The Univocity and Binary Nature of Truth

Count Timothy von Icarus

Intro:
I'm going to make a case against both of these assumptions. :cool:

A major difficulty for modern thought has been the move to turn truth and falsity into contradictory opposites, as opposed to contrary opposites (i.e. making truth akin to affirmation and negation). For an example of contradictory opposition, consider a number's "being prime." A number is either prime or it isn't. To say that a number is prime is to say that it is not-not-prime (i.e. double negation). For contrary opposition, consider darkness and light. Darkness is the absence of light. On a naive view, we might suppose there can be pitch darkness, a total absence of light, or a sort of maximal luminescence. The two are opposites, but they are not contradictory opposites. To say of a room that "it is light" is not to say that it admits of no darkness. Shadows are still cast in bright rooms.

No doubt, the move to make truth and falsity contradictory opposites (and thus binaries) has at times been a useful one. It is convenient to be able to assign a binary (0,1) value to propositions as a measure of their truth. For instance, it makes computation far easier.

However, I think that, if we are not careful—and we have not been—this move becomes a major step down the road to deflationism vis-à-vis truth. This is a view that I think is every bit as untenable and radical as either solipsism or epistemological nihilism, its advocates just tend to obscure this fact by ultimately deficient appeals to "pragmatism." Deflation is equivalent with saying that truth is predicated equivocally. Hence, we have "very many truths (plural)."

Reducing truth to a binary seems to edge us towards primarily defining truth in terms of "propositions/sentences" and, eventually, formalism alone, and so deflation. This is as opposed to primarily defining truth in terms of knowledge/belief and speech/writing.

The key difference is that, in the latter, there is a knower, a believer, a speaker, or a writer, whereas propositions generally get transformed into isolated "abstract objects" (presumed to be "real" or not), that exist unconnected to any intellect. Such propositions are true or false (there is no gradation) simpliciter. Such a view seems to require some dubious assumptions.

The Bad Assumptions:

First, the move to making truth primarily a property of isolated propositions seems to need to assume that propositions are intelligible in isolation from one another (meaningful simplicitier). Pace coherence theorists, we will be forced to assert that "horses have four legs" is true in such a way that its truth is not dependent on truths about "what legs are" or "what horses are," etc. This problem seems particularly tricky for those who don't want to claim that propositions are a sort of lower-case "p" platonic abstract object (whereas the idea of propositions as abstract objects is also implausible).

Seconds, for the term "true" to have any content, it must not to apply equally to all things; falsity must be at least a possibility. For my part, it's unclear to me how we can have falseness without an intellect. For instance, stars, rocks, numbers, and trees are not true or false, but rather beliefs and statements about them are. Nor will it do to have truth and falsity be properties of "language," as isolated from any consideration of language users. Rocks do not come to know things by having truths carved into them, and in a lifeless universe of random shifting sands, a proposition that happens to be spelled out in English by pure chance means nothing to anyone (even potentially).

Hence, we might take up the previously common supposition that truth has something essentially to do with the relationship between the intellect and reality. I would go a step further: "truth is primarily in the intellect and only secondarily (or fundementally) in things." Signs, statements in language, etc. can be true or false in virtue of what they mean, and meaning is likewise primarily in the mind, secondarily in things.

So, without having to make any commitments to any specific sort of correspondence or identity relationship between thought and being, we can simply leave it as "truth is the conformity or adequacy of thought to being."

This gets us to the other difficulty of reducing truth to a binary. Our knowledge does not seem to fit this binary neatly. Doubtless I can "know my friends," but it appears than I can know them "more or less"—"better or worse." I know some Arabic and Latin, but I could certainly know them better. And we often speak of coming to "truly know people" or which movies are "truer to life," etc.

Yet if truth primarily relates to beliefs, how are we to make sense of this? Is knowing someone better or worse just a matter of knowing more true propositions about them and affirming fewer false ones?

Here we get to a third common assumption at work in the drive towards truth as a univocal binary: the idea that all knowledge and belief is reducible to atomic propositions, that knowledge is the type of thing that can be atomized or is a whole that is merely the sum of its parts.

I would reject this on the grounds that lone propositions are not intelligible in themselves, in isolation. Nor does one "know a language" as a heap of isolated propositions. Further, the meaning of individual propositions often turns on our understanding of the meaning of others. Phenomenologically and psychologically, the drive to atomize knowledge—true belief—into something like a mere "database" of atomic propositions also seems implausible. This is not how we experience knowing. This move seems to have more to do with what is easy to formalize than anything else. In this, it seems like the equivalent of demanding that the lost keys be under the streetlight because it is easiest to see there.

Truth as Primarily Related to Belief and the Communication of Beliefs:

If truth primarily relates to the intellect, and so to beliefs, and these do not conform to a neat binary, then why should our consideration of truth do so? Because it is simpler? Yet we could just as well make use of the simplifying assumption, knowing it misses something, without having to lose sight of the fact that it is just this, a simplifying assumption.

If we were to insist on a "quantification of truth" (I wouldn't), we could consider both the accuracy of statements (how much they leave out) and their vagueness. With the former, we can consider cases where statements are misleading through omission (resulting in an inadequacy of the intellect to being), whereas in the latter we have cases like "how many grains of sand make a heap?" or "how tall is 'tall' vis-á-vis the truth of 'Achilles is tall.'?" Even someone who is two feet tall is still "tall" in some sense.

A key consequence of truth being based on contrariety is that it is not equivalent with affirmation and negation.

