...at least if they believe in infallible divine foreknowledge.
I'm not aware of any empirical research to back this up, but my strong anecdotal impression is that theistic philosophers who take an interest in free will are, in the vast majority of cases, libertarians. Now, libertarians come in all sorts of different flavors, but the relevant features for our purposes right now are just:
(a) a belief that humans do indeed have free will &
(b) incompatibilism about free will and determinism
Now, historically, many smart people have worried about the compatibility of divine foreknowledge with free will, but (at least given the positions formed in response to the question of *determinism* and free will) it's not clear what the big deal is. As long as you believe in future facts, there's no problem with (a) believing that there are facts about what undetermined radically self-caused free decisions people will make in the future, and that(b) God, being omniscient, knows all such facts, without anything about that knowledge undermining the libertarian picture.
One problem, though, is that this would seem to commit anyone who believed both (a) and (b) to a form of backward causation. Free decisions I will make in 2020 are causing God's knowledge of them in 2010. Some people view the thought of any sort of causal sequence where the effect precedes the cause with extreme discomfort. Can theistic libertarians, then, make sense of things *without* postulating a process of backward causation whereby future facts cause present divine mental states?
Well, here are a couple of easy ways out, that allow the theistic libertarian to believe that God's knowledge includes knowledge of precisely which free decisions we'll make in 2020:
(i) Deny that this is *foreknowledge*, or
(ii) Deny that it is infallible
Some theologians argue that God is, in some sense, "outside of time." It's controversial whether there's even any coherent way to make sense of this idea, and I'm pretty skeptical, but that's a complicated and interesting subject for another time. For the moment, just note that it amounts to (i). God's atemporal knowledge of all of time wouldn't be foreknowledge, so this amounts to giving up on the project of making sense of divine foreknowledge without determinism or backward causation.
More creatively, one could argue that, even in an indeterministic universe, certain sorts of evidence about the present give one a very high degree of justification for one's beliefs about what people will do in the future, enough so that (if they are true) those beliefs count as knowledge. Surely, all evidentially-based human knowledge of the future is of this kind, whether or not we live in an indeterministic universe. After all, even in a deterministic universe, there's always the possibility that we're misinterpreting the evidence. Despite this, surely we at least sometimes know at least some things about what will happen in the future. Surely, in an indeterministic universe, God, with His complete and flawless knowledge of every aspect of the present, would have extremely well-justified beliefs about what will happen in the future, beliefs that, by parity of reasoning, would count as knowledge if those beliefs were true. So far, so good, but given indeterminism, surely some of God's beliefs about the future would be *false*, right?
Well....
If a clock is broken at 8 O'clock, it's possible that every time anyone ever happens to look at it, it will be either 8 AM or 8 PM. If a coin is fair, it is nevertheless just barely possible that it happens to come up heads every time it happens to be flipped. Perhaps, through a massive, bizarre coincidence, God's fallible knowledge of the future never happens to fail. To claim that this is how God has an entirely accurate and complete knowledge of the future would be massively ad hoc, but it's just barely in the logical space of possibilities.
Still, this doesn't seem to be what people typically mean by divine foreknowledge. It seems to me that, built into ordinary usage of the concept, is the notion that God's foreknowledge is infallible. It's not just that God's beliefs have always and will always luckily happen to be true, but that there's a deep sense in which it would impossible for God to make a mistake.
So, how about reconciling infallible divine foreknowledge with libertarianism without backward causation?
Many theists seem to think this can be done with "middle knowledge." God knows what you would do under certain circumstances, and God knows which circumstances will arise, therefore even without (a) determinism, or (b) God just having direct access to future facts, it is still the case that (c) God knows absolutely everything that will happen in the future.
Now, first notice that we're attributing to God not just knowledge of the "counterfactuals of freedom" of people who already exist, but also of people who will come into existence in the future. Thus, without God having direct epistemic access to the future, God knows the exact details of every free decision that will ever be made by every person who will come into existence 10,000 years in the future.
Now, for the theistic compatibilist (who accepts determinism), that's no problem--given determinism, everything about the character of future people, what kind of decisions they will make, etc., is a function of genetics, environment, etc., and is ultimately all built into the present physical state of the universe. If God knows everything about the present and everything about the laws of nature, He can extrapolate the total state of the universe 10,000 years in the future, including (given a compatibilist understanding of freedom) every free decision made by those future people.
