Tag: truth

The Sorites Paradox – Maybe It’s Not What We Think It is.

It has been asked how, if at all, one might resolve the Sorites paradox. I am not convinced a solution is possible, and in this paper I will explain the responses I have become aware of, and why they fail. In the end, I will conclude that there is no solution to the paradox, but I will offer a few suggestions for a way forward.

The first response might simply be to reject the first premise of the argument. In other words, simply deny that a man with 10 hairs is in fact bald, or that 100 grains of sand is in fact a heap. In essence, this would render vague predicates useless at best, meaningless at worst, since no predicate that allows for a vague border case would be permitted to apply to anything. There is one way in which we might stretch this into plausibility, but I will address the other responses first, before returning to this in the conclusion.

The second response is to set some arbitrary boundary. This means selecting one one among the indefinite number of secondary premises beyond which all others will be false. For example, we might say that thirty-thousand and one grains of sand is the boundary below which we no longer regard a collection of grains to be a heap. At first glance, this approach might seem plausible. After all, we do this frequently in practice: setting the legal drinking age, or the number of credit-hours required to count as a ‘full-time’ student, for example. However, there are two core problems with this. First, from the context of the formal argument, there is no good reason to reject any of the subsequent conditional statements, and there appears to be no means by which we could discover a reason. The implicit modus ponens of the conditional compels us to accept them all. Second, as Wright (Vagueness, 1997) pointed out, vague predicates are inherently coarse by virtue of their intended use. So attempts to impose some sort of specificity would destroy their meaning.

The next approach would be to attempt to define a knowledge gap within some middle range of propositions between the edge false and edge true statements. On one interpretation of the idea, we could use a three-value logic, in evaluating the propositions. At some point, starting with grain one, the proposition ‘this is a heap’ would cease being false, and would instead be valued ‘unknown’ or ‘undefined’. Later, the unknown state would transition to true, once we’ve reached the next threshold. This would make it possible to judge the argument invalid, since any number of its premises were neither true nor false. However, this seems to be attempting to win on a technicality, and it suffers from the same problem as the arbitrary boundary solution, in that we have no real way of determining when the states should change.

The next response might be some form of Edgington’s “degrees” of truth (Vagueness, 1997). But this suffers from it’s own serious flaws. For example, consider the statement ‘it is raining’. That has a ‘degree’ of truth of .5. It’s negation, ‘it is not raining’ will have a degree of truth of .5. The consequence of this, is that the following propositions have exactly the same truth value: ’It is raining, and it is raining’, ’It is raining, and it is not raining’. The same problem exists with our heap of sand. So, again, we’re left with no clear way to determine the truth of the conditionals in the Sorites case.

In the end, there does not seem to be any clear resolution to this paradox. However, I would offer one suggestion. vague predicates, in addition to being inherently coarse, also seem to be describing inherently subjective experiences or judgements. While Sorites arguments seem to want to talk about objective properties of objects. Perhaps there is no solution to the paradox, precisely because “tall” or “heap” or “red” or “bald” is not in fact a property of the object being considered, but a property of the experience the subject has of that object. The paradox is perhaps trying to square subjective interpretation with objective matters of fact. And that’s why it cannot be resolved.

ISP Launch Event: Three Talks On Three Philosophers

This weekend I attended the launch event for the International School of Philosophy here in London. Three Talks on Three Philosophers was intended to showcase the kind of thought one could expect from the new school, as well as provide an opportunity for philosophical learning to the local community (greater Islington, mainly). Sam Freemantle, the founder of the new independent school, provided the first of the three lectures, in the form of an overview of his Phd thesis, “Reconstructing Rawls”. Following Sam, Adrian Brockless offered a passionate argument for a more thoughtful kind of education grounded in Socratic questioning. Lastly, Professor Ken Gemes of the University of London treated us with an extended version of his talk on Nietzsche’s Death of God.

Serendipitously, I also listened this weekend to a new reading of the introduction to Allan Bloom’s “The Closing of the American Mind” (a book I read years ago). I say “serendipitously”, because it turns out to be a powerful lens through which to interpret the messages coming out of Saturday’s lectures. In particular, the lectures of Professor Gemes and Mr. Brockless, which were laden with themes that could easily have been attributed to Bloom. The erosion of truth and goodness as absolute values (both in society and in the academy), the corruption of the academy to purposes other than the pursuit of the good life, the need for a renewal of these core values, the seemingly intractable challenge of re-establishing them in an educational environment so democratized and demoralized that even the hint of such an effort will raise accusations of elitism. All of these were core concerns of Allan Bloom, and his voice was clearly resonating in the words of both Professor Gemes and Mr. Brockless. Though, I suspect neither of them would agree.

