Now I know how the poor guy who goes back into the Cave must feel... :roll:

Allow me to try and clarify my disagreement.

As Pfhorrest explained:

Clavius' Law says that "if (not-P implies P) then P" — Pfhorrest

Before Clavius' Law can be applied, you require the bracketed statement (not-P implies P).

In order to arrive at the bracketed statement, you have argued:

If inventing an idea EID is possible, then that possibility Poss(invent EID) must have always existed. Since Poss(invent EID) is essentially linked to EID, it follows that EID must also have always existed. Hence, if it is possible to invent an idea, then the idea must have always existed, and can therefore not be invented. — Tristan L

However, I disagree that the implication holds, because I disagree with your second sentence: "Since Poss(invent EID) is essentially linked to EID, it follows that EID must also have always existed."

I have asked you a few times to clarify what "essentially linked" means here, but I have found your explanations to be brief and opaque. You initially explained:

That Poss(EID) and EID are essentially linked means that the wist (essence) of one involves the other, in this case the wist of Poss(EID). Poss(EID) is defined in terms of EID, so that (namely its wist) which makes Poss(EID) what it is has to do with EID. Hence, there’s a wistly link tying Poss(EID) to EID. — Tristan L

and more recently:

The possibility is defined in terms of the widea, so it couldn’t be what it is without the widea any more than B could be what it is without your leg (or the widea of breaking). — Tristan L

I take this to mean that the possibility of (inventing) the idea is defined in terms of the idea itself. Even if this were the case, you still have not explained how this "essential link" relates to, or assists, your argument: that the possibility (of inventing the idea) has always existed, therefore the idea has always existed. How does this "essential link" of definition provide actual existence to what is merely possible?

It seems your argument must apply not only to ideas, but to anything, since the possibility of any thing's existence can be defined only in terms of that thing. Does the possible existence of unicorns also imply their actual existence?

Also, are you arguing that my leg has always been broken? (Hint: it's not.)

Now I get what you’re saying. Interesting thoughts!

I think that things stand as follows: All things are abstract and therefore eche and uncreatable, but information can be created (though not destroyed). When it becomes certain that an idea EID will be found, the proposition that EID would be found becomes true, which is equivalent to a corresponding piece of information’s coming into being. If the proposition is true from the start by deterministic must, or if it becomes true by chance, the piece of info doesn’t get its existence from a mind; in the former case, it exists by forced necessity, and in the latter case, it springs into existence from nothing, without any maker. If and only if the proposition’s truth is brought about by free will does the belonging piece of info get its existence from a mind, and this is thus a case of true creation.

In short, when someone finds an abstract idea by only his own free will, he (used gender-neutrally) only discovers that idea, but be makes, creates, invents a piece of information belonging to a (likewise abstract) proposition about the idea.

You’ve brought up some interesting points, some of which I have already addressed in my rather lengthy answer last time, and some of which need me to explain more of my theory.

I take this to mean that the possibility of (inventing) the idea is defined in terms of the idea itself. Even if this were the case, — Luke

How could that not be the case? Likewise, how could the proposition that your leg is broken, as well as the proposition that your leg isn’t broken, be what they are and exist without your leg?

how this "essential link" relates to, or assists, your argument: that the possibility (of inventing the idea) has always existed, therefore the idea has always existed. How does this "essential link" of definition provide actual existence to what is merely possible? — Luke

Well, if something actual F is wistlily tied to something Þ through a wistly link U, then Þ must be actual too, for F is actual by premise, and U is actual since it is wistly. In my argument, Þ is a generic idea, and F is the possibility that someone might think of Þ (or any proposition about Þ for that matter). F and U are actual, so Þ is actual, too.

what is merely possible — Luke

There is no such thing as a merely possible thing. All things are eternal, abstract, actual, and soothfast. Moreover, my argument for the actual existence of all ideas doesn’t even need possibility. Let’s take any idea EID which is fully, completely, totally and absolutely unthinkable. Then it’s not possible for anyone to ever think of it. Still, the very fact that EID is unthinkable exists actually, so EID must exist actually, too. Indeed, not-actual existence leads to a contradiction: Assume that some thing x doesn’t have actual existence. Then that very (supposed) fact has actual existence (as does its negation). But this fact is defined in terms of x. Hence, x must be actual after all. Likewise, if any thing þ didn’t exist, it would have the property of not-existence, but since having properties needs existence, þ must exist after all.

It seems your argument must apply not only to ideas, but to anything, since the possibility of any thing's existence can be defined only in terms of that thing. — Luke

Well observed! Indeed, a broader shape of my argument is that all things are actual and eche, and its original purpose is to serve as part of an argument that all things are abstract, th.i. not-physical, not-mindly, not-spatial, not time-bound, and onefold (simple). In this thread, though, only its application to ideas is of relevance, which is why I’ve restricted myself to ideas here.

Does the possible existence of unicorns also imply their actual existence? — Luke

Certainly it does.

For one, unicornhood certainly exists. In fact, it must exist so that the very proposition that unicorns don’t exist even makes sense.

Moreover, each individual unicorn actually exists in the sense that the property of being a unicorn with a rainbow-colored horn and through-seeable wings exists, the property of being a unicorn with a 1-metre-long horn and a scorpion-tail exists, asf.

