the context specifying the exact meaning of the proposition. It is therefore possible that two people (or the same person at different times or in different respects) will quite properly use the same sentence to assert *different* propositions.
My example above did not address this issue, so I will give another example here, of a person with a still different context: a second beginning physics student has made an error in understanding the nature of the concept "M." He has formed a valid concept of a slightly different aspect of reality, and he currently thinks that this is the valid concept referred to by the word "M" in the mathematical sentence. But, given his understanding, the proposition expressed in his context by "E=MC^2" is false. (It does not matter at this point whether the student knows that this proposition is false.)
In a case like this, we can legitimately say that "E=MC^2" expresses a true proposition for the first student, and a false proposition for the second student. The reason, though, is not that there is some exception to the law of the excluded middle, nor that there is a contradiction in reality. The reason is that the meaning of sentences, like all knowledge, is contextual.
This issue comes up often in considerations of scientific theories that have been discarded over time. The skeptic claims that since people once knew that the earth was flat, and since we now know that the earth is a sphere, knowledge is never certain. The error of the skeptic in this instance is failing to take into account the contextual nature of meaning. When someone in the past asserted that the earth was flat, they meant (or ought to have meant!) only that "given my current context of knowledge, based on local observation by walking around where I live, the earth appears to be flat."
If someone were to make a *contextless* claim that absolutely under all conditions of future knowledge the earth would appear to be flat, then that claim would be beyond the evidence available. No one could claim to know such a thing. Consciousness has identity, which means in this context that we know what we know and no more -- but no less, either. All valid propositions include a specific context, a context sufficient to fully specify the meaning of the proposition. Sentences (for good reasons) do not always need to fully specify that context.
2. TruthWhat are the facts of reality that give rise to the concept of truth? As with many epistemological concepts, there are two basic categories of facts: metaphysical and epistemological. Metaphysically, the concept of truth recognizes that existence exists independently of everyone's consciousness. Epistemologically, the concept of truth recognizes that the conditions of knowledge which make a proposition meaningful are not sufficient to establish that the proposition is, in fact, an identification of reality.
A valid proposition is true when whatever it asserts about reality is actually the case. A valid proposition is false when whatever it asserts about reality is not actually the case. A false proposition is a self-contradiction, as I discuss in the next section.
To more fully understand the concept of truth, we can examine the Conceptual Common Denominator and the distinguishing characteristics involved. Recall that the CCD of a concept is "the characteristic(s) reducible to a unit of measurement, by means of which man differentiates two or more existents from other existents possessing it."
True propositions are a kind of proposition. Truth is a property of some propositions. All valid propositions have meaning, which implies that they have some cognitive relationship to reality, either positive or negative.
(Recall that if some collection of concepts does not stand in some cognitive relationship to reality, then the collection fails to meet the standards set by man's cognitive needs, so that the collection is not a proposition.)
True propositions are those which stand in a positive relationship to reality, i.e. those which correctly identify (refer to) a fact of reality. False propositions are those which do not. (The negation of every false proposition is therefore true.)
The characteristic reducible to a unit of measurement, by means of which we may differentiate true propositions from other propositions is: correspondence to reality. This measurement is a simple either/or. It is not necessary for me to have actually *made* the measurement in any given case, for a particular proposition to be true, any more than it is necessary for me to have seen a particular chair and done the measurements involved in deciding that it is in fact a chair, for it to be a chair.
Now we can answer the question: To what are we referring when we designate some propositions as "true"? We refer to the fact that they are mental entities formed from valid concepts and arranged cognitively in a manner consistent with man's cognitive needs which all possess the _same_ characteristic distinguishing them from all other propositions: that they actually identify (correspond to, refer to) a fact of reality.
3. Falsehood as self-contradictionEvery true proposition can be recast in a form analogous to "X (which means X, the existent, including all its characteristics) is: one or more of the things which it is." That is, "X is what it is." Every false proposition, similarly, can be recast analogously to "X (which means X, the existent, including all its characteristics) is: one or more of the things which it is not." Or, "X is not what it is." (See ITOE, p. 100.)