But....for a theistic libertarian, just how does this work? For the sake of simplicity, let's stick with the (presently non-existent) children of present people. Given His knowledge of present-tense facts about you and the person who you will one day have kids with, combined with His knowledge of facts about which external circumstances will arise, God can have foreknowledge of which people will come into existence. How, however, does He know (without direct access to future facts) what decisions those (presently non-existent) children will make under various circumstances, unless that's simply a function of their genetics and environment? Given a view of free will that says that a decision can't be simultaneously determined and free, middle knowledge of presently non-existent people would seem to obviously, trivially rule out free will.
It gets worse. Even for God to have short-term infallible foreknowledge of the future actions of presently existing people without having direct access to future facts, determinism creeps back in. After all, if, given present facts about the agent's character, unavoidable external circumstances, etc., their eventual decision is unavoidable--which is what it amounts to to say that a being with infallible knowledge of all those present facts would therefore have infallible extrapolative knowledge of their future decisions--then those decisions are causally determined. The agent can't do otherwise in the sense of "can do otherwise" that differentiates libertarians from compatibilists.
Of course, there are "softer" versions of libertarianism whereby it's OK for most decisions to be causally determined given previous facts about character, etc., provided that certain key "character-forming decisions" are radically free from deterministic chains of cause-and-effect. Even those kinds of moderate libertarian views won't help here, though, given that God would not have had even short-term infallible foreknowledge of those key character-forming decisions.
One way or the other, without backward causation (i.e. direct divine access to future facts), either you have to give up on across-the-board infallible divine foreknowledge or you have to give up on indeterminism. It looks to me like anyone who wants to combine classical theism (complete with infallible divine foreknowledge) with a libertarian view of free will would be well-advised to get over any squeamishness they might have about future facts and backward causation.
Thoughts?
Tuesday, June 29, 2010
Monday, June 28, 2010
The 110th Philosophers' Carnival
OK, that was the opening credit sequence for the HBO show Carnivale, which might not actually be strictly relevant to the Philosophers' Carnival. Good show, though.
Moving on to actual philosophy, over at Chaospet, cartoon philosophers Gabe and Nestor discuss a problem with the Cosmological Argument for the existence of God.
At Flickers of Freedom, Randolph Clarke wonders about Frankfurt-style omission cases:
"It's widely accepted that in a standard Frankfurt-style case, the agent can be responsible for what she does, despite the presence of something poised to make sure that she does that very thing. These standard cases involve agents who ACT and, despite the would-be intervention, are responsible for their ACTIONS. Are there similar cases in which agents OMIT to act, there's a similar would-be intervention, but the agents are still responsible for their OMISSIONS?"
Read The Rest Here
Elsewhere in he same tent, Roy Baumeister wonders why addicts don't just man up and decide to stop being addicted. How hard can it be?
OK, actually, the previous paragraph represents an extremely unfair caricature of what's actually a quite nuanced and interesting discussion of the relationship between free will and addiction, which you can read here.
"I have been wondering about what we can learn from the addiction literature about free will. I'd like to hear people's thoughts on this. I am not an expert on the philosophy of drugs (i am experimental social psychologist with expertise in self-regulation and a smattering of other stuff), and i am just going in and reading the literature to see what i can see. I try to have no preferences other than to figure out what's up, and simply to follow the data.
"It seems there are two very different positions. One is that addicts lose free will, though only specifically with respect to the addiction, and they retain free will (and moral responsibility) in most or all other respects. The other position is that there is no loss of free will and that maintaining addiction is voluntary behavior.
"It looks like addicts themselves and the medical establishment firmly favor the no-free-will position. But then it is self-serving for them, and they do not mostly have large impartial data sets. In contrast, the researchers, who do have these broad data sets, are somewhat more divided..."
Keep Reading
At the next tent over, they're still talking about free will. Hey, anyone who's ever taught an Intro class knows that this is one of the philosophical subjects that beginning students get the most fascinated by. It only stands to reason that a *carnival* of philosophy should include a decent helping of it. Cotton candy, rollercoasters and free will! Also some other philosophical subjects in the next tent over, but meanwhile, at On The Human, Christopher Suhler and Patricia Churchland raise concerns about whether recent empirical work undermined the kind of control that would seem to be necessary for free will and moral responsibility.