For Professor Gemes the worry is societal, and spans generations. He began his talk with the story of the madman from Nietzsche’s The Gay Science, which illustrates the central problem for Nietzsche, as Gemes sees it: absent the catalyzing mythology of christianity, why would we continue to cling to it’s core values of truth and goodness? Given that the values of honor and glory held by civilization before Christianity seem more seductive, why wouldn’t we return to these, and abandon truth and goodness, in the absence of a dogma that focused us on them? According to Professor Gemes, Nietzsche believed we were clinging to truth as a value, by way of some sort of “hangover” from Christianity, and he wanted to know why. I think Nietzsche may have been disadvantaged by his proximity to the downfall of Christianity in the west. Over a century on now, in the “post-truth” era, it appears we have indeed begun to abandon truth and goodness as ultimate values, and have indeed begun replacing them with honor and glory once again.

Nowhere is this shift more clearly and startlingly present, than in the academy. Mr. Brockless highlighted this inadvertently, I believe, in his lecture. Using the Socrates of Gorgias and The Republic as a mentor, Brockless crisply argued for a conception of higher education that differentiates itself from the contemporary academy, by focusing on the pursuit of truth through “authentic” learning that exposes students to “meaning and understanding of the human condition”, rather than on the career advancement goals and academic advantages of its students. This plea explicitly demands that truth be reseated in our minds as an absolute value, pursued for its own sake. Although Mr. Brockless’ lecture came before Professor Gemes, his is a direct response to Nietzsche, in the form of a resounding and explicit affirmation of truth and goodness, above honor and glory, at least as far as the academy is concerned. To that end, Brockless counseled a return to the ancient classics, and glowed with a reverence for the Socratic dialogues themselves, even recommending them as a starting point for students.

Interestingly, a popular new voice has also converged on this question. I’ve recently seen a lecture by Jonathan Haidt of New York University, in which he suggests that a “new schism” ought to take place in the modern university, involving the realignment of ultimate values. In his view, these divergent ultimate values are “truth” versus “justice” (actually, “social justice”, which he contends is unjust at times). But rather than pressing for the conquest of truth over social justice, Haidt advocates for an amicable divorce. Haidt centers his lecture on a vision of education very similar to Brockless, in which universities that adopt truth as a core value dedicate themselves firmly to free expression, and open dialogue and debate in which no idea is off the table. In other words, the Socratic tradition. The same tradition Brockless described during the question and answer period of his lecture.

Allan Bloom’s book was a vanguard in this discussion, I think. Some might suggest that perhaps there really is no problem, and this is all just varying degrees of predictable conservatism occasionally surfacing above the white noise. After all, these sorts of complaints have been around for almost 50 years, and yet the generations leaving university then and now don’t seem to be too much different from each other. But are they really so much the same? Bloom (and proteges like E. D. Hirsch) would point to the degradation of “dead white males” in the academy, and their gradual replacement with relativist and anti-absolutist dogmas (in addition to the impulse toward radical activism) — and the pervasive cultural ignorance and growing hostility to truth of new students — as certain indicators. I’m not sure that Haidt, Brockless, or even Gemes would necessarily agree with that. But one thing that all of these voices seem to agree on, regardless of the reasons grounding it, is the loss of truth and goodness as guiding star values in our overall culture, and most profoundly, in the academy.

The question is what, if anything, should we do about it? Brockless and Haidt have slightly divergent opinions on this. One suggests lobbying to reestablish the traditional mission of all higher education, the other recommends a more “free market” answer (if I can call it that), by bifurcating the institution into two competing organizations, one focused on truth, the other on justice. Neither of these speakers’ solutions are entirely satisfying to me. I think this problem is bigger than all of us, and may be inevitable. I wonder if Nietzsche thought so, too.

Getting A Handle On The Truth

What is truth?” ~ Pontius Pilate

This is an interesting and surprisingly difficult question. If you look in the OED, what you’ll find there are entirely circular and self-referential explanations: “the quality or state of being true“, ” that which is true or in accordance with fact or reality“, and “a fact or belief that is accepted as true“.

So, the poor souls that rely on the dictionary are left with, essentially, “truth is what’s true”, and “what’s true is what we agree are the facts of reality.” But what if we’re wrong and we still agree? Or worse, what if we disagree, but one of us is right? This can’t be the last word on this topic. What can we say with any confidence about truth, as such? To put it in the words of Bertrand Russell:

“We may believe what is false as well as what is true. We know that on very many subjects different people hold different and incompatible opinions: hence some beliefs must be erroneous. Since erroneous beliefs are often held just as strongly as true beliefs, it becomes a difficult question how they are to be distinguished from true beliefs. How are we to know, in a given case, that our belief is not erroneous? This is a question of the very greatest difficulty, to which no completely satisfactory answer is possible. There is, however, a preliminary question which is rather less difficult, and that is: What do we mean by truth and falsehood?” — The Problems of Philosophy (p. 77)

Thinking on the question a bit, I realized I’m not quite sure what I mean. So, I decided to take a brief look at what what philosophy has had to say on the subject over the centuries, to see if I might find something I’m willing to accede to, at least in the short term.