The meaning of any proposition is what it asserts about reality, and the meaning of any concept or proper name is what it refers to in reality. The law of identity, which says that entities are are what they are, is implicit in every conceptual cognition. Therefore, every proposition implicitly rests on the law of identity. This means, too, that each concept or proper name in the proposition implicitly accepts that the law of identity applies to its referent, i.e. that the referent is what it is. The existent referred to, we silently acknowledge, is what it is -- its characteristics constitute its identity.
As we saw above, every valid proposition is either true or false. Therefore every valid proposition implicitly rests on either "A is A" or "A is not A." The former correspond to reality; the latter do not. Because every proposition *asserts* something in reality, every false proposition *asserts* some contradiction in reality.
It is critical here to go back to our discussion of truth for a moment, and reconsider the fact that it is possible to form a valid proposition without knowing the truth status of that proposition. It is therefore possible to examine a contradictory proposition without realizing that the proposition is contradictory. Contradiction is a fact about valid false propositions which depends on the propositions relationship to reality, not upon our full awareness of that relationship. Failure to realize this is one of the greatest sources of confusion with respect to the traditional dichotomies of "analytic versus synthetic" propositions or "logically true versus empirically true" or "logically possible versus empiricaly possible."
It is true that some *sentences* violate the rules of construction appropriate to man's means of cognition, e.g.
"Quarks are not quarks," such that we can know without further investigation that the sentence does not designate a true proposition. In all other cases, some degree of additional evidence is necessary to determine truth value -- as we will see in the next section.
4. The role of evidenceEvery valid proposition can, in principle, be related to evidence. No invalid proposition can be related to evidence.
It is relevant here to recall that a sentence is not a proposition and that the meaning (or lack thereof) of a sentence is dependent upon context. A sentence which expresses a meaningful proposition when I say it may *not* express a meaningful proposition when someone else says it.
Clear examples can be found in the context of debate with religionists. The religionist makes some claim about religion, such as "God loves you." The rational newcomer asks: "Who is God? What are you talking about?"
Some vague answers are given. The rational person pushes onward: "How do you know that?" Very quickly the truth comes out: the religionist doesn't *mean*anything. Meaning is reference, and the religionist offers no evidence to explain to what he is referring with the term 'God'.
Less clear examples come in political debate. Socialists boldly claim that their system is scientific and better for man. But when pressed, it becomes clear after a time that this claim is very vague. If we refute it in one meaning, suddenly we find that the meaning is changed. If we offer the evidence of the failure of Soviet Russia, then that is because, for some reason, that wasn't *really* socialism. If we offer theoretical objections, showing for example that socialism is incompatible with the epistemological requirements of effective production, the socialist suddenly wants to talk about 'market socialism'. But when we push along that line, he quickly moves back to just socialism. Eventually, when no precise meaning can be found for his verbalizations, we realize that we've been duped: this is a word game, not an exercise in thinking about reality.
In cases like the ones I've been discussing, the state of evidence is so abysmal that we can't even understand the nature of the claim. The sentence does not assert a proposition. But when a valid proposition *is* asserted, that is, when we *do* understand the meaning, then investigation can take place.
Here, as before, we must not drop the context of the meaning of the proposition, nor should we confuse the sentence with the proposition. Many propositions, recall, incorporate presumptions not mentioned in the sentence. If I say "It is cold outside today" you cannot assess what proposition is being asserted, until you know the context. And if you do NOT know the full context, you are likely to make an error in your assessment.
When I say "It is cold outside today" I mean here, in Bloomington, Indiana. I also happen to mean (though you had no way of knowing this until I tell you) "cold relative to the usual temperature in Bloomington at this time of year." It is June, and it is 68. If you didn't understand the full meaning of my claim, you might assess the evidence and jump to the wrong conclusion, claiming "It is not cold outside; it is 91 here in Alabama" or "It is not cold outside; it is 68 in Bloomington and 68 is comfortable." Both those claims are true, but have no bearing on my proposition. Sentences are not propositions and do not usually carry the full context.