"An important notion in moral philosophy and many legal systems is that certain circumstances can mitigate an individual’s responsibility for a transgression. Generally speaking, such situations are considered extenuating in virtue of their exceptional influence on a person’s ability to act and make decisions in a normal manner. The essence of the case for diminished responsibility is that these special circumstances impede the ability of a normal person to exercise self-control.
"In recent years, however, this notion of diminished responsibility has come to wider attention in a quite unexpected way. Some researchers, drawing on findings from social psychology, have argued that situational forces may play a much larger role in behavior than traditionally assumed. The situational forces in question are often entirely ordinary, mundane and seemingly trivial. Given that such influences are pervasive, the general issue raised concerns control in commonplace cases. According to a condensed version of this view – which we call the Frail Control hypothesis for convenience – even in unexceptional conditions, humans have little control over their behavior...."
Keep Reading. And do be sure to check out the comment thread, where Gil Harman, Eddy Nahmias, John Martin Fischer and many others pile on to raise various interesting objections to and questions about all of that.
Moving on to the epistemology tents, at Certain Doubts, Keith DeRose explores the relationship between experimental philosophy and epistemic contextualism.
"The tale that Jonathan Schaffer and Joshua Knobe (henceforth, 'S&k') tell in 'Contrastivism Surveyed' is a tragic one for what we may call 'standard contextualists' about knowledge attributions. First, they report (word of this has been 'out on the street' for a while now) that a recent wave of work in Experimental Philosophy threatens to undermine the intuitive basis that contextualists have claimed for their view. Given the importance of that intuitive basis for the view, this would be very bad news indeed for contextualists."
You, dear reader, will be shocked to learn that not everything about this story is as it initially appears. To read the rest, see the blog post here or jump straight to the paper here.
Over at Experimental Philosophy, Jonathan Weinberg responds:
"I've had a chance to read Keith DeRose's very interesting & rich engagement with some of the experimental epistemology literature, and there's a lot in it that's clearly going to be useful to x-phi practitioners to learn from & absorb. (See some nice discussion of it already ongoing here.) But I also think that there are some ways, in a couple of places, in which Keith is subtly underestimating some of the ways in which one can conduct a different kind of investigation with survey methods than one can from the armchair....."
Want to see what the subtle mistake is? Read on.
Elsewhere in the Experimental Philosophy tent, Joshua Knobe discusses an overlap between recent x-phi work and something he heard on NPR:
"A recent episode of the NPR show 'This American Life' takes up the question of group agency and, in particular, the degree to which people are willing to ascribe psychological states to corporations.
"Oddly enough, the presenters end up getting into an argument about precisely the issue that Adam Arico addressed in his very nice experimental paper...."
Just between the two of us, reader, I must admit that my first reaction was "wow, he got through a whole episode of 'This American Life' without falling asleep? Huh." That said, the issue itself is interesting, so do read on.
(And, speaking of Knobe, do check out the bloggingheads video thingie he did with the previously mentioned Roy Baumeister.)
At Clear Language, Clear Mind, Emil Kirkegaard provides a helpful review of Quine 101, on the refutation of scientific theories:
"This will not involve many science facts as the discussion is wholly philosophical in nature. This is an epistemological, not scientific essay, it just happens to use some facts of science...."
Of course, in Quine 102, we learn that the categories of "scientific" and "epistemological" are continuous with each other, but that's next semester. For know, you can read the rest of Emil's post here.
Speaking of the interface between science and philosophy, Brian Leiter speculates that a recent government study from the U.K. about fetal sentience will "drive the anti-abortion crazies...well...crazy."
Of course, those who are convinced by Judith Jarvis Thompson's sick violinist argument (and, for the sake of full disclosure, I'm fairly strongly on record on that subject), would continue to be pro-choice even if the Royal College had found that fetuses were fully-developed little people, composing haikus and pondering their own existential dread in there, but the empirical results that Leiter cites are still interesting.
