To the extent that one has explored the logical space and found it empty of non.black ravens or pocketed stuff or whatever, to that extent it is probable that the space is empty. — unenlightened

I am fine with this common-sense approach for everyday living, especially if we substitute "one is confident" for "it is probable." What bothers me is the claim that we can meaningfully calculate a mathematical value for this "probability," as well as the claim that the observation of a non-black non-raven or a non-empty non-unenlightened's-pocket somehow affects the assessment.

If there is one white one and sixteen black ones, would you bet on the white one being the last one out of the bag, or some other place? — unenlightened

That is a different scenario. If I knew nothing about the contents of the bag, and had already drawn 16 black ones, I might very well be tempted to bet that the last one would also be black - and I would be dead wrong.

If I have looked at 16 of my 17 pockets and found them empty, I have probable grounds for thinking that the last one will be also empty. — unenlightened

Not really. Why would you think that? The contents (or lack thereof) of the first 16 pockets have no bearing whatsoever on the contents (or lack thereof) of the 17th pocket.

All unenlightened's pockets everywhere in the universe are empty. — unenlightened

One more point - you also have to stipulate that this was true when the observations occurred. Even then, it is only strictly true if those observations were simultaneous; otherwise, something could have appeared in the first pocket that you checked by the time that you got to the last one. Furthermore, the fact that your pockets were empty then does not warrant the claim that they are still empty now and will remain empty in the future. This gets at my earlier comment about a universal proposition having to include all potential members in the class, not just its actual members.

The difference is that you actually observed all of your pockets. The OP is claiming that a single observation provides evidential support for a universal proposition. @Tom's proof shows that this is not the case - but it no longer applies once you have observed all members of the class, at which point you know whether the universal proposition is true (p=1) or false (p=0).

If a lion is in the bushes then the leaves will rustle
The leaves are rustling
Therefore there's a lion — TheMadFool

This is a deductive fallacy, but it is a textbook case of retroductive (or abductive) reasoning. "There's a lion" is a hypothesis, a plausible explanation for the rustling leaves. We have reason to suspect that it is true (and behave accordingly), but no warrant for claiming to know that it is true.

Seeing one tiger attack and devour another deer should be logically sufficient to realize tigers kill deer. — TheMadFool

It is logically sufficient to conclude that some tigers kill deer. Since a deer cannot know in advance whether any particular tiger that it encounters happens to be one that kills deer, it has reason to suspect that all tigers kill deer (and behave accordingly), but no warrant for claiming to know that this is the case.

The bottom line is that deductive logic is about explicating our premisses - figuring out what else we know, based on what we know that we know - not determining what actions we should take accordingly; especially in scenarios like these, where it is obviously prudent to err on the safe side rather than find out the truth of the matter.

I have just proved that observational support for for a universal statement is impossible. If you think such support exists, and in particular that the observation of green apples provide support for any such statement, you have just been proved wrong. — tom

Why do you keep addressing this to me? My statement that you quoted has absolutely nothing to do with universal propositions. Observation of a green apple merely proves that the particular proposition, "some non-black things are non-ravens," is true (p=1).

It was meant to be equivalent to "if something is a raven then it is black" (which is why this is the phrase I've been using since page 3/4. — Michael

You used universal propositions, not singular propositions, in the OP. Now you are claiming that the two propositions of interest are both singular - "if a is a raven, then a is black," and its contrapositive, "if a is not black, then a is not a raven." In this example, a is a green apple, so it is trivial to say that a is not black and not a raven; both propositions are true (p=1). A second observation of a green apple, call it b, would go with a different pair of singular propositions - "if b is a raven, then b is black," and its contrapositive, "if b is not black, then b is not a raven"; again, both are true (p=1). By definition, you cannot say anything general in a singular proposition.

I'm not sure the relevance of potential non-black things. Can't this just be about actual non-black things? — Michael

A universal proposition does not assert the actual existence of anything in the subject class, so it must apply to all potential things in the subject class.