But the fact that the same sentence can express different propositions in different contexts does not mean that two people cannot communicate to each other and both consider the *same* proposition. And once two people are considering the *same* proposition with the *same* meaning, either that proposition is true or that proposition is false. Period. It is at this level that claims of "It is true for you but not for me" amount to subjectivism. When two people are considering the same proposition, it is referring to exactly the same facts of reality. This single proposition says "X is what it is" or else it says "X is not what it is." *This* is the question of truth or falsity, and it hinges critically on the facts of reality. Because X is what it is, and claims to the contrary are not identifications of reality. And claiming that X is what it is, *is* an identification of reality.
The remarks I just made are not affected by the level of knowledge of the two speakers -- so long as they both have enough knowledge to understand the proposition and so long as they are both considering that same proposition. It is certainly possible that one of the two will *know* that the proposition is true, while the other one will *not know* that the proposition is true. Knowledge is contextual.
It is entirely possible, then, that I will have a valid proposition whose truth status I do not know. I can still evaluate the level of evidence for it, of course. It could be possible, or probable.
PropositionsBy Ken LivingstonDate: Tue, 6 Sep 1994 17:51:54 ESTFrom: Ken Livingston LIVINGST@vaxsar.vassar.eduTo: Multiple recipients of list AYN-RAND firstname.lastname@example.orgSubject: Re: Opening essayI want to add my voice to those who have thanked Jimmy Wales for his fine opening salvo in the discussion of ITOE. It has the virtue that it both clarifies a number of important distinctions and raises vital questions. Some of the questions it raises for me are these.
1. The idea that a word is the means of transforming concepts into mental concretes struck me as an odd notion the very first time I read it, and it only becomes more peculiar to me as time passes. In what sense is the concept not already a mental concrete? Some distinctive event must occur in the brain upon which the concept as a psychological phenomenon supervenes. In what sense is that not concrete? There is a strong intimation in ITOE that there are no concepts without words, and that therefore the conceptual faculty is peculiar to human beings.
The evidence overwhelmingly suggests that this is not so. The conceptual function, which integrates and differentiates, is characteristic of all organisms with specialized cells for mediating perception-action links (basically, that's going to include most animals), though of course the sophistication and complexity of the conceptual *systems* that these organisms can develop vary widely. And there does seem to be a genuinely large gap in complexity between humans and the rest of the animal kingdom. I do not doubt that language is key to this gap. But it is not necessary for the establishment of concepts, nor even for relatively sophisticated systems of concepts. Indeed, the recent developmental literature strongly suggests that it is the acquisition of the abstract concept of "categories" that enables the explosive development of the lexicon between about 15 and 18 months of age (see, e.g., paper by Gopnik and Meltzoff in the journal Child Development, August 1987), not the other way around. So it seems to me that the theory of concepts is going to have to be broadened beyond the one outlined in ITOE, and that will entail a broadening of the notion of propositions as well. I think it perfectly reasonable to believe that my dog manipulates certain very sensible propositions -- i.e., rule-governed sequences of simple concepts.
On this last point, Jimmy's excellent distinction between sentences and propositions (which many philosophers of mind fail to make at just the wrong moments -- see the work of Paul Churchland, e.g.) looms large.
Propositions comprise a larger set than sentences, not only when viewed across the phylogenetic scale, but within the minds of individual humans as well. And the same goes for the relationship between concepts and words.
2. One of the things that Objectivists have understood well during all of the years when cognitive scientists and philosophers were spinning their wheels in the muddly terrain of possible-world semantics and other arcane theories of meaning is that meaning is at bottom about reference. Jimmy does a very nice job of highlighting that fact, and an excellent job of distinguishing the conditions for meaning and the conditions for truth. But there are some problems here that won't go away, and I'd enjoy some discussion of at least a couple of them.
First problem: On a referential account, the meaning of a concept is what it picks out in reality. And Jimmy writes that "each concept or proper name in the proposition implicitly accepts that the law of identity applies to its referent...The existent referred to...is what it is -- its characteristics constitute its identity." That seems right to me as far as it goes, but a concept picks out a class of things which are not generally identical to one another -- that's what the mechanism of measurement omission buys you. So, the referent of a concept isn't *all* of the characteristics of the members of the class of things to which it refers, only those in the common denominator.