St. Thomas makes the case for this (he also adds some good arguments):

I answer that, True and false are opposed as contraries, and not, as some have said, as affirmation and negation. In proof of which it must be considered that negation neither asserts anything nor determines any subject, and can therefore be said of being as of not-being, for instance not-seeing or not-sitting. But privation asserts nothing, whereas it determines its subject, for it is "negation in a subject," as stated in Metaph. iv, 4: v. 27; for blindness is not said except of one whose nature it is to see. Contraries, however, both assert something and determine the subject, for blackness is a species of color. Falsity asserts something, for a thing is false, as the Philosopher says (Metaph. iv, 27), inasmuch as something is said or seems to be something that it is not, or not to be what it really is. For as truth implies an adequate apprehension of a thing, so falsity implies the contrary.

Summa Theologiae - I:I, Q.17, A4, R

https://www.newadvent.org/summa/1017.htm#article4

The benefit here is that we avoid falling into a very common false dichotomy:

Either there is one univocal measure of truth, but which all propositions can be correctly assigned the proper binary value, or truth varies according to the construct/game in which it is defined.

We also get a more nuanced view of truth that can extend beyond sign systems. For instance, there are the "false crabs," likenesses that are more or less "true to life," the "true knight" who will defend the innocent rather than robbing them, etc. The truth by which someone is a "true knight" or an artifact is "true to its purpose" is not identical with the truth by which "5 is prime" is true, but neither is it unrelated. All involve judgements about the adequacy of intellect to being.

Avicenna introduces a hierarchy to this analogy, based truths that are prior in the order of existence, which is also a helpful expansion.

Count Timothy von Icarus

I will just note that the path from the elimination of analogy vis-a-vis goodness and beauty to total equivocity (extreme relativism or nihilism) is quite similar. Philosophy first removes the option of analogy. It then discovers that a single univocal measure of goodness, truth, or beauty is seemingly impossible. Faced with this result, it has a "slide into multiplicity" and produces a multitude of isolated truths, goods, and beauties, with each varying by culture, individual, or even context.

bongo fury

Influenced by chapter IV of Nelson Goodman's Languages of Art, I go for unanimity and a ternary nature of truth.

A bright room can be controversially white (or a voltage controversially on), and a shadow controversially black (the voltage controversially off), but the whites (or on's) are uncontroversially not blacks (not off's).

Grain collections that are heaps are uncontroversially not pittances and vice versa, but not all of both are uncontroversially one or the other. Some are controversially somewhere in between. But none are even controversially both. The two fuzzy borders (of "heap" and "pittance") are kept far enough apart.

Obviously this is relative to a system. Sometimes the system catches on, other times a continuous spectrum is preferred.

Obviously too there can't be free expression for Humpty Dumptys.

antonym — bongo fury

Leontiskos

Seconds, for the term "true" to have any content, it must not to apply equally to all things; falsity must be at least a possibility. For my part, it's unclear to me how we can have falseness without an intellect. For instance, stars, rocks, numbers, and trees are not true or false, but rather beliefs and statements about them are. Nor will it do to have truth and falsity be properties of "language," as isolated from any consideration of language users. Rocks do not come to know things by having truths carved into them, and in a lifeless universe of random shifting sands, a proposition that happens to be spelled out in English by pure chance means nothing to anyone. — Count Timothy von Icarus

There is a rather long ongoing discussion on this topic beginning on page 12 of another thread.

the idea that all knowledge and belief is reducible to atomic propositions, that knowledge is the type of thing that can be atomized or is a whole that is merely the sum of its parts. — Count Timothy von Icarus

See:

At the end of the day it is not merely sentential. Knowledge/truth is more than a set of sentences. — Leontiskos

-

St. Thomas makes the case for this — Count Timothy von Icarus

This is interesting insofar as Thomas delineates an assertion of falsehood from a negation, which we came up against in the threads on Kimhi.

But I don't see Thomas saying that the true and the false are not contradictories, nor do I see Aristotle saying that. Classically, true/false are contradictories:

“opposite assertions cannot be true at the same time” (Metaph IV 6 1011b13–20) — SEP on Aristotle and Non-Contradiction

(The law of the excluded middle must also be mixed in.)

Edit: For Aristotle contraries allow for an unexcluded middle, but true/false do not, therefore true/false are not contraries. Cf. Metaphysics IV.7 - 1011b23.

Leontiskos

↪Count Timothy von Icarus

, I think you are saying that because knowledge can be more or less, therefore propositions about knowledge can be more or less true. For example, "I know how to build a bridge." That is a claim that could be true in degrees, so to speak, spanning from the child with his Erector set to the engineer building a suspension bridge. But I don't see how we go from this idea to the claim that true/false are contraries and not contradictories. Perhaps you need to define what you mean by "contrary."

Count Timothy von Icarus

↪Leontiskos

But I don't see Thomas saying that the true and the false are not contradictories, nor do I see Aristotle saying that. Classically, true/false are contradictories:

What about the quote from the OP?

I answer that, True and false are opposed as contraries, and not, as some have said, as affirmation and negation [i.e. contradictory]. In proof of which it must be considered that negation neither asserts anything nor determines any subject, and can therefore be said of being as of not-being, for instance not-seeing or not-sitting. But privation asserts nothing, whereas it determines its subject, for it is "negation in a subject," as stated in Metaph. iv, 4: v. 27; for blindness is not said except of one whose nature it is to see. Contraries, however, both assert something and determine the subject, for blackness is a species of color. Falsity asserts something, for a thing is false, as the Philosopher says (Metaph. iv, 27), inasmuch as something is said or seems to be something that it is not, or not to be what it really is. For as truth implies an adequate apprehension of a thing, so falsity implies the contrary.

https://www.newadvent.org/summa/1017.htm#article4

opposite assertions cannot be true at the same time” (Metaph IV 6 1011b13–20)

Yes, something cannot be black and not-black, just as a sentence cannot be true and not-true. This is because being involves contradictory opposition, as does affirmation and negation. For instance, opposing universal and particular assertions would involve negations of each other (i.e. the square of opposition).