Each genome is a finite sequence of A’s, T’s, G’s, and C’s, so there’s an actual, fixed one-to-one mapping between the set of all genomes and the set IN of all natural rimetales (numbers). Hence, all genomes exist. This includes genomes that code for unicorns. Also always existing is the property of being a genome that codes for a unicorn, as well as its extension, the set of all genomes that code for unicorns. However, not for every genome g is the proposition E(g, Universe, 2020) / E(g, Earth, 2020) that at some time not after 2020, some physical nucleotides in this universe / on Earth are arranged according to g true. If we substitute a unicorn’s genome for the generic genome g, it happens that E(g, Earth, 2020) is (as far as we know) false in 2020 and ever after because no unicorns have yet (as of 2020) evolved on Earth. So there’s no piece of info belonging to E(g, Earth, 2020). That’s what we mean when we say that unicorns don’t exist on Earth. On the other hand, if we replace unicorns with elephants, the belonging piece of info does exist, which is what we mean when we say that elephants exist. See also my answer to “The meaning of the existential quantifier”.

In short, all things, including all ideas, exist and are abstract, actual, and eche (eternal), and only information might not exist or only possibly exist. The assumtpion that a thing doesn’t actually exist directly leads to contradictions, for how can the not-actual be actually thought about, and how can the not-actual actually be not-actual? The existence of a piece of information is equivalent to the truth of a proposition. The falsehood of that proposition is equivalent to the existence of a piece of info belonging to the proposition’s negation. If neither piece exists, the proposition and its negation have truth-value UNDETERMINED. Our speech isn’t well-suited to talk about info, though, so it’s better to only talk about (abstract) things and the truth-values of propositions. However, I can’t explain my whole theory here.

Also, are you arguing that my leg has always been broken? — Luke

No, as I’ve said here:

However, it does mean that the state-of-affairs and the proposition that you would break your leg has always existed, as has its negation. (Hint: it's not.) — Tristan L

It’s only the case that the corresponding piece of information, which would be concrete, thankfully doesn’t exist.

how this "essential link" relates to, or assists, your argument: that the possibility (of inventing the idea) has always existed, therefore the idea has always existed. How does this "essential link" of definition provide actual existence to what is merely possible?
— Luke

Well, if something actual F is wistlily tied to something Þ through a wistly link U, then Þ must be actual too, for F is actual by premise, and U is actual since it is wistly. In my argument, Þ is a generic idea, and F is the possibility that someone might think of Þ (or any proposition about Þ for that matter). F and U are actual, so Þ is actual, too. — Tristan L

My attempted translations of your "wistlily" language into standard English:
=>(1) If the actual possibility that someone might think of an idea is essentially tied to the idea through an essential link (U), then the idea must be actual too, for the possibility that someone might think of the idea is actual by premise, and the essential link is actual since it is essential.

=>(2) If the actual possibility of an idea is essentially tied to the idea via an essential link, then the idea must be actual too, for the actual possibility of an idea is a premise and the essential link is actual since it is essential.

Sorry, I still don't follow. The possibility of an idea is tied to its actualised counterpart by an essential link. Therefore, the idea is actual? Because the essential link is actual since it is essential?

How does the "essential link" facilitate the leap from 'the idea is possible' to 'the idea is actual'. And how do you distinguish between possible ideas and actual ideas?

There is no such thing as a merely possible thing. All things are eternal, abstract, actual, and soothfast. Moreover, my argument for the actual existence of all ideas doesn’t even need possibility. — Tristan L

I suspected this to be your position, which is why I asked you pages ago why you even bother with possibility. You may also recall my more recent observation that you only draw an artificial distinction between possible and actual existence.

Assume that some thing x doesn’t have actual existence. Then that very (supposed) fact has actual existence (as does its negation). But this fact is defined in terms of x. Hence, x must be actual after all. — Tristan L

A fact about x exists, therefore x is actual? Sorry, I still don't accept it. E.g.:

Facts about dinosaurs exist. Therefore, dinosaurs are actual.
Facts about the extinction of dinosaurs exist. Therefore, the extinction of dinosaurs is actual.

How can it be both?

Does the possible existence of unicorns also imply their actual existence?
— Luke

Certainly it does.[...]

So there’s no piece of info belonging to E(g, Earth, 2020). That’s what we mean when we say that unicorns don’t exist on Earth. — Tristan L

Unicorns certainly do actually exist, but also unicorns don't actually exist?

how can the not-actual be actually thought about, and how can the not-actual actually be not-actual? — Tristan L

Quite easily: myth, fiction, make-believe, possibility.

The existence of a piece of information is equivalent to the truth of a proposition. The falsehood of that proposition is equivalent to the existence of a piece of info belonging to the proposition’s negation. — Tristan L

If there can exist "a piece of info belonging to [a] proposition's negation", then "[t]he existence of a piece of information is ((not necessarily)) equivalent to the truth of a proposition".

It’s only the case that the corresponding piece of information, which would be concrete, thankfully doesn’t exist. — Tristan L

Are you drawing a distinction between actual existence and concrete existence? Because (otherwise) this appears inconsistent with your claims about possible existence (of my broken leg) implying actual existence.

