No, = is what you use between objects, ⟷ is what you use between statements. Another symbol sometimes used for equivalence of statements is ≡.

I feel stupid.

As I was working on a response to your last post, there were some things I was puzzled about and obviously you've been puzzled by some of what I was writing recently. I started to worry that we were losing the thread of the argument. So I decided to go back through everything and I realized there was something about your position that I had fundamentally misunderstood.

A long time ago, you admitted that the argument from design is not deductive but inductive. I had been assuming that the issue, since then, was how to make that induction work, and I've gotten caught up in the details of that. I now realize that, as far as you were concerned, the inductive argument was actually complete at that moment, as soon as you agreed that it was an inductive argument. From your point of view, the conclusion of the argument, that order is always attributable to conscious agency, was established a long time ago. That the universe, being ordered, must be the work of a conscious agency, is just an application.

There are two peculiarities about this. One I should have understood, because it's pretty fundamental to the way the argument from design works. The other is interesting.

At first, a lot of us reached for examples from nature of things that are ordered, apparently without any conscious agency taking a hand--crystals, normal distributions, complexity, etc. None of this was relevant, as it turns out, because of the way the argument works.

It's an induction. You throw every ordered thing you can find into a box, then take them out one-by-one and check to see if they are the result of conscious agency. There's trillions upon trillions of human artifacts in the box--the usual watches, tidy rooms, and 747s--and then there's the universe. The whole universe. A single object that is ordered, like one of the billions of watches in the box. Although a typical scientist might see what humans have done as an unimaginably small dataset compared to all she could conceivably learn from looking at the vastly hugely mind-blowingly big universe, here the tables are turned: the entire universe is just one more ordered thing, just another wristwatch. Of course, that's how the argument from design works, and I feel stupid for having forgotten that.

But here's where it gets interesting. Say you have a hypothesis that all ravens are black. You put every raven you can find into a box, then take them out one-by-one and check to see if they're black. Suppose among all those ravens--black, black, black, black--there's one that somehow is indeterminate in color. From one direction it looks blackish, from another kinda grey, from another nearly brown. You could stop, and decide that the induction fails because here's a raven that is not definitely black. Who knows how many more of these there are? Doesn't matter anyway, one's enough to scuttle the project. Or you could decide, weird raven, let's set it aside for now and check the rest. You go through the whole box, find nothing but black, and conclude that the induction is still pretty strong. Now what about that indeterminate-color raven? Having finished your work, can you now say, my inductive argument shows it must be black? Er, no. It's still indeterminate in color, despite the strength of the induction. It's not even probably black.

Now suppose that the one indeterminate-color raven is, for some reason, kept, unexamined, in a separate box, and you go through the entire box of black ones first. Then you can conclude, without even opening the box containing the last one, that so long as there's a raven in there, the inductive argument shows that it's black.

So that's exactly what happened here. Every possible instance of order in nature was lumped together as one single data point, the universe, and then that data-point isn't even examined. It's held back until we've gone through all the watches and tidy rooms and 747s, the conclusion is established, and then we apply our inference to the universe--it's ordered, must have been ordered by someone.

Well, that's cheating. It's not supposed to matter what order you examine your data points in. If you reach an instance of order that isn't clearly the work of a person--maybe it's the first one you pulled out of the box, maybe it's the 587th--you're done. Even if you decide this is just an outlier and set it aside, once you're done you don't get to go back and say the induction showed that the universe must be the work of a person. It's still an outlier, induction or no induction.

The argument cheats. It compresses almost all of the data available into a speck, and then it even hides that speck to make sure we don't look at it and wonder why it's not obviously like everything else.

Side notes:
(1) "Science is just as bad." I had forgotten that this was your real point. Well, no. After the raven study, a scientist will report that very nearly every raven is black, but there's at least one outlier, and conclude that we'll just have to learn more about the process of raven pigmentation.
(2) "It still makes it likely that the universe, being ordered, is the work of a conscious agency." True enough, if you treat every doodled smiley face as a datapoint equal to the entirety of universe, oh yeah the odds are going to be on your side. If, instead, you actually look at nature instance by instance, you'll find overwhelming evidence of self-organization at every level can you think of, all of it happening without any sign of a conscious agent behind it all.
(3) "It's no less likely that the universe is the work of a conscious agency." Could be, but I'd spend a lot of time in point number 2 before reaching a conclusion.