Obviously, the truth of a statement often depends on its context. "Peanuts are healthy" is true as respects most men, and false as respects the person with the peanut allergy. Truth and falsity are mutually exclusive in cases where the truth (or falsity) of a statement would both affirm and deny being without qualification (being and non-being are contradictory).

Thomas also says that univocal predication is proper to the discipline of logicians. If you're building a syllogism, then the truth or falsity of your premises vis-a-vis predication should involve contradiction. It would be problematic if they didn't.

I always assumed Thomas's point here was pointing back to Avicenna and ontological truth. There is also truth as adequacy of being to the divine intellect (truth most perfectly) addressed in the prior question (16).

↪Leontiskos

Perhaps you need to define what you mean by "contrary."

Truth represents a perfect adequacy between the intellect and being. Falsity is the absence of this adequacy. If any inadequacy makes a belief or statement false, that seems to be quite problematic. For one, it would mean that all or almost all of the "laws" of the natural sciences are false, along with our scientific claims.

A theory or hypothesis might not perfectly conform to reality, but this doesn't make it completely inadequate either.

Pretty sure you can relate this to the Square of Opposition as well. For instance, "all elephants have big ears” cannot be true at the same time as “no elephants have big ears," but they can both be false. Whereas with "all elephants have big ears" and "some elephants do not have big ears" one must be true and the other false.

A major difficulty for modern thought has been the move to turn truth and falsity into contradictory opposites, as opposed to contrary opposites (i.e. making truth akin to affirmation and negation). — Count Timothy von Icarus

I answer that, True and false are opposed as contraries, and not, as some have said, as affirmation and negation. (Aquinas)

Kimhi is helpful here:

A capacity meta logou is categorematic: it is specified by a verb -- say, to heal -- and its positive and negative acts are contraries. A logical capacity is syncategorematic: it is specified by a proposition, and its positive and negative acts are contradictories. — Thinking and Being, 61

He adds this footnote:

Capacities meta logou are two-way capacities because they involve logical capacities. It is because doctors must judge how best to heal their patients that they can also judge how best to poison them. — Thinking and Being, 61

On this understanding of Aristotle, a contrary pair will display positive and negative acts involving a verb, whereas a contradictory pair either affirms or denies the truth of a proposition. Roughly, (A thinks p, A thinks ~p) vs. (p, ~p).

So yes, the distinction you're making between contraries and contradictories is extremely important. The essential unity of the thinker with the thought, the knower with the world, can only be shown by rejecting, as Kimhi does, the idea that a proposition can be true or false in the absence of some context of assertion.

So, without having to make any commitments to any specific sort of correspondence or identity relationship between thought and being, we can simply leave it as "truth is the conformity or adequacy of thought to being." — Count Timothy von Icarus

Predating Tarski by several centuries! And the challenge to that, coming from people like Kimhi and Sebastian Rödl (who I'm now reading with great interest) is, Are we sure that thought and being exist in the sort of relationship that needs to be "conformed" or "adequated"? Can we paint a plausible picture that is at bottom monistic? I'm still working on that, and I want to do an OP soon that lays out some of Rödl's ideas about the Fregean force/content distinction.

Wayfarer

Reducing truth to a binary seems to edge us towards primarily defining truth in terms of "propositions/sentences" and, eventually, formalism alone, and so deflation. This is as opposed to primarily defining truth in terms of knowledge/belief and speech/writing.

The key difference is that, in the latter, there is a knower, a believer, a speaker, or a writer, whereas propositions generally get transformed into isolated "abstract objects" (presumed to be "real" or not), that exist unconnected to any intellect. Such propositions are true or false (there is no gradation) simpliciter. Such a view seems to require some dubious assumptions. — Count Timothy von Icarus

I would argue that the underlying 'dubious assumption' here is that the world, and by extension truth, exists independently of any mind or knowing subject. This move to isolate propositions as abstract objects, true or false simpliciter, overlooks the relational nature of truth. From an idealist perspective, truth emerges within the interplay between the knower and the known, and severing this connection risks reducing truth to a sterile formalism. Hence also:

The essential unity of the thinker with the thought, the knower with the world, can only be shown by rejecting, as Kimhi does, the idea that a proposition can be true or false in the absence of some context of assertion. — J

Sebastian Rödl — J

I've read about his books and tried to tackle some of his papers, but I'm finding him difficult reading. I would be pleased if there was another here with some interest.

Count Timothy von Icarus

↪J

So yes, the distinction you're making between contraries and contradictories is extremely important. The essential unity of the thinker with the thought, the knower with the world, can only be shown by rejecting, as Kimhi does, the idea that a proposition can be true or false in the absence of some context of assertion.

Agreed, although I don't know if "context of assertion" is the right framing. Beliefs can be true or false without being needing to be "asserted."

↪J

Are we sure that thought and being exist in the sort of relationship that needs to be "conformed" or "adequated"?

Well, presumably we need to be able to explain false beliefs and false statements. There is adequacy in the sense of "believing the Sun rotates around the Earth" being, in important ways, inadequate.

Can we paint a plausible picture that is at bottom monistic?

Monistic in what sense?

So yes, the distinction you're making between contraries and contradictories is extremely important. The essential unity of the thinker with the thought, the knower with the world, can only be shown by rejecting, as Kimhi does, the idea that a proposition can be true or false in the absence of some context of assertion.

Agreed, although I don't know if "context of assertion" is the right framing. Beliefs can be true or false without being needing to be "asserted." — Count Timothy von Icarus

I don't much like "context of assertion" either, but the deeper challenge here is whether, in fact, a belief can be true or false without being asserted. I know that sounds absurd, but so much depends on how we construe "assertion," and the long thread on Kimhi a few months back revealed a lot of work to be done on this question.

Are we sure that thought and being exist in the sort of relationship that needs to be "conformed" or "adequated"?