All at once. It's not like any of them negate or contradict each other by being true. Deterministic events can happen, randomly.

Why is this? Non-linear causality.

My attempted translations of your "wistlily" language into standard English — Luke

The word “wistlily” (“essentially”) is an adverb, while “wistly” (“essential”, German “wesentlich”) is the belonging adjective (how-word), and both belong to the nameword “wist” (“essence”, German “Wesen”). You might want to brush up your English grammar. Also, my speech is better and righter English, whereas your so-called “standard English” is sadly a pretty messed up language which

• has a broken case system (e.g. using the second-person plural accusative and dative pronoun “you” for the second-person singular nominative pronoun “thou”, the second-person singular accusative and dative pronoun “thee”, and the second-person plural nominative pronoun “ye”),
  
• doesn’t distinguish between present participles and gerunds (which is especially problematic in philosophy; for instance, “being” means both the state of being, called “Sein” in German and more properly “beon” in English, and that which is, called “Seiendes” in German and properlier “beonde” in English),
  
• uses “here” and “there” also in the sense of “hither” and “thither”, respectively,
  
• and more than half of whose wordstock has been brought by force by romanized Viking invaders

– to name some problems. Old English is such a fair tongue, like German (Theech), Arabic, and Gothic (Gotish). But I digress.

Your questions have forced me to reveal more of my theory, making some of my answers rather lengthy, but I think it’s worth it. I find this talk very interesting indeed.

Sorry, I still don't follow. The possibility of an idea is tied to its actualised counterpart by an essential link. — Luke

Let me swuttle (explain) the main possibility argument I’ve put forth so far. Let EID be any thinkable idea. Consider the proposition IsThoughtAbout(EID) (that for some mind m and some time-point t, m manifests in the concrete world at t and thinks about EID at t). Now regard the proposition PossIsThoughtAbout(EID) (that IsThoughtAbout(EID) is possible at the start). This one is true from the start (as you have admitted). Like every proposition, including IsThoughtAbout(EID), PossIsThoughtAbout(EID) is (abstract and) actual anyway, but the fact that it’s true will hopefully show even the hardest-boiled skeptic that PossIsThoughtAbout(EID) is actual. Now, PossIsThoughtAbout(EID) is defined as the proposition that EID has property PossIsThoughtAbout; by its very wist, it says something about EID. So the actual entity PossIsThoughtAbout(EID) is tied by a wistly and thus actual link to EID. It neededly follows that EID must be actual, too.

I could have used a property other than PossIsThoughtAbout, such as the property ideahood of being an idea, the property of abstractness, the property of being the selfsame as onesself, or the property PossiblyExists of possibly existing. I just found using PossIsThoughtAbout to be particularly convincing. Note that PossIsThoughtAbout doesn’t work for an unthinkable idea EID, in the sense that PossIsThoughtAbout(EID) is false in that case, but that the other properties work even in that case.

Let’s now try to understand how things likely really stand:

Mindhood is eche (eternal), abstract, and actual (echeness follows from abstractness, of course). Every idea EID is eche, abstract, and actual. Every time-point is eternal, abstract, and actual. Every mind is eche, abstract, and actual. All properties, including IsThoughtAbout and PossIsThoughtAbout, are eche, abstract, and actual. All propositions, including – for every idea EID – IsThoughtAbout(EID) and PossIsThoughtAbout(EID), are eternal, abstract, and actual. However, IsThoughtAbout(EID) (for some idea EID) isn’t necessarily true at all time-points. In particular, it needn’t be true from the start. When it isn’t true (yet), but only undetermined, the belonging piece of info exists only possibly, but not actually (yet). As soon as IsThoughtAbout(EID) becomes true (and obviously stays true forever after), the corresponding piece of info gets actual existence (and holds on to it forever after). If IsThoughtAbout(EID) for some reason becomes false (e.g. because some demon permanently blocks minds from manifesting in the concrete world), its belonging piece of info loses even its merely possible existence. But Mindhood, all minds, all time-points, all ideas, all properties, and all propositions stay in actual existence, of course. The only beondes (see above for the meaning of “beonde”) which are actualized are pieces of information. All the others are things and so simply actual.

Where does invention come into play? Well, for every idea EID, every mind m, and every time-point t, regard the propsition IsThoughtAboutByAt(EID, m, t) that EID is being thought about by m at t. Now let EID be an arbitrary idea. If a mind m brings about the truth of IsThoughtAboutByAt(EID, m, t) for some time-point t by its own free will alone, it is the only maker of the info-piece belonging to IsThoughtAboutByAt(EID, m, t). In that sense, the mind m is a full inventor of that info-piece. If another mind n does the same (and therefore in particular does it independently of m), it is also a full inventor, but of another info-piece. The two minds are co-inventors of two different pieces of information involving one and the same idea EID in similar ways.

Unicorns certainly do actually exist, but also unicorns don't actually exist? — Luke

You accuse me of confusing PossiblyExists(EID) with EID, which I clearly don’t as the former is a proposition and the latter isn’t, when it is in fact you who seems to mix EID up with the (always existing) piece of info belonging to PossiblyExists(EID), or (much likelier) even the (not always existing) info-piece belonging to IsThoughtAbout(EID). You even seem not to be fully aware of EID itself, strengthening what I wrote here.