As Russell is careful to point out in the book I just referenced, any real understanding of truth must start first with understanding what knowledge is. But even this is tricky. I wanted to simply stipulate to the classical definition, in order to shorten this post. But what we find in the traditional definition of knowledge, is yet another circular reference: knowledge is Justified True Belief. In other words, that which is known is that which satisfies all of the following three conditions:

  1. It is believed
  2. That belief is justified
  3. That belief is true

For the sake of brevity, I’ll let the Stanford encyclopedia explain these three conditions in detail, and I’ll set aside common objections to this formulation of knowledge for a later post. Nevertheless, in spite of Stanford’s assertion that “the truth condition is largely uncontroversial“, I think the fact that truth is present in the definition of knowledge is a serious problem for philosophy because it makes the two terms fundamentally dependent upon each other: truth is that which is known is that which is the truth.

As such, I find it hard to blame the dictionary for its circularity when it relies for its definitions on an academic discipline that can’t seem to provide a clear answer to this question. What’s more, I think it’s a little disingenuous for “serious” philosophers to scoff at Ayn Rand for her insistence on unjustified “axioms” like “Existence Exists“, or to laugh at Christians who, facing no real alternative, rely on Jesus’ pronouncement that actually it is he personally who is “…the way, the truth, and the life…” (John 14:6).

To be completely clear, my aim here is not to argue that there is no such thing as truth, or that we cannot know things or cannot justifiably claim to know the truth — or worse, that we should just throw our hands up and simply declare it to be whatever we want it to be. To do so, I’d have to employ the very tools of thought that I’d be condemning. All I am suggesting is that maybe we’re not as sure as we think we are, and that maybe we need to rethink some of these fundamental questions.

What Everyone Else Thinks

As one might expect, given what I have stated above, there are actually numerous philosophical theories of truth. The most popular among them, the “correspondence theory“, offers the greatest appeal to common sense. This theory is probably where the OED gets it’s turn of phrase “in accordance with fact or reality”. The theory states that “a proposition is true provided there exists a fact corresponding to it.” But what does “correspondence” mean? And what, exactly, are facts? Russell makes a lot of hay on this second question, in his own conception of correspondence. In short, this definition “works”, but it’s not entirely satisfying (as Russell notes in the above quote).

Some argue for something called “coherence“, in which each new statement is compared to a complete set of beliefs, and rejected if it does not “fit” within that collection. This theory seems to fail on two grounds: first, that it is not necessary for the collection of beliefs to have any relation to reality, and secondly, as Russell again points out, because of the first problem, there can be many equally “coherent” belief systems existing side by side. How do we know which one to choose? The problems point to a third problem, that I think also plagues the pragmatist, constructivist, and consensus theories of truth. Namely, that they all elevate mere belief to the ontological status of a fact, by virtue of some ex post facto rationale. What’s more, this equivocation seems to go unnoticed (or worse, dishonestly ignored) by the theories’ adherents.

What I think

I find Kant’s idea of the conjunction between the noumenal and phenomenal world somewhat compelling. Although, probably not for reasons Kant would approve. Science shows us that there is a reality that is outside the reach of the senses. Perhaps truth, then, is the extent to which we can apprehend these non-phenomenal parts of reality, and reconcile them with the phenomenal parts. Already, science has provided us with all sorts of tools for doing this (telescopes, microscopes, sensors, meters, etc.). If this is true (somewhat ironically), then the way to the truth is through scientific inquiry. This is certainly a different route to truth via science than the pragmatists propose, but I think the destination may be the same.

On the other hand, although I don’t quite understand his theory, Alfred Tarsky‘s emphasis on semantics got me to wondering.

I have heard truth described by some as a relationship between physical reality and conscious awareness. This is not quite the same thing as correspondence, because the focus here is not on the objects in the relation, but the relation itself. It’s an interesting idea, but I think this isn’t quite complete. Because, if conscious awareness of reality is all that is necessary for a “truth” relation, then beavers and ants and birds would be capable of apprehending the truth. Clearly, then, it must something more.

That difference is language. Truth is as much a semantic concept, as it is a metaphysical one. Like knowledge, the definition of truth is concerned with the objects of mind and reality, and primarily with the nature of the relationship between them. But what is it about the nature of this relation, that makes it truth? I think it is the meaning we assign to that relationship, and the value discovered in the contents of that relationship.

In short, truth is a kind of semantic value judgment of the perception of reality as it is apprehended, by a mind capable of apprehending and valuing. But what does this mean, in practice? Is this just another way of formulating correspondence? Not quite. Is it the same as claiming that the truth is whatever we want it to be? Not quite. Is it pragmatism in another suit of clothes? I don’t think so.

But I’m struggling to find the words necessary to develop the idea any further. And perhaps that’s a clue to the problem with all of these theories. Maybe the problem lies precisely with the fact that our language is woefully lacking, when it comes to the task of describing these sorts of relationships. This is why I am beginning to wonder if we don’t need a new language, or a new way of thinking, or of describing our thoughts, before we can properly answer this question.