Why can't I have "is a statement" and "is false" in predicate logic? — Pippen

The short answer is: to avoid crap like this. The predicate logic we use was designed to formalize mathematics. It's supposed to help, not hinder, and there is no reason to think you can do everything in it.

The long answer is: in part Tarski, and in the other part some metalogic I don't know.

Partial explanation, ignoring the metalogic, which someone else would have to speak to: truth is the fundamental primitive in the system. It's already there, so there's no reason to introduce an "… is true" predicate. (This is easy to overlook because modern notation dropped Frege's early assertion stroke and judgment stroke. Start reading "p" as "It is true that p" and you'll see what I mean.)

If you had an "… is true" predicate, you'd want to apply it to propositions. But it's not perfectly clear that propositions are objects. What we've got is a way to say things like "If x is divisible by 5, then x is not prime." Does what's in between the quotation marks look like an object to you?

Keep in mind: you should not be able to get the result you want. Your argument, in brief, is that if A is false and A is equivalent to B which is neither true nor false-- wait, what? If it is equivalent, this won't happen. If they're not equivalent, then you've nothing to say. Pick your poison.

I think what you really have is an "apparent" paradox. That is, an ambiguity. You use the ordinary English word "equivalent" to mean something like, "Another way to say this is …" but then you take it to mean "must have the same truth value."

And how can a symbol be understood as a 'physical configuration' at all? The whole point about symbols is that they are abstract, which is exactly why meaning can be transferred via symbols so easily. — Wayfarer

Yeah but, your post isn't made of abstract types, it's made of concrete tokens, which brings us right back to where we started from. Hurray!

That just means the soft sciences are harder.

You can't do this in classical logic because you would need the predicates "… is a statement" and "… is false". You can't have either of those. Classical logic is swell, but it gets some of its swellness from being carefully circumscribed.

If your point is only that this sentence can't be represented within classical logic, then duh.

I still say the English sentence in question can justifiably and consistently be considered false.

Logic is a tool, one of my faves, but it does not sit in judgment of natural language, which may very well be just as formal only vastly more complex and powerful.

Hey Sam.

I'm looking back at the criteria you offered as candidates for judging the strength of an argument based on eyewitness testimony, and there's an issue I'd be interested to hear you address. Here are some snippets:

First, a high number of testimonials gives a better picture of the events in question. So the greater the number the more likely we are to get an accurate report, but not necessarily — Sam26

Second, seeing the event from a variety of perspectives will also help to clear up some of the testimonial reports — Sam26

((Third)) When dealing with a large number of testimonials you will almost certainly have contradictory statements, this happens even when people report on everyday events. Thus, one must weed out the testimony that does not fit the overall picture, and paint a picture based on what the majority of accounts are testifying to. — Sam26

I added some emphasis, from which you might deduce my question…

When we first discussed these criteria as a group, I think most of us assumed we were discussing criteria for assessing the credibility of a description of a single event based on the accounts of multiple witnesses. I made comparison to a close play at second witnessed by tens of thousands of people only one of whom was within ten feet of the play, but who could be in a worse position than the umpire team watching video footage from other angles.

As it turns out, you're not talking about a single event with multiple witnesses, but an event type, and each event has only a single direct witness, though there may be corroboration from medical staff, etc.

You yourself just mentioned accounts of the resurrection of Jesus as a comparison, which again is a single event multiple people give testimony about.

To start with, I think we should look for new comparisons to understand the structure of the argument. Some that come to mind are controversial diagnoses like fibromyalgia or Gulf War syndrome. But the method for judging those issues is relatively clear if difficult, and even if for some time no conclusion can be reached.

I really can't think of a good comparison for your case. It seems we would have to look at other inherently subjective experiences, but maybe you have a clearer sense of this than I do. (I understand there are sometimes arguments-- arguments!-- about whether anyone actually enjoys something, say, the music of Tom Waits.)

I suppose it could be argued something like this is what we do practically all the time. None of us, as the man said, can see the beetle in another's box, but somehow we almost all come to believe we're almost all having broadly similar experiences.

In sum, the issues are:

• One event with multiple witnesses vs. multiple events each with a single witness.
• Establishing the existence of the event type by exemplar when the exemplars themselves are controversial or subjective.

Interested to hear your thoughts.

In summary, my problem is why nobody interprets the statement "All sentences are false" as "All sentences are false and this very sentence is false", because in this version the whole thing wouldn't be true or false. I just don't see an error in infering one from the other. — Pippen

You can make the inference if you like, but the second version is also false, as I showed a month ago. I'll do it again:

Let S be "S is false and all statements are false".