How, exactly, can one misinterpret the claim "there's a 0.5¹²" that every egg in that (closed) cartoon is a white egg? — Michael

By believing that the actual color of the eggs is somehow indeterminate until one opens the carton. It is not; it is a fact that either they are all white (p=1) or that at least one is non-white (p=0), unless we are going to treat this as a quantum physics scenario like Schroedinger's cat where each egg is neither white nor non-white until one observes it.

I beg to differ! If there is such a thing as probabilistic support for a universal statement, then green apples do indeed support "all ravens are black". — tom

Please read what you quoted from me again.

Notice that the observation of a green apple can have no effect whatsoever on any of these probabilities. It only tells us that the probability that non-black non-ravens exist is 1; i.e., some non-black things are non-ravens. — aletheist

I said that the observation of a green apple only supports - in fact, proves - the particular proposition that some non-black things are non-ravens.

Long story short: probability is extremely subjective. — Michael

You were quoting someone else here, but it expresses precisely why I take exception to using the term "probability" in this way, rather than "confidence" or "degree of belief." It gives a false connotation of objectivity to what is a fundamentally subjective assessment.

But if you insist on your understanding, then I think that this post is still relevant. — Michael

We do not know the value of n, the total number of non-black things, or 1/x, the probability that a randomly selected non-black thing is a non-raven. Your equations presuppose that n is finite and that 1/x<1; i.e., that some ravens are non-black. If we include not just all actual non-black things in n, but all potential non-black things, then n is infinite, and the probabilities are identical before and after the observation of a green apple, regardless of the value of 1/x. If all ravens are black, then 1/x=1, so both probabilities are 1, regardless of the value of n.

Note that you shouldn't conflate "if something is not black then it is not a raven" with "everything that is not black is not a raven". — Michael

The only way I can see that these two propositions are not logically equivalent is if the first one is treated as singular, rather than universal; and in that case, it is no longer logically equivalent to the original proposition, "All ravens are black."

Original: For all x, if x is a raven, then x is black.
Contraposition: For all x, if x is not black, then x is not a raven.
Singular: If a is not black, then a is not a raven.

The existence of x is not asserted by the first two, but the existence of a is asserted by the third.

The actual mathematics of probabilities includes the fractions between 0 and 1. — Michael

Indeed - when working with random samples, not individual cases. Returning to the deck of cards, if we anticipate drawing one from a truly random location in the stack, then the probability is 1/52 that it will be the ace of spades. Once we have actually drawn it, then it either is the ace of spades (p=1) or it is not (p=0). Shuffling and then taking the top card is not the same situation, because which card is on top is no longer random once the shuffling is done; at that point, it either is (p=1) or is not (p=0) the ace of spades, even before we look at it. On the other hand, before shuffling, the probability is 1/52 that the top card will be the ace of spades, assuming that the outcome of the shuffling is truly random.

If we have an egg-making device and know that there's a probability of 0.5 that any egg it makes is white (say we have an actual random number generator that if odd produces a white egg and if even produces a brown egg) then we know that there's a probability that every egg it makes, assuming it makes 10, being white is 0.5¹⁰. — Michael

So far, so good.

And we can use this reasoning even the machine has already made the eggs. — Michael

This is where I disagree - the reasoning is not the same. Once the machine has actually made the eggs, how many of them are white is a fact. If they are all white, then the probability that they are all white is 1; if any of them are non-white, then the probability that they are all white is 0. Our knowledge (or lack thereof) about how many are white vs. non-white is irrelevant to the associated probabilities.

The underlying idea here is that everything actual is subject to the principle of excluded middle, such that any given proposition about it is either true (p=1) or false (p=0). By contrast, anything general is not subject to the principle of excluded middle, such that intermediate probability values are possible for random samples thereof. A card in general is neither the ace of spades nor not the ace of spades; the probability that a randomly selected card in a standard deck is the ace of spades is 1/52. Unless all eggs are white, an egg in general is neither white nor non-white; in your example, the probability that a randomly selected egg is white is 0.5.