That test is really odd. I got it to spit out "Empiricism" which I'm vaguely okay with, but I knew that's what I was making it say because I like the other options in the poll even less.

I feel dirty.

Luck is the residue of design. — Branch Rickey

On topic too.

There's a neighboring idea, roughly that as you widen the extension you decrease the content. If your predicate applies to the entire domain of discourse, you're no longer saying anything. Not only has that been an ineffective argument, there's something about it I feel a little skittish of.

No property possessed by the whole universe can be knowable. Agree? — Mongrel

Those who accept the argument from design not only disagree, but think their view is obviously correct.

I tried maybe four or five variations on this theme and got nowhere. We're trying something else now.

I'm just allowing, for the sake of argument, that the concept could be innate and usable. (Someone might have cleverly bestowed this concept upon us, after all.)

I'm not seeing how composition helps. There would still have to be a concept that you can just know applies to the universe without comparing the universe to anything else. There may be concepts you can manage because you get to compare the universe to parts of itself, but in the case of designedness, all the parts fall under the concept too.

EDIT: fixed an autocorrection.

Looking back, I think there's a spot where I skipped a step.

The problem we encounter immediately though is that concepts are comparative by nature. Even though it is conceivable that, having acquired, say, the concept [red], you could tell something is red without comparing it to anything not red, you could not possibly acquire such a concept in the first place. — Srap Tasmaner

This is unclear.

A concept more or less neatly divides the universe into things that fall under it and things that don't. That matches up just as neatly with how we acquire concepts: here's something that's red and here's something that isn't. (Allow me a bit of simplification here.)

I'm also allowing the possibility that you could apply a concept you have, even if you don't have to hand something that falls under it and something that doesn't.

I also argue that the concept of designedness you need cannot be acquired in the usual comparative way, so if we have such a concept it must be innate. The concept itself is also somewhat odd in that is true of the universe as a whole and everything in it, but I am not relying on that, as I have explicitly allowed that you might still be able to apply the concept if you have it.

The question that's left is whether we do possess such a concept and possess it innately.

Good one.

No, you don't have to devote yourself to math. I'd like to say it's logic you want to learn, but it's not that either. Logic is the formal way of doing something that's much broader than logic, namely reasoning.

To improve your reasoning skills, you're looking, to start with, for what they call "critical thinking" in schools these days. There are lots of introductory textbooks out there. (I have no idea what to recommend.) They'll all cover the basics of evaluating arguments, spotting fallacies, etc.

A couple of books you might also want to look at are Thank You For Arguing which is about rhetoric-- most CT texts I think treat this only as something for you to be wary of someone else using: and How Not to Be Wrong which covers a lot of the mathematical concepts you might find useful.

Beat you to it.

It's easy enough to form expressions that seem to refer to something, like "the millions in my bank account." If you substitute that expression for one that does refer to something, say, "the dozens in my bank account," you can form sentences that seem to be about something that isn't. But they aren't. At least if you understand "about" in the most natural way.

I just don't have it in me, man. If you ask me a more specific question, I'll try to answer.

That deflationary impulse is powerful too, I'll grant you. I'm keeping an open mind for now.

We do want to preserve the intuition that a proposition is true if things are the way it says they are, don't we?

You might have to introduce the two conditionals first, just depends on what rules you have, but yes.

I read a bit about truth-makers after I posted this, and what you say here makes sense. I'm going to think about this stuff some more.

I can't understand you. Can you simplify? — TheMadFool

If there's something specific you don't get, ask me.

I'll play devil's advocate.

The object that makes it true that Bernie Sanders is not the President is Donald Trump. [ Being POTUS ] is a property only one object can possess at a given time. Since Trump possesses this property, no other object does.

Alternatively, if we're not locked into objects, it could be the fact that Donald Trump is POTUS.

One other point, just on Quine, is that he not only believed he could happily get along without modal logic, he also believed classical logic had no use for singular terms at all.

And now I'm done speaking for Quine. I still think his work is a pretty good place to start doing philosophy, especially if you come from logic and mathematics.

Of course, the mere fact that we can define substitutional quantifiers in terms of objectual quantifiers and vice-versa already shows that a facile reading of Quine's maxim is at least problematic... — Nagase

The conversation between Barcan, Quine, and Kripke (and who else?) is interesting reading on this point.