How does the "essential link" facilitate the leap from 'the idea is possible' to 'the idea is actual'. — Luke

An essential link is actual, and it links an actual thing to another thing. Hence, this other thing must be actual, too.

And how do you distinguish between possible ideas and actual ideas? — Luke

All ideas are actual (and possible too, of course). What you mean by “actual idea” seems to be a piece of info associated with a proposition about the idea (more on this above), or perhaps you mean an idea for which info belonging to a certain kind of proposition about it (namley propositions that say that a mind has thought about the idea) exists.

I must admit that in what I’ve written so far, I’ve made a mistake. I’ve treated pieces of info as if they were things and thereby abstract when they are in fact another kind of beonde. That’s not my fault, though, for our speech is only well-suited for talking about (abstract) things and rather ill-suited for talking about beondes of another kind such as information. This is why I think that it’s better to talk about propositions and their truth-values rather than info-pieces and their existence or not-existence. Likewise, we’d better only talk about possibility in the context of truth-values of propositions rather than existence/non-existence of information. Even more: Our faculty of thought isn’t very well-suited for thinking about concrete beonde, I think. Think about it: what an abstract entity is is very clear, but when you deeply think about the notion of a concrete object, you’ll see the notion become ever fuzzier and less meaningful until it melts away and evaporates in the end.

If there can exist "a piece of info belonging to [a] proposition's negation", then "[t]he existence of a piece of information is ((not necessarily)) equivalent to the truth of a proposition". — Luke

What I mean is that for every proposition Þ, the proposition TRUE(Þ) that Þ is true is logically equivalent to the proposition that the info-piece belonging to Þ exists. Accordingly, the proposition FALSE(Þ) that Þ is untrue (“un-” ≠ “not-”) is logically equivalent to the proposition that the info-piece belonging to the negation ¬Þ of Þ exists, and the proposition UNDETERMINED(Þ) that Þ is undetermined is logically equivalent to the proposition that neither the info-piece belonging Þ exists nor the info-piece belonging to ¬Þ exists.

The possibility of an idea is tied to its actualised counterpart by an essential link. Therefore, the idea is actual? Because the essential link is actual since it is essential? — Luke

Yes to both, as long as you replace “actualised” with “actual”.

You may also recall my more recent observation that you only draw an artificial distinction between possible and actual existence. — Luke

For things, I’ve shown that possible existence necessarily lets actual existence follow. In the case of info, that’s not the case, but as I’ve said, thinking and talking about info is tricky.

A fact about x exists, therefore x is actual? Sorry, I still don't accept it. E.g.:

Facts about dinosaurs exist. Therefore, dinosaurs are actual.
Facts about the extinction of dinosaurs exist. Therefore, the extinction of dinosaurs is actual.

How can it be both? — Luke

Firstly, dinosaurs are still alive and kicking and can even be very smart, as can be seen in this video, for instance. What they would have to add to this discussion, I wonder ... :wink:

Therefore, let’s replace dinosaurs with sauropods in your example. I don’t see where the contradiction lies. Are you doubting the actualness of sauropods in earnest?

Here’s my account of the situation:

Sauropodhood is abstract (and thus eternal) and actual, as is the proposition than sauropodhood manifests in flesh and blood in this universe at some time. This proposition became true when sauropods first evolved, so at that time, the info-piece belonging to that proposition came into being (and would stay there forever). The existence of this info-piece is what most folks likely mean when they say that sauropods exist (in contrast to unicorns, for instance), probably including you and certainly me. All of this is in accordance with the fact that facts about sauropods exist. Likewise, the proposition that the sauropods go extinct, that is, that after some time-point, sauropodhood no longer manifests in this universe in flesh and blood, is abstract and actual. It’s even true, so the corresponding piece of info exists. All of this is in accordance with the fact that facts about the proposition that sauropods go extinct exist.

Quite easily: myth, fiction, make-believe, possibility. — Luke

Myth and fiction are both about soothfast (real) things. It’s just that those things don’t manifest in a certain way, th.i. certain propositions about the abstract things involved (such as unicorns) aren’t true (at least in our world) and often even false. We call myth, fiction, and the like “make-believe” only insofar as you treat them as asserting the truth of those not-true propositions (for example interpreting LOTR as assering that Frodohood manifests in flesh and blood on this Earth in our world). As I’ve discussed above, possible existence belongs in the realm of info, not the world of things.

Are you drawing a distinction between actual existence and concrete existence? — Luke

Of course I am. How could I otherwise claim that abstract things actually exist?

But don’t get me wrong: I certainly think that abstract and thus not-concrete being, which is always actual, is not inferior to concrete being. While I don’t follow Plato in regarding abstract being as superior – indeed, I’m spellbound by time and therefore the temporal and concrete world, leading me (in part) to develop a new logic and a new theory of time and chance –, I do hold that abstract being is purer than concrete being. Concrete being is being-at/in/..., whereas abstract being is just being. The info that sauropodhood manifests in flesh and blood on Earth in this world exists at time-points, in a possible world; the info that Alice thinks EID comes into being in her mind (again in a world at a time); but sauropodhood and EID simply are.