Likewise, unless all ravens are black, a raven in general is neither black nor non-black. The problem is that we have no way to determine the probability that a randomly selected raven is black, because we do not know what proportion of ravens is black. If it turns out that all ravens are black, then the probability that a randomly selected raven is black is obviously 1. For the contrapositive formulation, unless all ravens are black, a non-black thing in general is neither a raven nor a non-raven. Again, we have no way to determine the probability that a randomly selected non-black thing is a raven, because we do not know what proportion of non-black things are ravens. If it turns out that all ravens are black, then the probability that a randomly selected non-black thing is a raven is obviously 0.

Notice that the observation of a green apple can have no effect whatsoever on any of these probabilities. It only tells us that the probability that non-black non-ravens exist is 1; i.e., some non-black things are non-ravens.

Now consider the other proposition "if X is black then X is not a raven". This is consistent with "if X is not black X is not a raven", but it is not consistent with "if X is a raven then X is black", so the two statements do not have the same truth value in every model. — Metaphysician Undercover

To clarify, the model (often called a "world") in which these two propositions are consistent is one in which ravens do not exist; hence X is not a raven, regardless of whether X is black or not black. This goes back to the point about universal propositions not asserting the existence of anything.

The claim is "if something is not black then it is not a raven". The probability that it is true isn't 0 if we have a green apple. — Michael

Truth is not a matter of probability. It is either true (p=1) or false (p=0) that if something is not black then it is not a raven. The observation of a green apple is irrelevant; the proposition is still either true (p=1) or false (p=0). Our subjective confidence in the truth of the proposition is also irrelevant; it is still either true (p=1) or false (p=0). This is precisely why I consider it misleading to conflate degree of belief with probability.

Let me put it this way: I will concede that people ordinarily talk about "probability" when they really mean subjective confidence, if you will concede that people ordinarily do not count the observation of a green apple as evidence that all ravens are black. I think that the first is a mistake and the second is fine, you think that the first is fine and the second is a mistake.

I think you may be arguing towards the subjective as being real, and indeed the ultimately real. — apokrisis

No, I am just taking exception to using the term "probability" for subjective confidence or degree of belief - as did Peirce, if I remember right. As a theist, physicalism is a non-starter for me; but as I said in the dualism thread, I am intrigued by Peirce's alternative of objective idealism, where mind is primordial and matter is the same "stuff" but with "inveterate habits."

So, using your logic, the probability of a non-black thing not being a raven is 1. — Michael

Now you are losing track of the quantifiers. Given the observation of a green apple, the probability that some non-black thing is a non-raven is 1. It tells us absolutely nothing about the probability that all non-black things are non-ravens; that is still either 0 or 1.

Out of curiosity, how do you deal with ontic uncertainty? Do you treat vagueness and propensity as elements of reality? — apokrisis

If by "vagueness and propensity" you mean what Peirce called 1ns and 3ns, then yes, that is the working hypothesis that I have currently adopted and continue to explore. So by "ontic uncertainty," I assume you mean what he called "absolute chance."

Would you go as far as extending the principle of indifference to nature itself? — apokrisis

Again, it depends on exactly what you mean by that. As should be clear by now, I am opposed to using the term "probability" when what we really mean is (subjective) "confidence" or "degree of belief."

It is perfectly correct to say that the probability of the top card of a shuffled deck being the Ace of Spades is 1/52. We don't simply say that the probability is either 1 or 0. — Michael

Only if we embrace a sloppy usage of "probability." You refuse to acknowledge the objective/subjective distinction. There is nothing strange about it.

I have shown you with maths that the probability of the statement being true increases after each successful observation. At no point have you explained the error in this reasoning. You just ignore it. — Michael

I have (repeatedly) explained the error in this reasoning - successful observations have no effect whatsoever on the (objective) probability of the statement being true. You just ignore it, so I will stop wasting my time now.