Play nice boys. Philosophy is fun!

Once again, you have inconsistent premises. P1 says LH is true; P2 says RH is true; P3 says LH and RH don't have the same truth-value. But you just said they do.

The problem is P3. You're trying to say that having a left hand or a right hand doesn't necessitate having the other. That's not what P3 says.

Take another shot at it.

I can give hints if you get stuck.

ascertaining the validity of the underlying quantification — TimeLine

I don't know what this means.

Are you talking about Quine specifically or about the usual semantics for classical logic?

Thanks. I was hoping you'd stop by.

If W. wasn't saying that then he must be implying that there is more to meaning than simply use. So maybe we shouldn't be calling it a "meaning is use" theory. — Harry Hindu

Maybe you should stop thinking "use" is a synonym for "emit" and then a lot of this would seem less idiotic to you.

If you're just starting to do philosophy, trying to define existence is not the place to start.

It is also possible to construe quantifiers substitutionally. This means you take "∃n F(n)" to mean "There is an expression we can put in place of 'n' such that 'F(n)' is true." So in a way, the quantifiers range over linguistic expressions rather than objects. There's something quite natural about this approach. You explain "∀x F(x)" as meaning "F(x) is always true," and so on. I'm still not clear on the advantages and disadvantages of the two approaches, but taking variables as standing for objects is by far the more popular approach.

You needn't let that rigor disappear. The American philosopher W. V. Quine famously said, "To be is to be the value of a bound variable." He took "there exists" to mean exactly what it seems to, and argued that if somewhere in, say, a theory of physics, you have an expression like "∃x F(x)" then your theory is committed to the existence, real-world actual existence, of something that is F.

(Apologies if you know all this. If not, the place to start is "On What There Is" collected in Ontological Relativity and Other Essays.)

Like when we define the truth of a formula of the form ∃n F(n) we say:
∃n F(n) is true iff there exists a natural number x such that F(x) is true
In that definition does the 'there exists' part mean the set theoretic provability of the existence or some kind of platonic metaphysical existence or some other kind of existence. — Meta

If the question is whether you are committed to interpreting ∃ metaphysically, maybe platonically, then the answer is no. "∃n F(n)" says only that F is true of something in the domain of discourse.

Of course you can go further and take a position on what the objects in the domain of discourse are, but just using quantifiers doesn't commit you to any particular view.

Are you saying the similarity is that there are principles at all, or that the principles themselves are similar? — Srap Tasmaner

there are principles at all
— Srap Tasmaner

That's it. — TheMadFool

Is the relation between my house and its principles the same as the relation between the universe and its principles? — Srap Tasmaner

To the extent that we can posit a creator of the principles. — TheMadFool

So we've agreed that the principles that somehow relate to the house or to my building the house are not similar to the principles that somehow relate to the universe or to God creating the universe.

If I understand your last post, the idea is that what matters is that the builder or creator is the source of the principles that relate to the project. My ideas about the house guide the building of the house and determine the result; God's ideas about the universe guide his creation of it and determine the result. To say something is designed is to say that it embodies some person's ideas. Is that it?

So, absent direct evidence like watching someone design and build something, we can tell something is designed if we can tell that the principles of its organization were someone's ideas. In the presence of something designed, we feel it was done deliberately, or intentionally, or on purpose, at any rate that it didn't just happen, that there was an agency at work in addition to natural processes.

We can be wrong about this. Sometimes trees just happen to grow in circles. But if they are very precisely spaced, or if they line up with constellations or something, we may suspect they were planted. An archaeologist can spot a broken arrowhead where laymen would only see one rock among others. Pattern is not everything though, because nature is full of patterns.

And now we're right back where we started, because the claim is that the existence of patterns in nature is indeed evidence that nature is the way it is deliberately. We clearly cannot reach this conclusion the same way we determine, say, that the shape of this rock must have been deliberately imparted to it by a skilled craftsman. That method is comparative. Natural processes are known to shape rocks in certain ways, and this isn't one of them.

Since we cannot evaluate the universe comparatively--we are not in a position to say something like, this neat, orderly universe appears to have been made deliberately, but those other messy universes seem to have just happened--we must hold that design, deliberate intent, etc. can be apparent in a thing without reference to anything else. The object must wear its designedness on its sleeve.