Finally, since every carnival has to end, drunken revelers vomiting out cotton candy and the creepy, mysterious voice of Management directing the carnival further down south--no, wait, I may be confusing the Philosophers' Carnival with the tv show Carnivale again, my bad--we finish up with a bit of applied philosophy. Here's Wooler.Scottus on the Knobe Effect:
"In this posting I want to consider one of the most famous findings in experimental philosophy. In 2003 Joshua Knobe discovered there is an asymmetry in the way we ascribe intentional acts http://en.wikipedia.org/wiki/Joshua_Knobe . The Knobe effect might be described as follows. If the manager of a company knowingly damages the environment in his search for greater profits then his action in damaging the environment is regarded as intentional. However if the same manager of the company knowingly benefits the environment in his search for greater profits then his action is regarded as unintentional. Logically it would seem the two situations are equivalent and we should regard both acts as either intentional or unintentional. Is it possible to explain the Knobe effect?"
Read on to find out.
That's it for the carnival this time. Check out the Philosophers' Carnival site to see future and past hosts and to submit your favorite blog posts. (And please, for the sake of the sanity of the next host, do try to restrain yourself from sending posts about financial planning tips or how Ayn Rand makes you feel about life, and stick to things that would, in some reasonably broad sense, be recognizable as philosophy!) The next carnival will feature on July 19th at Parableman - email Richard Chappell if you would like to host the carnival at some point in the future.
Wednesday, June 16, 2010
Monday, June 14, 2010
Wednesday, June 9, 2010
Philosopher's Carnival: Call for Submissions
I'll be hosting the next Philosopher's Carnival, on June 28th. (The current edition is here.) If you have a blog post that you'd like to submit, you can do so here.
Also, hey, if you feel inspired to write something new with this in mind, you've got plenty of time to do so. You have something you've been burning to say about truth-value gaps, dialetheism and the Curry Paradox, right?
Or....what's that, you say? You actually don't have anything to say about that?
Well, OK, then. Posts on all topics are welcome.
(...as are philosophically-themed comics. Yes, I'm talking to you, Ryan. Write me something.)
Also, hey, if you feel inspired to write something new with this in mind, you've got plenty of time to do so. You have something you've been burning to say about truth-value gaps, dialetheism and the Curry Paradox, right?
Or....what's that, you say? You actually don't have anything to say about that?
Well, OK, then. Posts on all topics are welcome.
(...as are philosophically-themed comics. Yes, I'm talking to you, Ryan. Write me something.)
Monday, June 7, 2010
A Revenge Paradox For Dialetheist Solutions To Curry
(Update: Never mind. See the comments.)
Dialetheists like Graham Priest and JC Beall think that some sentences are both true and false, but cleave to classical orthodoxy to the extent of continuing to insist that every sentence is either true or false. (The latter assumption is, in fact, crucial to the derivation of contradictions from the paradoxes.) Thus, Liar sentences get classified as both true and false, and the resulting contradictions are contained by rejecting classical logic in favor of paraconsistent logic. So far, so good.
For obvious reasons, this solution doesn't help with "Curry" sentences, like S1:
S1: If S1 is true, then everything is true.
If S1 gets classified as either (just) true or both true and false, triviality ensues. As such, it had best get classified as (just) false. Of course, this by itself doesn't get around the paradox, since, for familiar reasons, triviality ensues from he mere statement of S1's disquotational truth conditions. That is, however, beside the point for the purposes of this post. The important point is that, for a dialetheist who accepts that every sentence is either true or false but wishes to avoid triviality, the only option for the truth-value of S1 is that it is (just) false.
So far, so good. What, however, about S2?
S2: If S2 is either true or false, then everything is true.
Discuss.
Dialetheists like Graham Priest and JC Beall think that some sentences are both true and false, but cleave to classical orthodoxy to the extent of continuing to insist that every sentence is either true or false. (The latter assumption is, in fact, crucial to the derivation of contradictions from the paradoxes.) Thus, Liar sentences get classified as both true and false, and the resulting contradictions are contained by rejecting classical logic in favor of paraconsistent logic. So far, so good.
For obvious reasons, this solution doesn't help with "Curry" sentences, like S1:
S1: If S1 is true, then everything is true.
If S1 gets classified as either (just) true or both true and false, triviality ensues. As such, it had best get classified as (just) false. Of course, this by itself doesn't get around the paradox, since, for familiar reasons, triviality ensues from he mere statement of S1's disquotational truth conditions. That is, however, beside the point for the purposes of this post. The important point is that, for a dialetheist who accepts that every sentence is either true or false but wishes to avoid triviality, the only option for the truth-value of S1 is that it is (just) false.