Now we try assigning truth values to S to see if it is possible for S to be true or false. We may find that it must be assigned the value "true" in all models of English (that it is a tautology), that it must be assigned the value "false" in all models (that it is a contradiction), or that it can be true in some models and false in others, like most statements, or that it cannot be assigned a truth value in any model (like the Liar).

1. Assume S is true.
2. If S is true, then both conjuncts are true.
3. If both conjuncts are true, then the first is true, so it is is true that S is false.

This is contradiction, because at the moment we are assuming S is true. So there are no models of English in which S is true. But perhaps S is not false either, as you claim.

4. Assume S is false.
5. If S is false, then at least one of the conjuncts is false.

We now try each conjunct in turn. First conjunct:

6. Assume it is false that S is false.
7. If it is false that S is false, then S is true.

But we assumed in (4) that S is false, so this is a contradiction; thus there are no models of English in which S is false and its first conjunct is false. Second conjunct:

7. Assume it is false that all statements are false.

Here at last we have a possible truth-value assignment that doesn't immediately produce a contradiction. Thus all models of English must assign truth values this way: S is false (our assumption 4) and it is the second conjunct that is false, so it is also false that all statements are false. This is the only possible way to assign truth values without the model contradicting itself.

Your view I think is something like this: the usual way of determining whether a conjunction is a tautology, a contradiction, contingently true or false, or just not truth-apt at all, is to assign all possible truth-value combinations to the conjuncts and use a little truth table to see how the conjunction comes out. An arbitrary P & Q is

T & T : T
T & F : F
F & T : F
F & F : F

so it could be either true or false. On the other hand, P & ~P goes like this:

T & F : F
F & T : F

It's always false. So you're thinking that since you have, in essence, "[the Liar] & P" as your conjunction, we'll be unable to construct a truth table because the first conjunct is not truth-apt. True.

But conjunction is a short circuit with respect to falsehood, as disjunction is with respect to truth. If we can establish that one of a pair of conjuncts is false, we are never forced to evaluate the other conjunct to know that the conjunction as a whole is false. In my version, I never do assign a truth value to the first conjunct, but it doesn't matter. In essence we end up treating it as a pseudo-conjunction: blah-blah-blah P, and P happens to be a contradiction.

So we could skip most of the steps above and go that way instead. We show that "All statements are false" can only be false, which you agree to, and then short-circuit any conjunction it appears in.

I claim this is reasonable because whether to count some string of English words as a statement at all, as truth-apt, is up to us. There is no formal system on offer here to tell us whether some string is or isn't well-formed. We can rule out anything we like, but we can only rule in strings we can successfully assign a truth value to. We can't rule in the Liar. But we can rule in "All statements are false" by calling it always false, and we can rule in "This statement is false and all statements are false" by calling it always false. We're not compelled to, but we can.

ADDED: I would claim further that this approach is reasonable precisely on the grounds that we would ordinarily expect "All statements are false" and "This statement is false and all (other) statements are false" to be equivalent.

Your version has a truth-apt statement being equivalent to the Liar. If we can avoid that, we ought.

AND STILL MORE: Note that short-circuiting is consistent: "Dinosaurs are extinct" is contingently true; there are possible models in which it is false. But "Dinosaurs are extinct and all statements are false" is always false. "It's raining or it's not, and all statements are false" is always false, even though "It's raining or it's not" is always true.

Exactly so. What Burt Dreben meant when he said, "Great philosophers don't argue."

I don’t know if you do this intentionally or not, but you get bogged down in details as regard individual particulars. I’m asking a metaphysical question in relation to general ontological givens. — javra

Let's say I find the former more interesting than the latter, and you're the opposite. It's nice.

Is information—in and of itself—endowed with awareness? — javra

No-- but then the foundation for this question has not been established. Is information-- in and of itself-- endowed with color? With a sense of humor? With musicality or elegance?

If no, than I argue you have (at some abstract threshold whose particulars need not be here established) a duality between a) awareness to which information holds meaning and b) awareness-devoid information. Here, all meaning will pertain to awareness, which is an aspect of mind. Hence, if any notion of information or lack thereof is in any way meaningful, it will be so due to the presence of minds which interpret the given information. — javra

Okay.

Are you quite certain that when I try to figure out what I'm looking at and what it might mean to me, that it is information I am interpreting?

I just don't see the need to jump from information-using all the way to Husserl. Plants use information. Insects. I don't see Mind there, I just see a way of interacting with the environment that isn't eating it or whacking it.

We very nearly agree, I think. I see squirrels but not avalanches as information-using, until shown the error of my ways.