Then where does my math fail? — Michael

Sigh, I thought that we had made a breakthrough. Your math fails right here:

Prior to any observation the probability of the claim being true is (1/x)ⁿ. After a successful observation the probability of claim being true is (1/x)^{n - 1}. — Michael

Observation has no effect whatsoever on the probability of the claim being true, since the claim is either true (p=1) or false (p=0) regardless of any observation (or lack thereof).

And yet it is perfectly ordinary to talk about the probability of the first card we turn over being the Ace of Spades being 1/52. So I dispute your claim that probability is somehow distinct from epistemic concerns. — Michael

Like I said, this is a philosophy forum, not a casual conversation. Turning over the card has no effect whatsoever on whether it is the ace of spades.

The whole thing is about epistemology, so I don't understand your objection. — Michael

My objection was that probability is not the same thing as epistemic uncertainty.

The paradox is that if we observe a green apple then we can be more confident that all ravens are black. — Michael

At last! If we observe a green apple, then I suppose we can be very, very, very, very, very slightly more confident that all ravens are black. However, no one would take this kind of reasoning seriously; that almost infinitesimal increase in confidence would not lead anyone (except you, apparently) to count the green apple as evidence that all ravens are black - certainly not anywhere close to the same extent that observing a black raven would, and even that should only make us slightly more confident.

Probability isn't simply limited to either there being a probability of 1 or a probability of 0. — Michael

It is limited to 1 or 0 in any individual (i.e., actual) case, where there is a determinate fact of the matter.

We can talk about the probability that I won the lottery yesterday being 1/x million (whatever it is) and we can talk about the probability that nobody won yesterday being (1 - 1/x million)^{the number of players}. — Michael

Not if we want to be precise in our language; this is a philosophy forum, not a casual conversation. Our lack of knowledge about whether you or anyone else won the lottery yesterday has no effect whatsoever on the associated probabilities. Either you won, or you did not. Either nobody won, or somebody did.

Evidence is just whatever increases the probability that the statement is true. — Michael

Please stop repeating this falsehood. The statement is either true or false, regardless of the evidence; i.e., the evidence has no effect whatsoever on the (objective) probability of the statement's truth, only our (subjective) confidence about it.

And to continue with my example of the pack of cards, imagine that we tear one of the cards. What's the probability that none of the intact cards is the Ace of Spades? — Michael

If you tore the ace of spades, p=1; if you tore some other card, p=0. You are confusing probability with epistemic uncertainty.

So I don't understand what you mean by "probability". — Michael

Strictly speaking, probability only applies to the long run of experience, not to an individual case. In general, the probability is 1/52 that the top card of any randomly shuffled deck is the ace of spades; i.e., that is the value to which the proportion of cases where that happens will converge as the number of trials increases to infinity. However, in each individual case, the probability is either 1 (if it is the ace of spades) or 0 (if it is any other card). Again, you are confusing this (objective) fact of the matter with the (subjective) confidence that someone has before looking at the card.

I would count as evidence anything that increases the probability that the statement is true. — Michael

But nothing that you think, say, or do can increase the (objective) probability that the statement is true; it is either true (p=1) or false (p=0) all along.

As shown here, each successful observation increases the probability that the statement "if something is an egg then it is white" is true. — Michael

No, it increases your (subjective) confidence that the statement is true; and when you only have 12 things in a collection, each "successful" observation significantly increases that confidence. However, notice that it has no effect whatsoever on whether the 12th egg (or even the billionth) actually turns out to be white.

Given that the existence of green apples increases the probability that "if something isn't black then it isn't a raven" is true ... — Michael

Saying this over and over does not make it accurate. The existence of green apples has no effect whatsoever on the probability that "if something isn't black then it isn't a raven" is true. The observation of a green apple might have a very small effect on one's confidence that "if something isn't black then it isn't a raven" is true; but since such confidence is subjective, the (lack of) relevance of the observation will in most cases prevent it from being counted as genuine evidence.