Unicorns certainly do actually exist, but also unicorns don't actually exist?
— Luke

You accuse me of confusing PossiblyExists(EID) with EID, which I clearly don’t as the former is a proposition and the latter isn’t, — Tristan L

I didn't accuse you of anything. I noted the apparent contradiction in your statements that unicorns both do and do not actually exist.

I suppose by Clavius' Law, you could deduce that if black is white, then white is black, therefore white is black.

In response to your comment, though, if EID is not itself a proposition contained within 'PossiblyExists(EID)', then what proposition does 'PossiblyExists(EID)' express?

And btw how do you explain your contradictory statements that unicorns both do and do not actually exist?

An essential link is actual, and it links an actual thing to another thing. Hence, this other thing must be actual, too. — Tristan L

Clear as mud.

What you mean by “actual idea” seems to be... — Tristan L

When I say "actual idea", I mean an idea that someone has actually thought about or thought up (invented). But also something that is transferrable and that anyone (any mind) can think of/about. For example, E=mc^2.

What you mean by an actual idea seems to be particular to one mind at a given time, and so indistinguishable from an actual thought.

Even more: Our faculty of thought isn’t very well-suited for thinking about concrete beonde, I think. Think about it: what an abstract entity is is very clear, but when you deeply think about the notion of a concrete object, you’ll see the notion become ever fuzzier and less meaningful until it melts away and evaporates in the end. — Tristan L

I'm sure if I broke my leg it wouldn't be so fuzzy or meaningless.

The possibility of an idea is tied to its actualised counterpart by an essential link. Therefore, the idea is actual? Because the essential link is actual since it is essential?
— Luke

Yes to both, as long as you replace “actualised” with “actual”. — Tristan L

Clear as mud.

For things, I’ve shown that possible existence necessarily lets actual existence follow. — Tristan L

Shown? Where have you shown that the possible existence of unicorns lets their actual existence follow? In fact, you've stated that unicorns both do and do not actually exist.

let’s replace dinosaurs with sauropods in your example. I don’t see where the contradiction lies. Are you doubting the actualness of sauropods in earnest? — Tristan L

I'm not doubting. I'm noting the widely accepted fact that dinosaurs (or sauropods if you prefer) are extinct and no longer actually exist.

Here’s my account of the situation:

Sauropodhood is abstract (and thus eternal) and actual, as is the proposition than sauropodhood manifests in flesh and blood in this universe at some time. — Tristan L

I'm not talking about dinosaur-hood or sauropod-hood. That's something you've introduced.

This proposition became true when sauropods first evolved, so at that time, the info-piece belonging to that proposition came into being (and would stay there forever). The existence of this info-piece is what most folks likely mean when they say that sauropods exist (in contrast to unicorns, for instance), probably including you and certainly me. — Tristan L

I doubt it. Ask most folks and I'm sure they will tell you that dinosaurs (or sauropods if you prefer) don't exist, unlike the "info-piece".

All of this is in accordance with the fact that facts about sauropods exist. — Tristan L

I'm not disputing that facts about x exists. I'm disputing your assertion that facts about x exists implies that x exists.

Likewise, the proposition that the sauropods go extinct, that is, that after some time-point, sauropodhood no longer manifests in this universe in flesh and blood, is abstract and actual. It’s even true, so the corresponding piece of info exists. — Tristan L

They don't "go" extinct at some point. They are extinct.

As I’ve discussed above, possible existence belongs in the realm of info, not the world of things. — Tristan L

Are you suggesting that actual existence does not belong in the "realm of info"?

The info that sauropodhood manifests in flesh and blood on Earth in this world exists at time-points, in a possible world; the info that Alice thinks EID comes into being in her mind (again in a world at a time); but sauropodhood and EID simply are. — Tristan L

They "simply are" now -- after they have happened or someone has thought them up. Many ideas are possible, and many may go without being thought up (actualised), just as many physical arrangements are possible and many may go without being actualised. You expect me to believe that all possible ideas and physical arrangements are already actual even though many may never be actualised? I'm sure many people have survived life without breaking a leg.

By your logic, the possibility that all possibilities will not be actualised is itself actual (and therefore, all possibilities will not be actualised). But the possibility that all possibilities will be actualised is also actual (and therefore, all possibilities will be actualised). Just like the actual existence and non-existence of unicorns, how can both be true?

Clear as mud. — Luke

Although what one has shown may be brightly seen and crystal clear,
it’s useless if the other did his eyes with mud besmear...

I noted the apparent contradiction in your statements that unicorns both do and do not actually exist. — Luke

The problem is that you seem to obstinately refuse to understand the quite simple matter of distinguishing unicorns themselves from pieces of information involving them. Let me try to help you understand it better: The number 5 always actually exists, but when a die is thrown and shows a 5 on its upper face, the piece of info belonging to the (also eternal, abstract, and actual) proposition that the die-throw would result in 5 being shown comes into being, which is equivalent to the proposition becoming true. On the other hand, if 5 doesn’t show up on the die, the piece of info loses the possible existence that it originally had, which is equivalent to the proposition becoming false. Yet even then, the number 5 goes on to happily and actually exist. Has the matter now gotten a bit clearer to you?