On the other hand, despite the fact that we design and make thermostats to serve purposes we choose, the fact that they do function autonomously is interesting. The analogy that suggests itself, to me at least, is not between thermostat and organism, but between thermostat and subsystem of organism. There's a whole lot of stuff (parts of) our bodies do on their own, and some of it is information-related. I don't choose to see, do you?

(The technology we create is generally an extension of some capacity or subsystem of ours, in classic Baconian fashion. We can sense the ambient temperature through our skin and flip switches with our fingers-- why not wrap those functions in a box and hang them on the wall so we can go do something else?)

The point being that of causal agency: some givens hold causal agency (e.g. it is the squirrel that hides its nuts and remembers where they’ve been stashed so as to maintain its own livelihood) while some givens are devoid of causal agency: e.g., from the first pebble that commences it to the grand finale of optimal entropic equilibrium, the avalanche was all part of a complex causal chain that neither begins nor ends with the avalanche itself—at no point was there an avalanche-agency that commenced the effects of the avalanche of its own impetus.

To make choices—to hold causal agency—is to necessarily be aware of alternatives (otherwise, no choice can exist). Hence, it is to necessarily hold awareness and, thereby, to necessarily interpret (give meaning to) information. — javra

Does the squirrel know that it is hiding food? Maybe?! Does it choose to do this after considering the alternatives of perhaps leaving it out in plain sight somewhere? Does it know why it's hiding it food? We don't know much about the inner life of any other sort of animal, but it strikes me as implausible. Does the parasitic wasp know why it does those appalling things to beetles? Does it choose to after weighing the alternatives? It's the one doing those things, that much is certain.

I think we can assign agency absent the sort of rational deliberation you're describing. Even way off on the other end, is it really crazy to say the pebble moving caused the avalanche, just because you can find some other cause behind the pebble moving? If we're going to talk about causes in nature, do we have to always answer "the Big Bang" and call it a day? Why did the river flood? Is "Because there was unusually heavy snow in the mountains this past winter" a worse answer than "the Big Bang"? I'm totally confused here, unless this is a reductio of ever talking in terms of causes at all.

All of which leaves me flummoxed. How does this help understand how an organism uses information? Phototropism makes perfect sense without attributing any sort of mind to the plant, doesn't it? The plant responds to sunlight in a way that's advantageous for it, but it no more chooses to than we choose to use our senses. It's a specific way of interacting with your environment, different from sucking water and minerals out of the soil or jamming your roots into it.

I do think some people were saying that. — T Clark

If so, I ignored it. ;-)

I think I'm getting it.

If it looked like someone was saying the data have to be quantitative or you're not doing science, no, nobody was saying that, I think. Analyzing your data (of whatever kind) quantitatively is almost preposterously helpful, but maybe also not an absolute requirement. (For instance, in your cool example about iridium, measuring and quantifying the natural incidence of iridium, and comparing it to the observed incidence in the magic layer, is crucial.)

I am not completely satisfied with the answer, but again, at least it accounts for mental occasions and does not get it from magical fiat. — schopenhauer1

Yeah I could see that as a motivation.

It seems to me though, that once everything's mental, explaining why some things appear not to be is the new Hard Problem of Unconsciousness. Of course we don't have to deal with a bunch of rocks and clouds insisting that they don't have qualia dammit, so there's that.

The whole thing feels sketchy to me, but I couldn't guarantee there's a metaphysics that wouldn't, so I guess I'll leave it be.

Can you take another pass at this? I don't disagree with anything here but I'm not sure what the connection is ...

Honestly, it seems like what happens is the standard "I've received a signal" response but with language that process is sandboxed most of the time. (Always?) So as the audience I turn your signal into a hypothetical-- if your sound were absolutely trustworthy, this is the signal it would be, that sort of thing.

How kind of you to add to my reading list!

I think there is a belief that what does this transformation is understood, but I'm questioning that assumption — Wayfarer

I'm with you there. I don't understand it. I can see how a simple "causal" signal between animals would work, but even though language is similar to that in obvious ways, it's different enough that it puzzles me. What exactly happens when you understand a sentence that may or may not be true? Animal signals, by being involuntary, are inherently trustworthy.

I think of this as the "talk is cheap" problem.

So does the fact that no such 'perpetual motion' device has ever been made refute that claim? — Wayfarer

No, the way I put that sounds backwards, doesn't it? Landauer's theory blocks some imaginable Maxwell's demon type systems by pointing out the cost of recording the state of the system or resetting the sensor. And there's been some experimental confirmation for that.

I don't think it is the kind of transformation I was talking about in the OP — Wayfarer

Then I think you're not talking about information but semantic content, propositions, Frege's third realm, etc. Every reason to expect those to be connected, but there are steps in between.

