04 May 2012

The nature of Truth

The nature of Truth


I recently finished reading A User's Guide To Thought And Meaning by Ray Jackendoff. In it, he asks "What is truth?" and mentions several problems with what we might call the conventional view.

He didn't really answer the question, but on reading it, a surprising answer occured to me.


Truth is just what valid reasoning preserves.

No more and no less. I'll abbreviate it T=WVP

Not "about the world"

The conventional view is that truths are about the world, and valid reasoning merely doesn't drop the ball. I'll abbreviate it CVOT. To illustrate CVOT, consider:

All elephants are pink
Nelly is an Elephant
Nelly is pink

where the reasoning is valid but the major premiss is false, and so is the conclusion.

Since "about the world" plays no part in my definition, I feel the need to justify why it needn't and shouldn't.

"About the world" isn't really about the world

Consider the above example. Presumably you determined that "All elephants are pink" is false because at some point you saw an elephant and it was grey1.

And how did you determine that what you were seeing was an elephant and it wasn't pink? Please don't stop at "I saw it and I just knew". I know that readers of this blog have more insight into their thinking than that. Your eyes and your brain interpreted something as seeing a greyish elephant. I'm not saying it wasn't one, mind you. But you weren't born knowing all about elephants. You had to learn about them. You even had to learn the conventional color distinctions - other cultures distinguish the named colors differently.

So you used reasoning to determine that this sensory input indicated an elephant. Not conscious reasoning - the occipital lobe does an enormous amount of processing without conscious supervision, and not declarative facts - more like skills to interpret sights correctly. But consciously or not, you used a type of reasoning.

So the major premiss ("All elephants are pink") wasn't directly about the world after all. We reached it by reasoning. So on this level at least, T=WVP looks unimpeachable and CVOT looks problematic.

Detour: Reasoning and valid deductive reasoning

I'll go back in a moment and finish that argument, but first I must clarify something.

My sharp-eyed readers will have noticed that I first talked about valid reasoning, but above I just said "reasoning" and meant something much broader than conscious deductive reasoning. I'm referring to two different things.

Deductive reasoning is the type of reasoning involved in the definition, because only deductive reasoning can be valid. But other types of reasoning too can be characterized by how well or poorly they preserve truth in some salient context, even while we define truth only by reference to valid reasoning. Truth-preservation is not the only virtue that reasoning can have. For instance, one can also ask how well it finds promising hypotheses or explores ramifications. Truth-preservation is just the aspect that's relevant to this definition.

One might object that evolutionarily, intuitive reasoning is not motivated by agreeing with deductive reasoning, but by usefulness. Evolution provided us with reasoning tools not because it has great respect for deductive reasoning, but because they are "good tricks" and saved the lives of our remote ancestors. In some cases useful mental activity and correct mental activity part company, for instance a salesperson convincing himself or herself that the line of products really is a wonderful bargain, the better to persuade the customers, when honestly it's not.

True. It's a happy accident that evolutionary "good tricks" gave us tools that strongly tend to agree with deductive reasoning. But accident or not, we can sensibly characterize other acts of reasoning by how well or poorly they preserve truth.

Can something save CVOT?

I said that "on this level at least, T=WVP looks unimpeachable and CVOT looks problematic."

Well, couldn't we extend CVOT one level down? Yes we could, but the same situation recurs. The inputs, which look at first like truths or falsities about the world, turn out on closer inspection to be the products of yet more reasoning (in the broad sense). And not neccessarily our own reasoning, they could be "pre-packaged" by somebody else. This gives us no better reason to expect that they truthfully describe the real world.

Can we save CVOT by looking so far down the tower2 of mental levels that there's just no reasoning involved? We must be careful not to stop prematurely, for instance at "I just see an elephant". Although nobody taught us how to see and we didn't consciously reason it out, there is a reasoning work being done underneath there.

What if we look so far down that no living creature has mentally operated on the inputs? For instance, when we smell a particular chemical, say formaldehyde, because our smell receptors match the chemical's shape?

Is that process still about the world? Yes, but not the way the color of elephants was. It tells you that there are molecules of formaldehyde at this spot at this time. That's much more limited.

CVOT can't stop here. It wouldn't be right to treat this process as magically perceiving the world. A nerve impulse is not a molecule of formaldehyde. To save CVOT, truth about the world still has to enter the picture somehow. There's still a mediating process from inputs (a molecule of formaldehyde is nearby) to outputs (sending an impulse).

But by now you can see the dilemma for CVOT: in trying to find inputs that are true but aren't mediated by reasoning, we have to keep descending further, but in doing so, we sacrifice aboutness and still face the same problem of inputs.

Can CVOT just stop descending at some point? Can we save it by poositing that the whole process (chemical, cell, impulse) produces an output that's true about the world, and furthermore that this truth is achieved other than by correctly processing true inputs about the world?

Yes for the first part, no for the second. If we fool the smell receptor, for instance by triggering it with electricity instead of formaldehyde, it will happily communicate a falsehood about the world, because it will have correctly processed false inputs.

So we do need to be concerned about the truth of the inputs, so CVOT does need to keep descending. It has to descend to natural selection at this point. Since I believe in the unity of design space, I think this change of destination makes no difference to the argument, so I merely mention it in passing.

Since we must descend as long as there are inputs, where will it end? What has outputs but no inputs? What can be directly sensed without any mediation?

If there is such a level to land at, I can only imagine it as a level of pointillistic experiences. Like Euclid's points, they have no part. One need not assemble them from lower inputs because they have no structure to require assembly.