I suppose by Clavius' Law, you could deduce that if black is white, then white is black, therefore white is black. — Luke

That argument is indeed valid, but it is not sound, because the premise is false. Why are you still talking about Clavius’ Law? I only brought it up to explain a trivial logical matter to you which you seemingly didn’t (and still don’t?) understand.

And btw how do you explain your contradictory statements that unicorns both do and do not actually exist? — Luke

The supposed contradiction is not mine, but yours, and results from your failing to distinguish two quite distinct “things”, making you misinterpret me. See above.

In fact, you've stated that unicorns both do and do not actually exist. — Luke

I’ve really understood that you don’t understand what I mean, believe me. How many more times do you mean to show your failure to see my meaning?

I'm not doubting. I'm noting the widely accepted fact that dinosaurs (or sauropods if you prefer) are extinct and no longer actually exist. — Luke

Firstly: So you do doubt the actual existence of sauropods after all.

Secondly: You must be severely misinformed if you think that dinosaurs are extinct in 2020, or that this false proposition is widely accepted.

Thirdly: Do you really think that sauropods don’t exist in 2020? Do you really think that Arminius doesn’t exist in 2020? I’m afraid that if you do, you subscribe to an absurd belief. Since facts about sauropods and Arminius exist in 2020, so must sauropods and Arminius themselves. The matter is quite simple: Saurpods and Arminius simply and always exist. Sauropods live from about 215 mya to about 66 mya, while they don’t live from 13.7 bya to 215 mya, and they also don’t live from 66 mya to 0 mya. Likewise, Arminius lives from 18 BCE to 21 CE, while he doesn’t live from 13,700,000,000 BCE to 18 BCE, and he also doesn’t live from 21 CE to 2020 CE.

They don't "go" extinct at some point. They are extinct. — Luke

They are extinct in 2020 CE, and they aren’t extinct in 100,000,000 BCE. That they go extinct 66,000,000 BCE means that before 66,000,000 BCE, they aren’t extinct, and afterwards, they are.

I'm not talking about dinosaur-hood or sauropod-hood. That's something you've introduced. — Luke

Actually, you’ve introduced them. The moment that you even think about dinosaurs or sauropods (which you clearly did), you introduce dinosaurhood and sauropodhood, though you may be (and apparently are) not aware of it.

Shown? Where have you shown that the possible existence of unicorns lets their actual existence follow? — Luke

Here:

For one, unicornhood certainly exists. In fact, it must exist so that the very proposition that unicorns don’t exist even makes sense.

Moreover, each individual unicorn actually exists in the sense that the property of being a unicorn with a rainbow-colored horn and through-seeable wings exists, the property of being a unicorn with a 1-metre-long horn and a scorpion-tail exists, asf. — Tristan L

I could have used a property other than PossIsThoughtAbout, such as [...] the property PossiblyExists of possibly existing. — Tristan L

Let me elaborate on the latter point further: Let OH be an arbitrary unicorn. OH possibly exists. That very fact MaybeExists(OH) that OH may exist actually exists (the same goes for its negation, the state-of-affairs that OH certainly doesn’t exist). Obviously, MaybeExists(OH) is essentially connected to OH, so this link is actual. Since MaybeExists(OH) and the link between MaybeExists(OH) and OH is actual, OH must be actual, too. This doesn’t just work for unicorns, but for all possibly existing things, and shows all of them to be actual. The same goes for NOT(MaybeExists(OH)).

Regarding unicornhood, it must actually exist in order for the proposition that unicorns exist, as well as the proposition that unicorns don’t exist, to even make actual sense.

I'm not disputing that facts about x exists. I'm disputing your assertion that facts about x exists implies that x exists. — Luke

How can you dispute such a fundamental and obvious fact? Since the fact exists, and the connection between the fact and a thing which the fact is concerned with exists by the very wist of the fact, the thing must also exist.

I doubt it. Ask most folks and I'm sure they will tell you that dinosaurs (or sauropods if you prefer) don't exist, unlike the "info-piece". — Luke

Firstly, those people who tell you that dinosaurs are extinct in 2020 might want to have a biologist or paleontologist correct their false opinion. Secondly, most of us aren’t highly aware of what we mean when we say things, and in everyday life, we very often use technically wrong speech. I myself am no exception, and in a paleontology forum, for example, I’d have no reservation about saying, “It’s a shame that T. rex no longer exists” even though the statement that this magnificent animal no longer exists is technically fully false.

When I say "actual idea", I mean an idea that someone has actually thought about or thought up (invented). — Luke

Does the same apply to what you mean my “actual rimetale”? If yes, does that mean that you regard all the endlessly many numbers which no one has (yet) thought about as merely possible and not actual?

If that’s what you mean by “actual”, then it’s something quite different from what I mean by “actual”. What is abstract is at least as actual as the concrete, using my meaning of “actual”.

But also something that is transferrable and that anyone (any mind) can think of/about. For example, E=mc^2. — Luke

But the fact about the physical realm expressed by “E = mc2” has always existed, regardless of whether anyone would ever think of it. Also, how can Alice independently of Bob think about something that Bob invented?