So far, so good. What, however, about S2?
S2: If S2 is either true or false, then everything is true.
Discuss.
Wednesday, June 2, 2010
Are Meaningless Sentences (and Bits of Burning Candle Wax) Untrue?
Solutions to the Liar Paradox according to which paradoxical sentences are meaningless face all sorts of challenges. For one thing, the partisan of such a solution needs to have a plausible error theory to explain the widespread intuition that such sentences are meaningful. For another thing, they must find a way to defuse familiar "revenge" Liars, like $, below.
$ The sentence marked with a dollar sign is either false or meaningless.
These are major obstacles, and whether or not they can be plausibly overcome is a subject for another time. What I want to focus on is an objection which I find far less initially plausible, but which I hear a surprising amount of the time.
It goes, more or less, something like this:
"Even if Liar sentences are meaningless, they're still not true, right? Meaningless claims aren't true, so that solution doesn't even help with the Strengthened Liar. ('This sentence is not true.')"
Now, in whatever sense in which we are speaking sense when we say "meaningless sentences aren't true," surely it would be exactly equally correct to say that "meaningless sentences aren't false." Meaningfulness is surely a prerequisite for falsity, just as it's a prerequisite for truth.
Forget, for a moment, about the Liar and its kindred semantic paradoxes. Let's just think about a normal case of a sentence whose meaninglessness is much less controversial, like "Green ideas sleep furiously."
Now, given the two claims we just endorsed:
(1) Meaningless sentences aren't true.
&
(2) Meaningless sentences aren't false.
Given these two claims, Disjunctive Syllogism, Conjunction-Addition and the Principle of Bivalence (for every P, either P is true or P is false), we can easily derive a contradiction about a normal, non-paradoxical meaningless sentence like "Green ideas sleep furiously."*
Let's symbolize "Green ideas sleep furiously" as G. Given Bivalence, we've got our first premise:
1. Tr(G) v F(G)
Symbolizing (1), above, we've got our second premise:
2. ~Tr(G)
From 1, 2 and Disjunctive Syllogism, we can conclude:
3. F(G)
Symbolizing (2), above, we get:
4. ~F(G)
And finally, of course, from 3, 4 and Conjunction-Addition, we conclude:
5. F(G) & ~F(G)
So, given Bivalence and a couple of basic logical rules, the claim that meaningless sentences aren't true or false entails contradictions. Perhaps the very notion of meaninglessness as a separate category from truth and falsity is inconsistent!
But wait. Even if we're willing to give up on the claim that any sentence anywhere is meaningless, what about questions. Surely questions exist. Can questions be true or false? How about bits of burning candle wax? Are they true? No? Are they false? Also no? Well, if G symbolized not a meaningless declarative sentence but a question or a bit of burning candle wax, we could use precisely the same five-step proof to derive an outright contradiction about the semantic status of the question or the bit of burning candle wax.
Clearly, something has gone horribly wrong in our reasoning.
Here's what it is:
When we say "meaningless statements aren't true," we might be making one of two claims:
1-Let M(P) mean "P is meaningful." For every P, if ~M(P), then ~Tr(P).
or
2. Meaningless sentences aren't the sort of thing to which truth talk meaningfully applies.
If you mean 1, you're confused. (It's significant that no dialetheist has ever used the proof above as an argument for the existence of true contradictions. And if that argument were available with them, why would they bother to swim in the murkier waters of semantic paradoxes?) When we try to symbolize a meaningless statement and perform logical operations on them, we're engaged in a nonsensical category mistake, of exactly the same sort that we'd be engaged in if we tried to symbolize and perform logical operations on a big of burning candle wax.
If you think meaningless sentences aren't true, and when you say that, you actually mean to assert of every meaningless sentence the negation of the claim that that sentence is true, you are necessarily saying something meaningless. After all, given the universal intersubstitutivity of P and Tr(P) for every P, if you say that "Green ideas sleep furiously" is not true, meaning ~Tr(P)--where P is "Green ideas sleep furiously"--then you are, in effect, asserting ~P. As the philosophers of the Vienna Circle were so fond of pointing out, the negation of nonsense is nonsense.