If such pointillistic experiences exist, they aren't about anything because they don't have any structure. At best, a pointillistic experience indicates transiently, without providing further context, a single interaction in the world. Not being about anything, they can't be truths about the world.

So CVOT is not looking good. It needs its ultimate inputs to have aboutness and they don't, not properly anyways.

Does T=WVP do better?

If CVOT has problems, that doesn't neccessarily mean that T=WVP doesn't. Can T=WVP offer a coherent view of truth, one that doesn't need magically true inputs?

I believe it can. I said earlier that truth-preservation is not the only virtue that reasoning can have. Adbuctive reasoning can (under felicitous conditions) find good explanations and inductive reasoning can supply probable facts even in the absence of inputs. Bear in mind that I include unconscious, frozen, and tacit processes here, just as long as they are doing any reasoning work.

So while deductive reasoning doesn't drop the ball, other types of reasoning can actually improve the ball. Could they improve the ball so much that really, as processed thru this grand and mostly unconscious tower of reasoning, they actually create the ball? Could they incrementally transform initial inputs that aren't even properly about the world into truth as we know it? I contend that this is exactly how it happens.

Other indications that "about the world" just doesn't belong

Consider the following statements3:

  1. Sherlock Holmes was a detective
  2. Sherlock Holmes was a chef

Notice I didn't say "fictional". You can figure out that they're talking about fiction, but that's not in the statements themselves.

I assume your intuition, like mine, is that (1) is true (or true-ish) and (2) is false (or false-ish).

In CVOT, they're the same, because they're both meaningless (or indeterminate or falsely presupposing). (1) can't naturally be privileged over (2) in CVOT.

In T=WVP, (1) is privileged over (2), as it should be. Both are reasoning about Arthur Conan Doyle's fiction. (1) proceeds from healthy, unexceptional reasoning about them, while (2) somehow imagines Holmes serving the hound of the Baskervilles to dinner guests. (1) clearly proceeds from better reasoning than (2), and in T=WVP this justifies its superior truth status.

CVOT could awkwardly salvaged by saying that we allow accomodation, so we map "Sherlock Holmes" to the fictional detective by adding the qualifier "fictional" to the statements. But then why can't we fix (2) with accomodation too? Doyle never wrote "Cookin' With Sherlock", but it's likely that someone somewhere has. Why can't we accomodate to that too? And if we accomodate to anything anyone ever wrote, including (say) Alice In Wonderland and Bizzaro world, being about the world means almost nothing.

Furthermore, if we accept accomodation as truth-preserving, we risk finding that "All elephants are pink" is true too4 because "by pink, you must mean ever so slightly pinkish grey" or "by elephant, you must mean a certain type of mouse".

I could reductio further, but I think I've belabored it enough.

Circularity avoided in T=WVP

Rather than defining truth as what valid reasoning preserves, it's more usual to define valid reasoning as truth-preserving operations. Using both definitions together would make a circular definition.

But we can define valid reasoning in other ways. For instance, in terms of tautologies - statements that are always true no matter what value their variables take. A tautology whose top functor is "if" (material implication) describes a valid reasoning operation. For instance:

(a & (a -> b)) -> b

In English, "If you have A and you also have "A implies B", then you have B". That's modus ponens and it's valid reasoning.

I said tautologies are "statements that are always true", which is the conventional definition of them, but it contains "true". Again I need to avoid a circular definition. So I just define tautology and the logical operations in terms of a matrix of enumerated values (a truth-table). We don't need to know the nature of truth to construct such a matrix or to examine it. We can construct operations isomorphic to the usual logical operations simply in terms of opaque symbols:


Some other virtues of this definition


  • It recovers the Quinean disquotation sense of truth. Ie, a quoted true statement, interpreted competently, is true.
  • It recovers our ordinary sense of truth (I hinted at this above)
  • It recovers the property that truth has where the chain is as strong as its weakest link.


1 Or you trusted somebody else who told you the saw a grey elephant. In which case, read the argument as applying to them.

2 I'm talking as if it was a tower of discrete levels only for expository convenience. I don't think it's all discrete levels, I think it's the usual semi-fluid, semi-defined situation that natural selection creates.

3 Example borrowed from Ray Jackendoff

4 Strictly speaking, we would only do this for presuppositions, but if the speaker mentions "the pink elephant" at some point the reductio is good to go.


  1. T = WVP  is a statement about the relationship between truth and validity of reasoning, right?  I'm not worrying about circularity, I'm just trying to grok the relationship.  If we know which reasoning is valid, that tells us, at least, that anything it doesn't preserve isn't truth.  If we know what truth is, reasoning is valid only if it preserves that.  This leaves me wondering if valid reasoning preserves anything other than truth, and whether there is any invalid reasoning that preserves truth.

    Have you read Kuhn's Structure of Scientific Revolutions?  (I probably already know the answer to that, and it's slipped my mind.)  According to my notes from a few years ago, Chapter X has some possibly-related things to say about interpretation versus perception.  (I may have to put rereading that on my to-do list.)

    1. > T = WVP is a statement about the relationship between truth and validity of reasoning, right?

      Yes, except that I propose that it's the very definition of truth. That's the new part.

      > This leaves me wondering if valid reasoning preserves anything other than truth,

      Sure. Usually not very interesting things. For instance, there are always some terms preserved. Both the premiss and the conclusion mention elephants.

      > and whether there is any invalid reasoning that preserves truth.

      Not if you mean always preserves it.