Nevertheless, as to the duality between some X which is interpreting information and the information itself: Is the squirrel here deemed an inanimate interpreter? Is the thermometer deemed an animate interpreter? Or, else, is there somehow deemed to be no meaningful difference between animate givens and inanimate givens? — javra

I start by distinguishing, let's say, "obvious" output and "not obvious": the difference between, say, on the one hand, dominoes falling in sequence, where each does to the next something a whole lot like what was done to it, and, on the other hand, a squirrel seeing a cat and making a particular sound.

There's a similar mechanism at work in a thermostat. A little information comes in and, if everything's working, leads to a large-ish action that consumes free energy. It's easy to imagine the automatic thermostat replacing the guy whose job it was to watch a thermometer and switch the furnace on or off.

Anyway, that's my admittedly simple-minded starting point.

Now there can be something similar without life (or an extension of it like the thermostat), in, say, an avalanche. Little input, big output that spends a lot of free energy. And there's an obvious connection in the way life keeps its "subsystems" balanced at criticality. You can get sensitivity by creating tiny avalanche conditions and then waiting, maintaining those conditions, and then resetting after each tiny event. Like a thermostat.

Certainly there's a difference between a squirrel and an avalanche, or, better, between the squirrel's "early warning" subsystem and an avalanche, in that the latter doesn't reset for new input. But beyond that, I just don't see the avalanche as resulting from information at all in the way the squirrel's warning does. What's the difference? I think it's precisely the transformation of the input. An avalanche is a big output of the same sort as its tiny input.

So yes I lean toward seeing the use of information about your environment, rather than just being shoved about by it, as a hallmark of life. But the information is still obviously physical, just as living things and their environments are. And I don't immediately see the need to describe this use as interpretation.

Some solution attempts to Maxwell's Demon rely on a mathematical relationship between thermodynamic entropy and information entropy. So there's some precedent for using information as a physical concept. — fdrake

That seems true, but also not exactly the point of the OP. — Wayfarer

?

It's the central test case. If you can gather information about the state of a system without spending free energy to record that information (or to reset your sensor/doorkeeper) then you can do work for free, you can have perpetual motion. This leads directly to Landauer's claim.

what is it that performs the transformation of meaning between different media and different languages? I presume that the answer to that is that this is a function of rational intelligence. — Wayfarer

When a squirrel makes that "cat near my tree" sound, I don't think we need to call that rationality. It's involuntary, but it is exactly the kind of transformation we're talking about. (I'd rather talk about thermostats, but everyone will want to talk about the thermostat designer instead.)

I was afraid you would ask that.

Yes, I would think so, but it's not an area I know. Even without getting into neuroscience, there's various ways you might use biometrics, for instance. Personally I'm really interested in this sort of thing, which is in the neighborhood anyway.

Can you? — MikeL

Can I what? Explain how life arose on Earth? No.

If your argument is that I, Srap Tasmaner can't explain it, then you win, man.

If you mean that no one alive can, you probably win that one too. Maybe. People have theories. Maybe somebody's already got a perfectly good theory we just don't know it yet. I'm sure there are bars where you can't get away from the biologists sharing their theories of abiogenesis.

I took you to mean there was some reason why it cannot possibly be done, not now, not ever, not by anyone, that there is some logical obstacle that makes achieving this task impossible-- rather like Michael Behe's claim that the bacterial flagellum could not possibly be explained by evolution, that sort of thing. (Of course, he was wrong.)

It's that claim I don't understand. Especially not right now, with everything going on in biology these days. Don't you think there are more discoveries to come? Aren't you excited to see what "we" (by which I mean folks like Hoffman) learn?

What if I said 90% of people with a college education don't believe in God. — TheMadFool

Jeremiah's point is just this: what you are counting here, your data, is categorical rather than itself being quantitative. The fact that you counted doesn't change that. Suppose your data was height: then you could talk about the average height of your population, the average deviation, and so on. What about here? Is there an average belief in God? How much of your population has an unusually big belief in God (more than two or three standard deviations above the mean)?

so long as the other side is able to explain how life originated naturally: but they can't. — MikeL

I just don't see how you get from the "haven't" we could all agree on to the "can't" you insist on.

As you're reading Life's Ratchet, keep an eye on the dates in the later chapters. An enormous amount of what we now know about the internal workings of cells is no more than a decade or two old. The paint has barely dried on the machines and techniques that produced this knowledge.

Hoffman's book gives an overview of where biology is nowadays on what life actually is, how it works. Cells, it turns out, are nothing at all like what I learned in AP Biology a hundred years ago! That means we're only now beginning to see the shape of what a theory of abiogenesis would look like. It's helpful to know what you're explaining the origin of, don't you think?