Well, presumably we need to be able to explain false beliefs and false statements. There is adequacy in the sense of "believing the Sun rotates around the Earth" being, in important ways, inadequate. — Count Timothy von Icarus

Yes. One problem for being/thinking monism a la Kimhi is that it seems to imply that any valid thought also has to be true. That can't be right, so we need to work out whether there really is a concept of validity independent of truth. Again, sounds absurd -- there has to be, right?! -- but stand-alone "validity" turns out to be very tricky. The monist wants to be able to say that there is no disjunction between truth and validity -- that there is something ill-formed or incoherent about "A thinks ~p", as opposed to "A doesn't think p". This is the problem from Parmenides that Kimhi begin T&B with, you may recall: How can we think that which is not?

Can we paint a plausible picture that is at bottom monistic?

Monistic in what sense? — Count Timothy von Icarus

"Thinking cannot be dependent for its success on anything that is external to it." — Kimhi, 23

Monism in that sense, a tall order. Rödl, another monist as far as I can tell, subtitles his book Self-Consciousness and Objectivity as "An Introduction to Absolute Idealism."

Leontiskos

What about the quote from the OP? — Count Timothy von Icarus

I don't see it. A good entry point into Aquinas' topic is to read the objections, and none of the objections are claiming that true/false are contradictory. He is in large part asking whether they belong to a common genus, i.e. assertion. His answer is, "Yes, they belong to the common genus of assertion."

Yes, something cannot be black and not-black — Count Timothy von Icarus

And to say that something is not-black is to say that it is false that it is black. Something cannot be true and false, therefore the true and the false are contradictory:

Edit: For Aristotle contraries allow for an unexcluded middle, but true/false do not, therefore true/false are not contraries. Cf. Metaphysics IV.7 - 1011b23. — Leontiskos

Truth and falsity are mutually exclusive in cases where... — Count Timothy von Icarus

I would challenge you to give a case where truth and falsity are not mutually exclusive.

I always assumed Thomas's point here was pointing back to Avicenna and ontological truth. — Count Timothy von Icarus

Okay, that's fair, but ontological truth/falsity as they exist primarily in the intellect. I guess I didn't realize that in the OP you were talking about true/false as states of the intellect. For example, you critique a thesis regarding propositions, and seem to in some way question the LEM:

Such propositions are true or false (there is no gradation) simpliciter. Such a view seems to require some dubious assumptions... — Count Timothy von Icarus

Maybe it would be helpful to circle back and simplify the position you are challenging in the OP. What objectionable thesis does your opponent hold?

I can see that Aquinas would agree that the intellect which is true does not contradict the intellect which is false, in the ontological sense. But in this case we are not talking about predications or assertions of falsity. Surely we agree that "p is false" contradicts "p is true."

Truth represents a perfect adequacy between the intellect and being. Falsity is the absence of this adequacy. If any inadequacy makes a belief or statement false, that seems to be quite problematic. For one, it would mean that all or almost all of the "laws" of the natural sciences are false, along with our scientific claims.

A theory or hypothesis might not perfectly conform to reality, but this doesn't make it completely inadequate either. — Count Timothy von Icarus

Okay, that is helpful. But remember that falsity is a privation, not an absence. If the intellect has no truth it cannot have falsity.

Count Timothy von Icarus

↪J

I know that sounds absurd, but so much depends on how we construe "assertion," and the long thread on Kimhi a few months back revealed a lot of work to be done on this question.

:rofl: It does. Is the idea here that just thinking something is asserting it? Surely a woman can suspect her husband of cheating, and thereby hold a belief that is either true or false, without having to utter or write down that belief, right?

I have definitely felt stupid and laughed at myself for believing (false) things that I never expressed.

The monist wants to be able to say that there is no disjunction between truth and validity -- that there is something ill-formed or incoherent about "A thinks ~p", as opposed to "A doesn't think p".

Ah, I think I know a good one for this sort of thing. in Metaphysics, IX 10, Aristotle distinguishes between two kinds of knowledge/truth:

-Asytheta: truth as the conformity of thought and speech to reality (whose opposite is falsity); and

-Adiareta, truth as the grasping of a whole, apprehension (whose opposite is simply ignorance).

It might make sense to think about our knowledge of things as "passing back and forth between these two modes." For instance, because they are very complex topics, it took me a lot of reading and reflection to understand "Plotinus' conception of divine freedom" or "Hegel's dialectic." But now, having studied them, I can also consider them as unified wholes and understand or vet propositions that reference them without having to "unpack" all that I know about them. And it seems to me that the better one understands something the more one is able to consider it as an undivided whole (of course, the thing in question being more of a true unity matters too).

From my notes on similar ideas:

In Ad Thalassium 60, St. Maximus the Confessor argues for the superiority of unified and direct experience, as opposed to discursive reasoning/knowing. Similarly, in Philosophiae Consolationis (4.6), Boethius argues that reason is to the intellect as time is to eternity, and what “circle” is to “center.” This is because it is “proper” for reason to be “diffused” (diffundi, i.e., scattered or spread) about many things, and then to gather from them a single cognition (i.e., unifying the “Many” into a “One”). Pseudo-Dionysius makes a similar point, (De Divinis Nominibus, 7.2) claiming that souls have rationality insofar as they “diffusedly encircle” (diffusiue circueunt) the truth of multiple existent things. Conversely, the intellect considers one simple truth and grasps the cognition of a whole multitude in it.

So, to this question:

This is the problem from Parmenides that Kimhi begin T&B with, you may recall: How can we think that which is not?

Discursive knowledge involves combining, concatenating, estimating, etc. This is a "feebler" sort of knowledge. It is possible to combine things inappropriately, etc.