Unless you're willing to accept that green ideas fail to sleep furiously--and that there are true contradictions about the truth-value of every meaningless sentence--when you say that "meaningless statements aren't true", you'd better mean it in sense 2.
Now, like I said before, none of this helps the partisan of the meaninglessness view against revenge paradoxes crafted to fit the details of the view. (For example, given the discussion above, one might wonder about the following sentence, which we could call The Babbler: "This sentence is not the sort of thing to which truth talk meaningfully applies.") And that's fair enough.
Still, whether or not they are ultimately viable when we really look into the ins and outs of revenge paradoxes, intuitive difficulties and so on, meaninglessness solutions can't be batted away with the blunt instrument of pointing out that meaningless sentences aren't true.
*At least, that's one that most people take to be meaningless. (E.g. another commonly heard response to claims that Liar sentences are meaningless is "wait, you don't mean meaningless the same way that 'Green ideas sleep furiously' is meaningless, do you?") If, however, you hold semantic views on which 'green ideas sleep furiously' comes out as meaningless, please accept the following as a substitute:
Sentence S1: 'Green swimming red night fun fun fun!'**
**"But wait," I can hear some of you saying, "Sentence S1 isn't even well-formed!"
Well, I'd argue that any invocation of "well-formedness" as a consideration here misses several points at once. "Well-formed" means something fairly specific for symbolic formulas. It's not clear what it's significance is supposed to be when we start throwing it around with reference to natural language sentences. The closest natural language equivalent of the formation rules of formal systems would be the rules of grammar, and conformity to those is clearly neither necessary nor sufficient for meaningfulness. If someone accuses another person of having done something wrong, and the person being accused responds with Sentence S2:
Sentence S2: "Like hell I did!"
....everyone knows what is meant. If the accuser, trying to catch the accused person in an inconsistency, formalized Sentence S2 with a Greek letter, did the same with some of his other statements and and drew out some logical implications, no one would think the accuser was in the grips of any kind of deep conceptual confusion.
Now, someone trying to desperately hold on to some significant role for natural language "well-formedness" could try to say that the difference is that there are grammatically "well-formed" sentences that mean the same thing as Sentence S2, whereas no grammatically well-formed sentence means the same thing as Sentence S1, but, of course, by definition, no grammatically well-formed sentence *ever* means the same thing as any meaningless sentence, because meaningless sentences don't mean anything. That's what we mean when we call them "meaningless."
$ The sentence marked with a dollar sign is either false or meaningless.
These are major obstacles, and whether or not they can be plausibly overcome is a subject for another time. What I want to focus on is an objection which I find far less initially plausible, but which I hear a surprising amount of the time.
It goes, more or less, something like this:
"Even if Liar sentences are meaningless, they're still not true, right? Meaningless claims aren't true, so that solution doesn't even help with the Strengthened Liar. ('This sentence is not true.')"
Now, in whatever sense in which we are speaking sense when we say "meaningless sentences aren't true," surely it would be exactly equally correct to say that "meaningless sentences aren't false." Meaningfulness is surely a prerequisite for falsity, just as it's a prerequisite for truth.
Forget, for a moment, about the Liar and its kindred semantic paradoxes. Let's just think about a normal case of a sentence whose meaninglessness is much less controversial, like "Green ideas sleep furiously."
Now, given the two claims we just endorsed:
(1) Meaningless sentences aren't true.
&
(2) Meaningless sentences aren't false.
Given these two claims, Disjunctive Syllogism, Conjunction-Addition and the Principle of Bivalence (for every P, either P is true or P is false), we can easily derive a contradiction about a normal, non-paradoxical meaningless sentence like "Green ideas sleep furiously."*
Let's symbolize "Green ideas sleep furiously" as G. Given Bivalence, we've got our first premise:
1. Tr(G) v F(G)
Symbolizing (1), above, we've got our second premise:
2. ~Tr(G)
From 1, 2 and Disjunctive Syllogism, we can conclude:
3. F(G)
Symbolizing (2), above, we get:
4. ~F(G)
And finally, of course, from 3, 4 and Conjunction-Addition, we conclude:
5. F(G) & ~F(G)
So, given Bivalence and a couple of basic logical rules, the claim that meaningless sentences aren't true or false entails contradictions. Perhaps the very notion of meaninglessness as a separate category from truth and falsity is inconsistent!