The problem we encounter immediately though is that concepts are comparative by nature. Even though it is conceivable that, having acquired, say, the concept [red], you could tell something is red without comparing it to anything not red, you could not possibly acquire such a concept in the first place.

In this case, if designedness is to play the role demanded, it must be an innate concept. We must be born with the ability to recognize what is the result of deliberate, intentional design and what is not. And note that it has to be this particular concept. It will not do to say we are born with the ability to recognize patterns or something. No one is disputing that there are patterns in nature. What's at issue is whether those patterns are designed, whether the universe itself is designed, and we must be able to recognize this without comparing the universe to anything else.

Note also that the issue here is not whether there are different sorts of design. We could, for the moment, allow that there might be human design, ant design, divine design, and so on, and that it may be possible to acquire those distinctions through experience. The issue is whether they are all types of one and the same thing and whether you can tell they are just by looking, from the moment you're born.

Is the relation between my house and its principles the same as the relation between the universe and its principles?

The similarity is the existence of principles that is common to both a house and the universe. — TheMadFool

Are you saying the similarity is that there are principles at all, or that the principles themselves are similar?

Of course, in ordinary usage, people sometimes treat "believe" and "know" as, well, not quite opposites, but they don't treat believing as an ingredient of knowing the way philosophers often do. There's nothing at all unusual about someone saying, "I don't believe we're going to win tonight, I know we are!"

So I wonder what Moore's paradox looks like with the factive verb: "It's raining but I don't know it's raining." As before we treated "It's raining" as implicating belief, do we also take "It's raining" to implicate a claim to know it's raining?

And then tell me how the things on your two lists are similar.

I think Moore's paradox shows that use is an element of meaning but not exhaustive.

If we consider the statement "It's raining but I believe that it is not raining" then we quite rightly take it to be an absurd thing to say, even though "it's raining" and "I believe that it is raining" do not mean the same thing. And that's because in saying "it's raining" one is (usually) indicating that one believes that it is raining, and so the statement "It's raining but I believe that it is not raining" is a performative contradiction even if not a logical contradiction (thanks to The Great Whatever for this insight). — Michael

If in saying "It's raining," one is saying he believes it's raining, then it is logically contradictory to say "it's raining but I don't believe it's raining."

The contradiction arises because it's implicit that the speaker who states it's raining is the same speaker who states his belief that it's raining and it's assumed that a speaker can only assert beliefs even should he proclaim his statement as truth.

Contextually and implicitely you're saying "I believe it is raining but I don't believe it's raining," so you have a direct logical contradiction.

A performative contradiction (e.g. " I am dead" or "I ate my mouth") states an impossible performance. I cannot tell you I'm dead because death eliminates speech. I can't eat my mouth because my mouth does the eating.

The raining example you gave is 2 seperate propositions, and of a different form than my examples above. — Hanover

Shouldn't you be claiming that "It's raining but I believe that it is not raining" is equivalent to ""I believe it's raining and I believe I believe that it is not raining"? Then where is the direct logical contradiction?

"It's raining" is not equivalent to "I believe it's raining," nor does the former imply the latter, but arguably the former conversationally implicates the latter. What's odd here is that the implicature is apparently not cancelable. I honestly don't know what conclusion to draw from that.

The organization/order is what's common. — TheMadFool

Perhaps you could be more specific.

Suppose I built a house and God created this universe.
Tell me exactly what those two acts have in common.

0! = 1, and most mathematicians most of the time would say 0⁰ = 1. This is not a profitable avenue for you to stroll down.

I could agree with that.

As I read the history, and I'm not quite an expert, one of the things that happens in the LW and immediately post-LW era is the rise of the Oxford school, "ordinary language" philosophy. Despite the considerable differences, there's some overlap to sort out. What I find really interesting is what happened to OLP. Austin, Strawson, and Grice--much as they fought among themselves--are all taken up by linguists building out the new sub-specialty of pragmatics. As a school of philosophy, OLP seems just to disappear, but what actually happened is that it decamped to another department. There's stuff in Wittgenstein that you can also see as reaching for a field of pragmatics that doesn't exist yet, so he has to work really hard to show what he's getting at. And this is still a kind of analysis, absolutely.