That makes the problem of _salience_ central to the problem of how concepts are formed, and therefore to how they refer. Assuming that I've acquired the concept OBJECT, there are an enormous number of ways in which I might organize all of the objects around me in my study into categories. Why do I select the particular ones that I do? I don't see any way to avoid an answer that is essentially teleological in character, and at least in the human case (and probably quite far down the phylogentic scale as well) a proper theory of attention will also be required. The problem of concepts lives and breaths in its own context of other mental capacities.
Second Problem: I'm very worried about a theory of meaning in which meaning depends only on direct reference to an actual existent. When A. G. Bell conceived the telephone, were the concepts meaningless because no telephone yet existed? Is the concept of Galt's Gulch meaningless because there is no such place? Art and the world of human invention generally are full of concepts that do not refer to things that actually exist. One might try to fix up the theory by positing (minimally) that the things to which the concepts refer must be *possible* to be meaningful, but often one doesn't know whether the proposed invention is possible without lots of R&D. So does that mean that the concepts are meaningless until such time that it becomes clear that the invention is possible? Then what is the content of my thought during that period? Is it possible that meaningless thought could give rise to something real and concrete?
The answer (and it's an obvious answer for Objectivists, though apparently imponderable for many in the anti-realist camp philosophically), is to show how concepts, including fictional ones, are ultimately anchored or grounded in reality. Somewhere in the chain of concepts is a path back to things that are real and known by the evidence of the senses. Galt's miraculous motor is meaningful because we understand about real motors, real energy, and have the concept EFFICIENCY as defined in the real world. The fact that the propositions expressing the characteristics of this motor do not refer to an actual object isn't what's important, so long as the component concepts have real referents. But note what happens when you fix up the theory this way. The concept UNICORN, for example, is suddenly quite meaningful! It's a horsey sort of thing with a single horn in the midst of its forehead, white in color, etc. -- concatenations of quite meaningful concepts. So, it inherits its meaning from meaningful components. And the same kind of story (though the chain is longer and more fragile) is going to run for things like the concept GOD. The upshot is that I don't think we're going to be able to dismiss concepts like these as meaningless without dismissing as also meaningless the concepts that enable art and invention, and that would be an awkward conclusion. The domain of (human) concepts is complex in ways that itself resists simple classification.
The solution is to let the meaning/truth distinction cut a little differently. Unicorn is meaningful because its component concepts have real referents. In fact, it won't be long before the genetic engineers can build us one, I suspect. Those unicorns won't have magical control over strange powers, but even that idea is meaningful because it inherits the concepts of causality and force from reality. These magical concepts are meaningful, but it simply isn't *true* that any organism could actually have such powers -- this particular fictional deployment of meaningful concepts contradicts the laws of reality. That's why many of us, I suspect, find *science* fiction enjoyable but have little patience with pure fantasy. The problem isn't that it's meaningless, it's that it's absurd.
There are lots of other interesting issues raised by Jimmy's essay, but I've already gone on too long, so let me just list one more without extended comment.
3. Grounding the notion of truth in the concept of correspondence makes excellent sense and works smoothly until the issue of justification is raised. If the human mind is not omniscient, then from what vantage point is the correspondence relation itself to be examined and judged? Why aren't there ineffable propositions whose truth, real though it is, cannot be argued or demonstrated? The axioms are acknowledged by Objectivists to fall into this category, but are the axioms really the only propositions to which the restriction applies? And aren't the axioms themselves more circular than generally acknowledged? For example, the stipulation that a proposition is axiomatic just in case one cannot argue against it without deploying the proposition itself presumes some form of the principle of non-contradiction, doesn't it? I confess that I hate this whole issue (it seems to me that the answers are obvious and I find the issue boring), but I assure you that many particularly thoughtful people who are otherwise sympathetic to the philosophy get hung up on this sort of question, and I'd love to have fresh ammunition to spend. Any ideas?
Copyright 1995 Ken Livingston
Psychology and Cognitive Science
Poughkeepsie, New York 12601
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