As the maths shows, each successful observation increases the probability of the assertion being true, and so seems to me to count as evidence (even if weak evidence). — Michael

I think that there is an equivocation here on what we mean by "probability." You are really talking about our (subjective) confidence in the truth of a proposition, rather than its (objective) likelihood. "All ravens are black" is either true (p=1) or false (p=0), regardless of what we think.

The vast majority of people have a relevance requirement for evidence. The purported evidence needs to have something to do with what it's evidence for. — Terrapin Station

I agree. In this case, the relevance requirement is tied primarily to the subject (ravens), rather than the predicate (black). The fact that green apples are not black things is not nearly as relevant as the fact that green apples are not ravens.

Said another way, there is a relation between the perceived strength of evidence and the number of items in a collection to which we are attributing a universal property. There are vastly fewer ravens than non-black things, so each black raven that we encounter increases our confidence that "all ravens are black" by a much larger degree than each green apple that we encounter increases our confidence that "all non-black things are non-ravens." This may be the asymmetry of the two logically equivalent formulations that others have been trying to articulate. For most people, something counts as (even weak) evidence for the truth of a proposition only if it significantly increases our confidence.

I suspect that the popular persistence of substance dualism is grounded in the common-sense apprehension that there seems to be a significant and fundamental difference between our first-person/internal experience of the world and our third-person/external description of the world. It is still fairly well-ingrained in Western culture to account for this by assuming that "I" am a non-physical soul that "has" a physical body, and that they (somehow) routinely interact.

Charles Sanders Peirce scoffed at both dualism (of any kind) and materialism/physicalism, instead hypothesizing what I think is an interesting monist alternative: objective idealism. He did not claim that everything is mental, thoughts in the mind of God, etc.; instead, he acknowledged a distinction between mind and matter, but conceived it as one of degree rather than kind: "the physical law as derived and special, the psychical law alone as primordial ... matter is effete mind, inveterate habits becoming physical laws" (CP 6.24-25; 1891). In this context, the psychical law - the "law of mind" - is the "law of habit."

This view "holds matter to be mere specialized and partially deadened mind" (CP 6.102; 1892), such that "what we call matter is not completely dead, but is merely mind hidebound with habits (CP 6.158; 1892). Eventually, "dead matter would be merely the final result of the complete induration of habit reducing the free play of feeling and the brute irrationality of effort to complete death" (CP 6.201; 1898). We are successfully able to model much of nature mathematically - i.e., with necessary reasoning - because its (physical) habits are relatively fixed; not so with people, whose (mental) habits are considerably more malleable.

(4) The king of France is bald. — quine

Based on the thread title, I assume that you intend to be asserting here that the king of France exists and is bald, which would be consistent with (3). However, (4) is ambiguous enough in natural language that it could also be interpreted as asserting that any king of France is bald, regardless of whether the king of France (currently) exists.

(6) (∀x)(Fx → Gx)

Either way, I agree with @andrewk that there is no obvious reason why the expression in second-order logic would be any different, since you do not need to quantify over predicates.

Are you saying that the "____" is nothing, in an absolute sense? — Metaphysician Undercover

It is not anything in particular; i.e., it need not be something that actually exists. The relation is real apart from any individual relata.

The only difference is that the ___ provides a higher degree of vagueness than the word. — Metaphysician Undercover

Hmm, maybe you are finally starting to catch on. The relations as I formulated them are general, rather than singular.

Another way to think about it is that nothing exists without being in relations. In fact, existence is reaction, the state of being in dyadic relations with other things.

... I will not even consider a logically impossible perspective. — Metaphysician Undercover

Your logic is evidently too narrow.

But a relation can only follow from the existence of the relata ... — Metaphysician Undercover

"____ is red" is a monadic relation; its reality does not require an existing subject to fill the blank. "____ is larger than ____" is a dyadic relation; its reality does not require two existing subjects to fill the blanks. "____ gives ____ to ____" is a triadic relation; its reality does not require three existing subjects to fill the blanks. And so on.