We can chalk this up to finitude. You can explain it in naturalistic terms too. For perception to occur, signals in the form of various types of energy in the environment must be transformed into electrochemical signals within/between neurons before becoming “present” in phenomenal awareness. This transformation of signals is not lossless. Organism’s sensory systems must be extremely selective about what information they take in from the environment. Taking in even a small fraction of the total entropy an organism is exposed to in the ambient environment would cause it to be overwhelmed by entropy.

To see why, consider the total number of molecules interacting with the surface of an organism at any given moment. Even leaving aside the difficulties in being able to develop sense organs sensitive enough to take in all this information, it is clear that sensitivity to the environment at this level of granularity would require a massive neurological apparatus just to encode the incoming data, let alone sift through it for relevance. Thus, which signals are allowed to pass from the environment into an organism's nervous system must be curated such that most information does not pass into the nervous system. Representationalists are correct that this facet of sensory systems introduces a great deal of bias into perception, just not about some of their other assumptions IMO.

Terrance Deacon has some good stuff on this and the semiotics he (and everyone else in biology) uses is derived from the Scholastic Doctrina Signorum: https://www.researchgate.net/publication/281155120_Steps_to_a_science_of_biosemiotics

Thinking cannot be dependent for its success on anything that is external to it.

Maybe I'm misreading it, but this seems implausible. My success at diagnosing a disease as a doctor depends on the quality of my diagnostic equipment, not just my own thought. My success at correctly reading of the letters on the chart at the optometrists depends on the curvature of my eye's lens, etc. These are all external to thought.

Count Timothy von Icarus

↪Leontiskos

And to say that something is not-black is to say that it is false that it is black. Something cannot be true and false, therefore the true and the false are contradictory:

Something cannot be true and false because nothing can both be and not be anything, in the same way, at the same time, without qualification.

But sentences can be true and false with qualification. Consider: "Ron Artest is good." Well, he was an NBA starter, so if you were talking basketball back in his prime, this is true, he was good. If you're talking other behavior? Well he jumped into the stands to attack a fan who threw a drink at him and attacked some random uninvolved person instead. This seems to qualify as "not good." When it comes to logic, our predicates should be univocal, and this sort of ambiguity should be ruled out.

But even for propositions like: "you had a good day," the truth of this is not reducible to a binary. Sometimes, if asked if we had a good day, we don't really know. Does this mean that there is no truth as to whether or not anyone ever has a good day? That the sentence is not truth-apt? I don't think so.

Okay, that's fair, but ontological truth/falsity as they exist primarily in the intellect. I guess I didn't realize that in the OP you were talking about true/false as states of the intellect. For example, you critique a thesis regarding propositions, and seem to in some way question the LEM:

Well, the problem that I think is most acute is ascribing truth and falsity primarily to propositions. Actually, it seems that in a lot of philosophy they are the only bearers of truth. That's what leads to, IMO, bad conceptualizations of knowledge.

Surely we agree that "p is false" contradicts "p is true."

:up:

Provided the terms are clear. But I suppose my point is that contradiction in this case is used as the lens through which truth as a whole is analyzed. This leads to concepts like "the one true canonical database of all true propositions" and when concepts like this are shown to be flawed, there is a crash into deflation. Truth ends up being either univocal, and contained in "the one true set of propositions," or else entirely relativized (with some appeals to "pragmatism" as a backstop).

Leontiskos

What objectionable thesis does your opponent hold? — Leontiskos

So:

The Univocity and Binary Nature of Truth

...

I'm going to make a case against both of these assumptions. — Count Timothy von Icarus

Let me try to do what I want you to do. I will try to capture each position you oppose with a thesis:

The univocity of truth: "Truth" means only and precisely one thing.
The binary nature of truth and falsity: Propositions which are true and propositions which are false are qualitatively different, and have no mediating degrees between them.

Are these the positions you are opposing? Or is it something else?

Count Timothy von Icarus

↪Leontiskos

The first: Yes.

The second, no. My point is that it is not only or even primarily propositions that are true or false. We have beliefs that can be true or false. Presumably, even people who cannot speak have beliefs. We have theories that get falsified.. We have models that can be more or less true to what they model. Etc.

Propositions cannot be both true and false without qualification. However, we can have propositions that make statements about how true something is to some ideal. "This is a good car." Does this reduce to a binary? I don't think so. Is it simply not truth-apt? I don't think this works either, because a car that won't start is in an important sense not a good car. It isn't true to its purpose.

The same is true for "its dark outside." Darkness is contrary, but the adequacy of thought to being here is contradictory? No doubt it wouldn't make sense to say it is both dark and not-dark out without qualification.

Is the idea here that just thinking something is asserting it? — Count Timothy von Icarus

Not quite. Think of it in terms of Frege's "force" as equivalent to (one sense of) "assertion". The question is then: How does the "content" (of the force/content distinction) make itself known independently? If "p" is different from "I think p", how exactly does p come to be present to us? This quote from Rödl captures the problem:

Philosophers are in the habit of indicating the object of judgment by the letter p. There is an insouciance with respect to this fateful letter. It stands ready quietly, unobtrusively, to assure us that we know what we are talking about. For example, when we do epistemology, we are interested in what it is for someone to know—know what? oh yes: p. If we inquire into rational requirements on action or intention, we ask what it is to be obliged to—what? oh yes: see to it that p, intend that p, if p then q, and so on. However, if we undertake to reflect on thought, on its self-consciousness and its objectivity, then the letter p signifies the deepest question and the deepest comprehension. If only we understood the letter p, the whole would open up to us. — Self-Consciousness & Objectivity

This point of view is very congenial to yours, I would think, since Rödl is doubting whether "p" -- a proposition -- could possibly do the things, all by itself, that formalism says it can. A thinker is required.

Sebastian Rödl
— J

I've read about his books and tried to tackle some of his papers, but I'm finding him difficult reading. I would be pleased if there was another here with some interest. — Wayfarer

Me, definitely. Working my way through Self-Consciousness and Objectivity now.