But wait. Even if we're willing to give up on the claim that any sentence anywhere is meaningless, what about questions. Surely questions exist. Can questions be true or false? How about bits of burning candle wax? Are they true? No? Are they false? Also no? Well, if G symbolized not a meaningless declarative sentence but a question or a bit of burning candle wax, we could use precisely the same five-step proof to derive an outright contradiction about the semantic status of the question or the bit of burning candle wax.
Clearly, something has gone horribly wrong in our reasoning.
Here's what it is:
When we say "meaningless statements aren't true," we might be making one of two claims:
1-Let M(P) mean "P is meaningful." For every P, if ~M(P), then ~Tr(P).
or
2. Meaningless sentences aren't the sort of thing to which truth talk meaningfully applies.
If you mean 1, you're confused. (It's significant that no dialetheist has ever used the proof above as an argument for the existence of true contradictions. And if that argument were available with them, why would they bother to swim in the murkier waters of semantic paradoxes?) When we try to symbolize a meaningless statement and perform logical operations on them, we're engaged in a nonsensical category mistake, of exactly the same sort that we'd be engaged in if we tried to symbolize and perform logical operations on a big of burning candle wax.
If you think meaningless sentences aren't true, and when you say that, you actually mean to assert of every meaningless sentence the negation of the claim that that sentence is true, you are necessarily saying something meaningless. After all, given the universal intersubstitutivity of P and Tr(P) for every P, if you say that "Green ideas sleep furiously" is not true, meaning ~Tr(P)--where P is "Green ideas sleep furiously"--then you are, in effect, asserting ~P. As the philosophers of the Vienna Circle were so fond of pointing out, the negation of nonsense is nonsense.
Unless you're willing to accept that green ideas fail to sleep furiously--and that there are true contradictions about the truth-value of every meaningless sentence--when you say that "meaningless statements aren't true", you'd better mean it in sense 2.
Now, like I said before, none of this helps the partisan of the meaninglessness view against revenge paradoxes crafted to fit the details of the view. (For example, given the discussion above, one might wonder about the following sentence, which we could call The Babbler: "This sentence is not the sort of thing to which truth talk meaningfully applies.") And that's fair enough.
Still, whether or not they are ultimately viable when we really look into the ins and outs of revenge paradoxes, intuitive difficulties and so on, meaninglessness solutions can't be batted away with the blunt instrument of pointing out that meaningless sentences aren't true.
*At least, that's one that most people take to be meaningless. (E.g. another commonly heard response to claims that Liar sentences are meaningless is "wait, you don't mean meaningless the same way that 'Green ideas sleep furiously' is meaningless, do you?") If, however, you hold semantic views on which 'green ideas sleep furiously' comes out as meaningless, please accept the following as a substitute:
Sentence S1: 'Green swimming red night fun fun fun!'**
**"But wait," I can hear some of you saying, "Sentence S1 isn't even well-formed!"
Well, I'd argue that any invocation of "well-formedness" as a consideration here misses several points at once. "Well-formed" means something fairly specific for symbolic formulas. It's not clear what it's significance is supposed to be when we start throwing it around with reference to natural language sentences. The closest natural language equivalent of the formation rules of formal systems would be the rules of grammar, and conformity to those is clearly neither necessary nor sufficient for meaningfulness. If someone accuses another person of having done something wrong, and the person being accused responds with Sentence S2:
Sentence S2: "Like hell I did!"
....everyone knows what is meant. If the accuser, trying to catch the accused person in an inconsistency, formalized Sentence S2 with a Greek letter, did the same with some of his other statements and and drew out some logical implications, no one would think the accuser was in the grips of any kind of deep conceptual confusion.
Now, someone trying to desperately hold on to some significant role for natural language "well-formedness" could try to say that the difference is that there are grammatically "well-formed" sentences that mean the same thing as Sentence S2, whereas no grammatically well-formed sentence means the same thing as Sentence S1, but, of course, by definition, no grammatically well-formed sentence *ever* means the same thing as any meaningless sentence, because meaningless sentences don't mean anything. That's what we mean when we call them "meaningless."
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