What you mean by an actual idea seems to be particular to one mind at a given time, and so indistinguishable from an actual thought. — Luke

No; since I’ve shown that all ideas are actual, what I mean by “actual idea” is the same as what I mean by “idea”. I’m just trying to find out what exactly you mean by “actual idea”. It seems to be a chimera of information and (abstract) things. Some pieces of info are indeed particular to one mind at a given time, such as the info belonging to the proposition that Tristan thinks about the rimetale 2 in 2020 CE. Other pieces of info are not, however, such as the piece of info belonging to the proposition that for some time-point t and some mind m, m thinks about 2 at t. What you mean by “actual idea” seems to mostly be an info-piece of the latter kind.

I'm sure if I broke my leg it wouldn't be so fuzzy or meaningless. — Luke

As am I. However, I haven’t said that the notion of concrete beonde is meaningless, but rather only that the notion of concrete thing is meaningless. The notion of concrete information, on the other hand, is very meaningful, though still hard to grasp. If you broke your leg, the easiest way to think about it is in fully abstract terms: The proposition that you break your leg now is true now.

In response to your comment, though, if EID is not itself a proposition contained within 'PossiblyExists(EID)', then what proposition does 'PossiblyExists(EID)' express? — Luke

The proposition that EID possibly exists, just as “PossiblyExists(6)” refers to the proposition that the rimetale 6 has possible existence, and as “PossiblyExists(Luke’s leg)” means the proposition that your leg has possible existence. Is your leg the same as the proposition that it exists?

Are you suggesting that actual existence does not belong in the "realm of info"? — Luke

Not at all. I hold that actual existence belongs into both the world of the abstract and the realm of the concrete, whereas merely possible existence only belongs in the latter.

They "simply are" now -- after they have happened or someone has thought them up. — Luke

That’s a contradiction. If something simply is, it just is, without having to merely be-at or be-in or be-after.

Many ideas are possible, and many may go without being thought up (actualised), just as many physical arrangements are possible and many may go without being actualised. You expect me to believe that all possible ideas and physical arrangements are already actual even though many may never be actualised? — Luke

Yes. However, mind you that you’re conflating two things here by your use of the words “actual” and “actualized”. All those ideas are actual, yes. Of course they are! However, what you mean by “actualize” isn’t really actualization of the thing of which you predicate actualization; after all, what’s actual cannot be actualized. Rather, for every idea EID, you likely mean by “EID is actualized” the proposition IsThoughtAbout(EID) that the proposition that someone thinks about EID at some time is true. This truth constitutes the actualization not of EID, though, but of the info-piece belonging to the proposition IsThoughtAbout(EID). Likewise, for every physical arrangement PhAr, you probably mean by “PhAr is actualized” the proposition that the proposition that the Universe takes on arrangement PhAr at some time is true. In truth, this truth constitutes the actualization of the info-piece corresponding to that proposition. It may very well be that you aren’t fully aware of the ideas or the states themselves, leading to your misunderstanding.

I'm sure many people have survived life without breaking a leg. — Luke

Can you still not see the difference between a proposition and a belonging info-piece? For every person, the proposition that that person breaks a leg always exists. However, not for every person does the corresponding proposition ever become true (and in such a case, it becomes false when the person dies).

By your logic, the possibility that all possibilities will not be actualised is itself actual (and therefore, all possibilities will not be actualised). But the possibility that all possibilities will be actualised is also actual (and therefore, all possibilities will be actualised). Just like the actual existence and non-existence of unicorns, how can both be true? — Luke

And... the misunderstanding goes on... :roll:

Your use of the word “actualize” is unaccurate, see above.

Here, it’s very obvious that you conflate propositions with info-pieces.

the possibility that all possibilities will not be actualised is itself actual (and therefore, all possibilities will not be actualised). — Luke

That’s wrong. If it’s actual that some proposition A might be the case (th.i. if we have TRUE(MAYBE(A))), it doesn’t automatically follow at all that A is actually the case (th.i. TRUE(A) doesn’t follow). You incorrectly inferred TRUE(A) from TRUE(MAYBE(A)). When I say that some possibility is actual, I mean that it’s actual that the thing in question is possible. It isn’t essential that the proposition MAYBE(A) has truth-value T. What counts is that MAYBE(A) is an actually existing entity, which it is regardless of whether it has truth-value T, F, or U. However, that it has truth-value T shows in a particularly convincing way that it actually exists.

What you call “the possibility that all possibilities will not be actualised” is the propposition that no proposition is true, and while it actually exists, it’s not only not true, but outright false. You’re confusing actual existence with truth. This confusion underlies the rest of what you said and leads you to absurd and contradictory conclusions.

Is your leg the same as the proposition that it exists? — Tristan L

No. Is a unicorn? Or a dinosaur?

I hold that actual existence belongs into both the world of the abstract and the realm of the concrete, whereas merely possible existence only belongs in the latter. — Tristan L

Merely possible existence is concrete and not abstract? I would say it's the opposite. What is abstract then?

But the fact about the physical realm expressed by “E = mc2” has always existed, regardless of whether anyone would ever think of it. — Tristan L

Unlike facts, ideas don't exist if nobody ever thinks of them.