Leontiskos

Something cannot be true and false because nothing can both be and not be anything, in the same way, at the same time, without qualification. — Count Timothy von Icarus

Right.

When it comes to logic, our predicates should be univocal, and this sort of ambiguity should be ruled out. — Count Timothy von Icarus

Yes, on pain of equivocation.

But even for propositions like: "you had a good day," the truth of this is not reducible to a binary. Sometimes, if asked if we had a good day, we don't really know. Does this mean that there is no truth as to whether or not anyone ever has a good day? That the sentence is not truth-apt? I don't think so. — Count Timothy von Icarus

But is this a matter of the univocity of truth or of the ambiguity of language? And is the LEM being rejected if the truth-value is not binary?

Usually the non-binary response will be an attempt to distinguish different parts of the day instead of collecting it into a single whole.

Well, the problem that I think is most acute is ascribing truth and falsity primarily to propositions. Actually, it seems that in a lot of philosophy they are the only bearers of truth. That's what leads to, IMO, bad conceptualizations of knowledge. — Count Timothy von Icarus

Yes, I agree. This is happening a lot in that thread I referenced in my first post.

But I suppose my point is that contradiction in this case is used as the lens through which truth as a whole is analyzed. This leads to concepts like "the one true canonical database of all true propositions" and when concepts like this are shown to be flawed, there is a crash into deflation. Truth ends up being either univocal, and contained in "the one true set of propositions," or else entirely relativized (with some appeals to "pragmatism" as a backstop). — Count Timothy von Icarus

Okay, I sort of see that. I do think discursive/propositional knowledge needs to be grounded in something more, but I don't see the critiques of classical notions of truth as a great threat.

"I took a magnifying glass to every part of your vehicle and found a squeaky axle. Therefore I will not drive or trust it."
"Do you have some alternative vehicle to propose?"

...That's about how I view the attack on classical notions of truth. The naysayers look like contrarian novelty-seekers who are unwilling to engage in the foundational philosophical act of providing constructive alternatives. They take any imperfection to be a fatal flaw, and end in some variety of skepticism.

-

The second, no. — Count Timothy von Icarus

Okay, so how would you characterize the view you take exception to?

However, we can have propositions that make statements about how true something is to some ideal. "This is a good car." Does this reduce to a binary? I don't think so. Is it simply not truth-apt? I don't think this works either, because a car that won't start is in an important sense not a good car. It isn't true to its purpose. — Count Timothy von Icarus

Regarding an ideal, the nurse might ask, "On a scale of 1 to 10, how much pain are you in?" This obviously requires something other than a binary answer.

When I imagine a conversation beginning with, "This is a good car," I don't foresee non-binary truth values. The interlocutor might say any number of things:

Damn right it is!
It is a good car, but the rust is just beginning to set in.
I wouldn't call a car that cannot idle without killing "a good car."

I haven't read much on this specific subject, but I am not aware of anti-univocalists who think truth is not predicated univocally. And even if we are talking about truth as conformity to an ideal, this does introduce degrees of truth but it does not necessarily introduce equivocity.

T Clark

However, I think that, if we are not careful—and we have not been—this move becomes a major step down the road to deflationism vis-à-vis truth. — Count Timothy von Icarus

I wasn't familiar with the term "deflationism so I looked it up. I'm still not sure I understand what it means, so I'm not sure what I'm going to say is relevant to your discussion.

Ever since I started thinking about it from a philosophical perspective, I have believed that the idea of truth, what you call binary truth, is over-empathized in western philosophy. I don't think it is a property that is central to how real people know about the world and make decisions about their everyday lives. I'm not sure if that makes me a deflationist.

"truth is primarily in the intellect and only secondarily (or fundementally) in things." — Count Timothy von Icarus

As you note, truth only applies to propositions. If I understand what you've written, you and I agree that we don't generally know the world as a bunch of propositions. I'll go further - the nature of the world cannot be expressed in propositions except in a trivial and partial manner. As you say - ...the move to making truth primarily a property of isolated propositions seems to need to assume that propositions are intelligible in isolation from one another (meaningful simplicitier)."

This is a view that I think is every bit as untenable and radical as either solipsism or epistemological nihilism, its advocates just tend to obscure this fact by ultimately deficient appeals to "pragmatism." — Count Timothy von Icarus

Guilty as charged.

As I indicated at the beginning of this post, I'm not sure how relevant it is to your discussion.

Count Timothy von Icarus

↪Leontiskos

Usually the non-binary response will be an attempt to distinguish different parts of the day instead of collecting it into a single whole.

This works sometimes. I don't think it always does; that is, we cannot reduce thought down to "atomic propositions."

But even if we can, does this mean the higher level statement has no truth value at all?

Of course, there is also the issue of the adequacy of language to thought and experience and the true unity of composites described under one name.

But is this a matter of the univocity of truth or of the ambiguity of language? And is the LEM being rejected if the truth-value is not binary?

Both IMO. Language involve analagous predication because being involves analogy.

I don't see how LEM is directly at stake. LEM is defined in terms of negation and negation and affirmation are contradictories. If we say "it is dark outside" is true, then this entails that it is not "not dark" according to however "dark" is used in the first instance.

"I took a magnifying glass to every part of your vehicle and found a squeaky axle. Therefore I will not drive or trust it."

A fair characterization. But I think the view of truth as related primarily to isolated (often "atomic") propositions has a wide reach even outside of those who go all the way over into deflation. It affects a lot of analytic thought.

Okay, so how would you characterize the view you take exception to?

Here is one based on a class I had on the philosophy of AI:

Truth is something that applies to propositions (and only propositions). All propositions are either true or false. If this causes issues (which it seems it will), this is no problem. All propositions are decomposable into atomic propositions, which are true or false. Knowledge is just affirming more true atomic propositions as respects some subject and fewer false ones. Thus, knowledge can accurately be modeled as a "user" database of atomic propositions as compared to the set of all true atomic propositions.