Correct. It's speculative metaphysics. I don't necessarily expect it to be tested. — schopenhauer1

Admittedly, not my cup of tea, so I appreciate your patience with me.

From my point of view, it looks like a change in vocabulary. Does it look like something else to you? For instance, does it help you answer the question why there's something it's like to be a bat but not something it's like to be a rock? (Assuming there isn't.) Do we say it's because the constituent occasions of bats and rocks are organized differently? That looks to me like saying the sleeping potion works because it has a soporific power.

Wow. Thanks for the very thorough answer, since I don't know Whitehead at all.

Here's what I don't get right off though: we're trying to understand the difference between stuff that's A and stuff that's ¬A (speaking, ahem, loosely); Whitehead tells us that stuff that's A is B, and stuff that's ¬A is ¬B, the two different sorts of organization you describe. Could be helpful. Science does this. Why does this rock move the needle of my compass but this other one doesn't? Because one of them's a lodestone, and here's how that works, and here's how you can test it to see if it's true, and so on. If you posit an explanatory B, that gives you the opportunity to test for the presence of B by means that don't involve A, predict A when you've got B and then see if A turns up.

But in Whitehead's case, I assume we deduce the presence of the B-style organization only and everywhere we would before have just said we have something A. The description you give is evocative, it's interesting to think about, but it just piggybacks on what we already know. There will never come a time when you can say, here's something with B organization, let's see if it's got a soul.

Is "panexperientialism" going to include, say, rocks? Clouds? Neutrinos?

Supposing it does, does that solve your problem? Maybe you allow something "experience-ish" to be attributed to a grain of sand. Fine. What about the "what it's like to be an X"? Are you extending that to everything, or still reserving that to some smaller class?

But there's not something it's like to be sawgrass, right?

Is there something it's like to be E. Coli?

Do dogs have souls? How about the most recent common ancestor of dogs and us? Yes? What about spiders? What about the most recent common ancestor of us, dogs, and spiders? Or the most recent common ancestor of us, dogs, spiders, and sawgrass?

<shrug>
Mathematics is certainly not an empirical science. And it has a different notion of evidence. (Not just proof but also counterexample.) Even through the first half of the twentieth century, authors routinely referred to "the science of mathematics" and "the science of logic". Maybe it is worth calling attention to a shared sense of rigor.

But if it's not exclusive to, not originating with science, then why call it the scientific method? — darthbarracuda

Science is systematic common sense. I'm with @T Clark.

What sort of thing is a concept, apart from what shows in behaviour? — Banno

A way of classifying 'things' (broadly), I suppose.

There's some really abstract classifying it's pretty hard to imagine doing without language, but doesn't it also seem that language presupposes some ability to classify things, rather than engendering it?

One interesting inflection point between some animals and others might be their capacity to remember. Maybe one has to decide "food/not food", for instance, each time it encounters something, even if it's the same individual something over and over, while another might remember having already decided what to do when encountering that thing, or even another thing a lot like it.

Why not instead say that possession of a concept is always evidenced by behaviour, which in the case of some primates includes the sounds and marks they make?

Caution's nice.

Some of your points look to me like they could be, well, if not "settled" then at least addressed by research. An ape that learned to use a particular individual tool for a particular type of job might substitute a similar tool, might recognize when only one of two similar tools will work for a given problem, might, might, might, or might not. There's a threshold beyond which I'll be fine saying he knows everything I do about wrenches except how to talk about them. I don't know what that threshold is exactly, and I might need to see research even to figure that out.

They are your God. An adjusted Calvinism so you can feel so very scientific. You do have Faith that they exist, correct? — Rich

This is becoming abusive @Rich. I humbly suggest you stick to telling us what you think, and stop telling everyone else what they think. Nobody's asked you to psychoanalyze them.

I am not getting your point.

Suppose I was an accomplished mechanic who spoke only German. An English speaker could say truly both that I know how to use a wrench and that I don't know what a wrench is. The latter's just ambiguous. Just explaining the ambiguity is a pain in the ass:

• He knows what a wrench is; he just doesn't know what it's called in English. (Huh?)

• There is a type of thing, call it X; we call X's "wrenches"; he knows what X's are, but not that we call them "wrenches".

I just can't figure out if your position trades on this ambiguity or makes a point about it or what?!

Was that "yes", "no", or "not sure"?

Besides which, there are loads of reasons to think this claim is simply false. You'd have to have a language without the logical constants.

Even if you changed it to "All atomic sentences of L are false", then the question is: under what interpretation? Systematic falsehood under one interpretation is systematic truth under another.