Thus crispness is defined in the sense that the dimensionality of the Universe - its degrees of freedom - are as generally limited at they can get. — apokrisis

Just curious - is there a reason why you prefer "crispness" as the term for the opposite of "vagueness," rather than something like "determinacy" or "definiteness"? Is it just to emphasize that you are talking about a continuum, a matter of degree, rather than an absolute dichotomy?

So an understanding of things (being) is necessarily prior to an understanding of relations between things (becoming). — Metaphysician Undercover

Not necessarily prior, since identity is a relation. There is also the Christian concept of God as Trinity, such that Being and relations are both necessary and eternal. In any case, my view (contra @apokrisis) is that Peirce's final cosmology requires the reality of God as Ens necessarium.

Yet a "community of minds" approach to pragmatic inquiry would logically require everyone to have the same kind of experience in repeatable fashion under the same conditions. — apokrisis

As you probably know, Peirce claimed in the article that "any normal man" who engaged in the kind of Musement that he recommended, and did so "in scientific singleness of heart," would come to love and adore "his strictly hypothetical God" to the point of shaping his "whole conduct of life" accordingly, which according to Peirce "is neither more nor less than the state of mind called Believing." Of course, in the second additament - the one that actually appeared with the original article in The Hibbert Journal - he explicitly grounded this assertion in the admittedly dubious assumption "that my own intellectual disposition is normal." He also acknowledged "that no pessimist will agree with me," adding, "I do not admit that pessimists are, at the same time, thoroughly sane." :D

If your essay gets published, send me a link. — apokrisis

Will do, but it will be a while. I finally heard back from the journal editor today, confirming that he received the manuscript and is initiating the review process, which will likely take a few months.

And then his neglected argument was a very poor paper - quite un-Peircean in its lack of rigour. — apokrisis

I find it fascinating what a startling diversity of opinions there are about that article, even among Peirce scholars who have written at length about it. It seems to be quite polarizing. Personally, I think that anyone who expects it to provide a rigorous argumentation for theism completely misunderstands the purpose of the piece. I submitted an essay of my own about it to a journal about a month ago, and am still waiting to hear back.

I don't want to blame the drugs and the mania, but his moment of ecstatic transport on entering a church at a particular low point may be both an important personal phemenological sign for him, yet clearly the weakest kind of evidence for the kind of scientific pragmatism he espoused. — apokrisis

That experience happened in 1892; he wrote "A Neglected Argument" in 1908. Peirce did a lot of his best philosophical work in between, including the end of the Monist metaphysical series, the 1898 Cambridge Conferences lectures, the 1902 Minute Logic, the 1903 Harvard and Lowell Lectures, the Monist pragmaticism series, and most of the development of his mature semeiotic (key letters to Lady Welby came shortly afterwards). I do not find it plausible that he suddenly lost his marbles when he composed this particular article, especially after reading through the fairly extensive and consistent manuscript drafts (R 841-844).

Calling existence divine or mindful - the much vaguer hypothesis of immanent pantheism - you could get away with. And that was more what Peirce, in his religious unorthodoxy, was really going for. — apokrisis

This is a popular claim in some circles, but it is refuted by Peirce's explicit and emphatic statement in three different drafts that he did not mean by God something "immanent in" nature or the three Universes of Experience, but the Creator of them and all their contents without exception. The only hedge was that God as pure mind (or spirit) might not be completely independent of the (third) Universe of Mind. You can argue that no such statement ended up in the published version, but we draw lots of other quite definitive conclusions about Peirce's thought from his voluminous unpublished writings.

But in my view, if he had been less culturally influenced, and more faithful to his own metaphysical insights, he would have stuck with a strictly atheistic and anti-Cartesean pansemiosis. — apokrisis

With all due respect, this is nonsense. Peirce was no doctrinaire Christian, but he was quite clearly a theist, and there is no evidence to suggest that he was intellectually dissatisfied with that position. You seem to be projecting onto him your own (admittedly very impressive) adaptaton of his ideas and integration of them with modern scientific findings into a comprehensive atheistic framework.