"Artificial" seems to like the key word to apply here.

Alternatively, there are all the deflationary approaches, which often make some of the same assumptions, particularly that truth is primarily about propositions (or more broadly "how a community uses language.") There is the same issue here of missing the "adequacy of thought to being."

↪T Clark

If I understand what you've written, you and I agree that we don't generally know the world as a bunch of propositions.

Exactly, and not all knowledge is discursive knowledge. It's a sad philosophy that has to look at the climax of Dante's Commedia in Canto XXXIII of the Paradisio, his appeals to the inadequacy of language and memory, and say "well he's just sputtering nonsense." And it's just as sad to have to say something like "we can appreciate the words but not its rational content," since the Comedy is one of the very best (IMO the best) instances of philosophy breathed into narrative form.

Plato says something similar in Letter VII. He sort of explains why he uses images, dialogues, and symbolism instead of trying to write something like a dissertation—because what he wants people to understand cannot be communicated that way.

↪J

This point of view is very congenial to yours, I would think, since Rödl is doubting whether "p" -- a proposition -- could possibly do the things, all by itself, that formalism says it can. A thinker is required.

Well, according to narrow views of formalism there is very little it can do. It's just the rules, and an AI can do "logic" as well (probably better) than any man. But of course people always end up equivocating on this extremely narrow definition because if that's all logic was it would be completely uninteresting. What we really care about when we read about developments in formal logic is why people think these developments are worthwhile.

Not quite. Think of it in terms of Frege's "force" as equivalent to (one sense of) "assertion". The question is then: How does the "content" (of the force/content distinction) make itself known independently? If "p" is different from "I think p", how exactly does p come to be present to us? This quote from Rödl captures the problem:

I've only read Rödel on Hegel. This is the sort of thing that might get resolved with the distinction between objective and subjective logic, but I don't know how much he runs with the Logics.

Leontiskos

This works sometimes. I don't think it always does; that is, we cannot reduce thought down to "atomic propositions."

But even if we can, does this mean the higher level statement has no truth value at all? — Count Timothy von Icarus

I would want to think in terms of intellects and intention. If someone asks, "Did you have a good day?," are they asking a question with a binary answer-constraint, are they inviting someone to share about their day, or are they doing something else? And if someone says, "I had a good day," presumably they are making an assertion and all assertions are truth claims (in a rather binary sense).

I think the equivocity attaches to the term 'good' rather than to the truth value, but even an assertion utilizing analogical equivocity must have a determinate and assertable form. If it doesn't then there is not any unitary thing being asserted.

Think about an interaction between two co-workers:

"That was a great day!"
"Eh."

Now the co-worker who is responding may not be opposed to the material proposition, but rather to the emphatic sense in which it was said (and therefore its circumstantial meaning). The question for the equivocity of truth is this: if the first statement is not meant to be true in a univocal sense, then is it possible for the respondent to disagree with it? To agree? To even understand what is being said?

I am largely opposed to the idea that truth is analogically equivocal, even if it may be in a deep theological sense.

Both IMO. Language involve analagous predication because being involves analogy. — Count Timothy von Icarus

Language involves analogical predication, but that doesn't guarantee that truth is an analogical predication.

I don't see how LEM is directly at stake. — Count Timothy von Icarus

Okay, let's leave that aside for the moment.

A fair characterization. But I think the view of truth as related primarily to isolated (often "atomic") propositions has a wide reach even outside of those who go all the way over into deflation. It affects a lot of analytic thought. — Count Timothy von Icarus

True.

Here is one based on a class I had on the philosophy of AI:

Truth is something that applies to propositions (and only propositions). All propositions are either true or false. If this causes issues (which it seems it will), this is no problem. All propositions are decomposable into atomic propositions, which are true or false. Knowledge is just affirming more true atomic propositions as respects some subject and fewer false ones. Thus, knowledge can accurately be modeled as a "user" database of atomic propositions as compared to the set of all true atomic propositions.

"Artificial" seems to like the key word to apply here.

Alternatively, there are all the deflationary approaches, which often make some of the same assumptions, particularly that truth is primarily about propositions (or more broadly "how a community uses language.") There is the same issue here of missing the "adequacy of thought to being." — Count Timothy von Icarus

Thanks for the sketch. There is a lot going on here. It's hard to pinpoint the error, given that a number of errors seem to be at play.

I suppose I'll have to give this more thought. I have seen the same thing you are seeing, but I've never been able to muster a tidy critique.

Leontiskos

@Count Timothy von Icarus

It is worth noting that Aquinas sees truth in a largely discursive manner:

When, however, it judges that a thing corresponds to the form which it apprehends about that thing, then first it knows and expresses truth. This it does by composing and dividing: for in every proposition it either applies to, or removes from the thing signified by the subject, some form signified by the predicate... — Aquinas, ST I.16 Article 2. Whether truth resides only in the intellect composing and dividing?

And I read Aquinas as seeing created truth as univocal:

I answer that, In one sense truth, whereby all things are true, is one, and in another sense it is not. In proof of which we must consider that when anything is predicated of many things univocally, it is found in each of them according to its proper nature; as animal is found in each species of animal.

...

If therefore we speak of truth, as it exists in the intellect, according to its proper nature, then are there many truths in many created intellects; and even in one and the same intellect, according to the number of things known. — Aquinas, ST I-16 Article 6. Whether there is only one truth, according to which all things are true?

Of course both of these points become complicated in other parts of Aquinas. But there is a prima facie sense in which Aquinas sees thoughts (or "propositions") as the point of departure for a discussion of truth, at least for human beings; and in which truth is univocally defined as adequatio
rei et intellectus.