Of course, anyone would say I read my own biases into Peirce. — apokrisis

Sure, and so do I. I think that his greatness and complexity as a thinker are evident in the fact that his ideas defy easy categorization and can be adapted for many different purposes.

I make dangerously bold statements knowing that I'll really look stupid if I get the basic facts wrong. — apokrisis

My personality is not conducive to being quite that "reckless," so to speak; but I do see this as a place where I can try out new ideas as working hypotheses, figure out how well I can articulate them, and see whether they hold up to scrutiny.

So your insistence on these logical laws is not representative of Terrapin's position at all. — Metaphysician Undercover

Oh, good grief. My point was not to "represent" @Terrapin Station's position, but to draw out some consequences that I saw as entailed by his position. He disagrees with me about some (maybe all) of those implications. You are the only one who has introduced any talk of "forms" and "static states," so when you do so, you are not referring to the views of anyone in the conversation except yourself.

See, you are saying that X has one particular static form (state) at one moment (before the change), and another particular state at the next moment (after the change), but there is no time in between, during which the change occurs. So you have denied the possibility of real activity. All there is, is one particular state (static form), then the next particular state, and so on, each state being temporally contiguous, such that there is no time in between these states during which real activity could be occurring. — Metaphysician Undercover

Please read the exchange more carefully. I was saying that this is what @Terrapin Station's view entails, not that it is my own view.

One simple problem with that is that if a continuum can't be distinguishable, you can't have a plural there--you only have individuals if they're distinguishable. — Terrapin Station

One quick clarification - it is not that the potential individuals in a continuum are indistinguishable, it is that they are potentially distinguishable but actually indistinct. In other words, they only become distinct once they are actualized.

If something changes from not-Y to Y, then if we adhere to the law of excluded middle, there is no time in between, when the thing is changing, or "becoming" Y. — Metaphysician Undercover

Correct, but @Terrapin Station defines time as the series of changes itself, so of course he holds that there is no time in between. He explains this by claiming that the changes are contiguous, while I do not see how they can be anything but discrete (in his model).

Aletheist has been arguing that these two distinct forms must be temporally contiguous, that at one moment the thing has one form, and at the very next moment it has the other form. — Metaphysician Undercover

That is not what I have been arguing at all, since I have not said anything whatsoever about "forms." We have been talking about gaining or losing a (non-essential) property. If we were using Aristotle's framework and terminology - which we are not - then this would be accidental change, rather than substantial change. Furthermore, if there really is a "very next moment," then I have been arguing that time is discrete rather than continuous.

It could only potentially have distinguishable parts. It couldn't have potentially distinguishable parts. — Terrapin Station

Sure it could; as potential individuals, they are not distinct within the continuum, but they are capable of being distinguished by being actualized.

A continuum, per the definition you gave, can not have parts. — Terrapin Station

Sure it can; they just are also continua, not discrete singulars.

It doesn't potentially have water droplets. — Terrapin Station

In a body of water - a glass, a bowl, a pond, a lake, an ocean, whatever - there are no distinct drops, but they are (in principle) capable of being distinguished. That is all I was saying.

By the way, we haven't even started to analyze potential/possible--what those things really refer to ontologically. But that's going to just be another big mess. — Terrapin Station

Yes, so let's not go there, at least not for a few days.

Then a continuum can't be something with no distinguishable parts. — Terrapin Station

Actually indistinct, but potentially distinguishable - like the drops of water in the picture that @Rich posted, except that the number of drops is finite, rather than inexhaustible.

What do you make of Peirce's theism? It was unconventional, to be sure, but he still explicitly affirmed the reality (not existence) of God as Ens necessarium and Creator, most famously in his article about "A Neglected Argument."

Well, in that case, you simply can't have any two contiguous things no matter what. — Terrapin Station

You can in a true continuum, since every part of it is also a true continuum; e.g., the parts of a truly continuous line are also truly continuous lines, not points. I agree that your view precludes there being such a thing as a real continuum of this kind.