Count Timothy von Icarus

↪Leontiskos

I think the equivocity attaches to the term 'good' rather than to the truth value, but even an assertion utilizing analogical equivocity must have a determinate and assertable form. If it doesn't then there is not any unitary thing being asserted.

Peter Redpath makes a pretty convincing argument that it is never our terms that are (properly) analogical for St. Thomas (obviously when we equivocate we do have ambiguous terms). It is rather the predication of the term that is analagous.

Consideration of analogy and univocity vis-à-vis predication should focus on how we relate definitions/predicates to subjects, as opposed to considering concepts and definitions themselves to somehow "be analogous.” That is, for St. Thomas, analogical predication is primarily about judgements and relations, and only secondarily about the terms that are being related.

For example, when we say “good” of God, we are involved in analogical predication, since the manner of God’s being cannot be directly compared to the being of creatures. However, this does not mean we should take the predicate “good” to be “analogical” here, as if the “goodness of God” is somehow a loosely related to what we generally intend by the term “good.” Indeed, if God is “Goodness itself,” (i.e. that by which all things are good— https://www.newadvent.org/summa/1006.htm) it is unclear what it would mean for "our concept of goodness" to be an “analogy” of true goodness. If the “good for man,” the fulfillment of our telos, lies in the contemplation and adoration of God, there is a sense in which God’s goodness must be the paradigmatic example of all goodness, even if we, as finite creatures, can never fully understand goodness as it is univocally predicated of God.

Mistaking the “analogy of predication,” (i.e., how a term applies to a subject) for an “analogy of concepts” (i.e. what a term means) seems to risk opening the door on a pernicious slide towards equivocity, since the predicates we are working become ambiguous themselves. One example of this might be found in Luther’s response to Erasmus’ critiques of his understanding of predestination, to which Luther replied:

”If it is difficult to believe in God’s mercy and goodness when He damns those who do not deserve it, we must recall that if God’s justice could be recognized as just by human comprehension, it would not be divine.”

The issue here is not, of course, the claim that we might be capable of misunderstanding God’s justice. This is true. Rather, it is the claim that God’s goodness is inaccessible to us; that it would not be divine goodness if we recognized it as "goodness". Yet it is easy to see how the move towards such a position might be enabled if we begin to think of the term "good" in "God is good," as being itself analogous. But the good car is "most choiceworthy" of cars, just as God is "most choiceworthy" without qualification.

So, my contention would be that truth doesn't need to become analogical, merely our predication of it. When we modify ambiguous statements, we are making it more obvious how the term relates to the subject, not making it clear which term we are "really" using. Analogy is about how things relate.

The question for the equivocity of truth is this: if the first statement is not meant to be true in a univocal sense, then is it possible for the respondent to disagree with it? To agree? To even understand what is being said?

Sure, we can understand it. We can also have questions about how "great" is related to "the day." Just as "Frodo is tall" can be true if tall relates to him having any height at all (to having an extended 3D body), but false in the sense that "Frodo is taller than average for the humanoid beings of Middle Earth." The question is how the propositions relates to the adequacy of thought (and language) to being, or language to thought.

Again, the reduction of all knowledge to discursive knowledge plays a role here to. Language is often ambiguous for the sake of brevity, but thought can be unclear too. This gets back to Aristotle's distinction:

-Asytheta: truth as the conformity of thought and speech to reality (whose opposite is falsity); and

-Adiareta, truth as the grasping of a whole, apprehension (whose opposite is simply ignorance).

It is worth noting that Aquinas sees truth in a largely discursive manner:

In a certain sense yes, it is in discursive knowledge that we have judgements whose opposite is falsity as opposed to ignorance. However, he often seems to follow the Neoplatonic camp in elevating the primacy of simple apprehension of wholes as wholes.

And this is in Aristotle too, knowledge of principles is what allows us to know the Many through a One. It's what makes science possible, since (in Aristotle's eternal universe) there can be an infinite number of causes but not an infinite number of unifying principles. I see this largely jiving with these sources I mentioned before:

In Ad Thalassium 60, St. Maximus the Confessor argues for the superiority of unified and direct experience, as opposed to discursive reasoning/knowing. Similarly, in Philosophiae Consolationis (4.6), Boethius argues that reason is to the intellect as time is to eternity, and what “circle” is to “center.” This is because it is “proper” for reason to be “diffused” (diffundi, i.e., scattered or spread) about many things, and then to gather from them a single cognition (i.e., unifying the “Many” into a “One”). Pseudo-Dionysius makes a similar point, (De Divinis Nominibus, 7.2) claiming that souls have rationality insofar as they “diffusedly encircle” (diffusiue circueunt) the truth of multiple existent things. Conversely, the intellect considers one simple truth and grasps the cognition of a whole multitude in it.

If science was just logic, and it had to deal with univocal predication, this unifying process would be frustrated.

In proof of which we must consider that when anything is predicated of many things univocally, it is found in each of them according to its proper nature; as animal is found in each species of animal.

Right, yet "health" for a kangaroo is analogically related to "health" for a daffodil. They do not share the same measure. The relation of the term to the predicate is the same though when we want to speak about the health of different organisms in some overarching sense. We do not have an ambiguous term when we say "it is good for all organisms to be healthy."

T Clark

Exactly, and not all knowledge is discursive knowledge. It's a sad philosophy that has to look at the climax of Dante's Commedia in Canto XXXIII of the Paradisio, his appeals to the inadequacy of language and memory, and say "well he's just sputtering nonsense." And it's just as sad to have to say something like "we can appreciate the words but not its rational content," since the Comedy is one of the very best (IMO the best) instances of philosophy breathed into narrative form. — Count Timothy von Icarus

I've never read it. I'll add it to my list.

The Univocity and Binary Nature of Truth

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