I'm not disputing that facts about x exists. I'm disputing your assertion that facts about x exists implies that x exists.
— Luke

How can you dispute such a fundamental and obvious fact? Since the fact exists, and the connection between the fact and a thing which the fact is concerned with exists by the very wist of the fact, the thing must also exist. — Tristan L

Can you still not see the difference between a proposition and a belonging info-piece? For every person, the proposition that that person breaks a leg always exists. However, not for every person does the corresponding proposition ever become true (and in such a case, it becomes false when the person dies). — Tristan L

Except you are arguing that if facts about x (or if the possibility of x) actually exists, then x actually exists. Therefore, how can you maintain any distinction between propositions and info-pieces, or between possible existence and actual existence? By your logic, if my broken leg possibly exists, then my broken leg actually exists, and if unicorns possibly exist, then unicorns actually exist. If the possibile existence of x implies the actual existence of x, then whatever possibly exists actually exists.

Given your affirmation that the possible existence of unicorns implies the actual existence of unicorns, then how can you also maintain that "no unicorns have yet (as of 2020) evolved on Earth" and "That’s what we mean when we say that unicorns don’t exist on Earth"? If unicorns don't exist on Earth, then they don't actually exist, right? And if they don't actually exist, then you can't affirm (without contradiction) that their actual existence is implied by their possible existence.

Please tell me, if unicorns don't exist on Earth, then what type of existence do they lack if it is not actual existence? Alternatively (or additionally), what do you mean by "the actual existence of unicorns" if not that unicorns exist on Earth?

No. Is a unicorn? Or a dinosaur? — Luke

No, they aren’t, either.

Merely possible existence is concrete and not abstract? — Luke

What I mean is that everything abstract exists actually, and the only stuff that could have merely possible existence is concrete.

What is abstract then? — Luke

Whatever is not-physical, not-mindly, not-spatial, not-tidesome (not-temporal), and onefold (simple).

ideas don't exist if nobody ever thinks of them. — Luke

I have repeatedly asked you to provide justification for that unsubstantiated claim, and you have repeatedly repeated it without giving any justification whatsoever.

Except you are arguing that if facts about x (or if the possibility of x) actually exists, then x actually exists. Therefore, how can you maintain any distinction between propositions and info-pieces, or between possible existence and actual existence? — Luke

Yes, if a fact about x actually exists (which it does), or if a false or undetermined proposition about x actually exists (which it also does), then x actually exists. I don’t see where the problem lies. I can perfectly maintain a distinction between info and propo. Can you?

By your logic, if my broken leg possibly exists, then my broken leg actually exists — Luke

No; “Luke’s broken leg” in not a technically right noun-phrase. On the other hand, “that Luke’s leg is broken” is a right name-phrase, and it refers to the proposition that Luke’s leg is broken. This proposition actually exists, though it is false. Its negation, the proposition that Luke’s leg isn’t broken, also exists, but is true. Aren’t you mixing truth up with actual existence again?

and if unicorns possibly exist, then unicorns actually exist. — Luke

Unlike “Luke’s broken leg” and like “that Luke’s leg is broken”, for all features F1, F2, F3, ... , “being a unicorn with features F1, F2, F3, ...” is a proper name phrase which means a property.

If the possibile existence of x implies the actual existence of x, then whatever possibly exists actually exists. — Luke

True, if “whatever” refers only to things. With info, things stand differently, but as I said before, I think that our minds aren’t very well suited for thinking about info, and in the very workings of our speech seems to be hidden the assumtion that we’re only talking about things.

However, not all propositions are true. Some are true, in which case the belonging info-piece actually exists; some are false, in which case the belonging info-piece doesn’t exist at all; and some are undetermined, in which case the belonging info-piece exists possibly, but not actually.

Given your affirmation that the possible existence of unicorns implies the actual existence of unicorns, then how can you also maintain that "no unicorns have yet (as of 2020) evolved on Earth" and "That’s what we mean when we say that unicorns don’t exist on Earth"? — Luke

Because the property of actual existence is something very different from the property of having evolved on Earth by 2020. Similarly, the actual existence of the number 2 is very different from the truth of the proposition that a certain die-throw reasulted in a 2. The sentence “That’s what we mean when we say that unicorns don’t exist on Earth” uses the word “exist” wrongly, for its means something very different from existence.

If unicorns don't exist on Earth, then they don't actually exist, right? — Luke

No, that’s not true at all. Unicorns themselves exist actually as abstract entities, but certain propositions involving them aren’t true, such as the proposition that unicorns have evolved on Earth by 2020. Therefore, your next sentence

And if they don't actually exist, then you can't affirm (without contradiction) that their actual existence is implied by their possible existence. — Luke

starts from a false premise.

Please tell me, if unicorns don't exist on Earth, then what type of existence do they lack if it is not actual existence? Alternatively (or additionally), what do you mean by "the actual existence of unicorns" if not that unicorns exist on Earth? — Luke

Unicorns don’t lack any kind of existence. What we call “existence on Earth” isn’t existence at all; rather, it’s the property of manifesting on Earth in flesh and blood. And as it happens, the proposition that unicorns have that property isn’t true. Like all things, unicorns have possible and actual existence as abstract objects. By “the actual existence of unicorns”, I mean the fact that unicorns are fully existent and just as actual as numbers, properties, functions, souls, and all the other actual beondes (which includes all things).

ideas don't exist if nobody ever thinks of them.
— Luke

I have repeatedly asked you to provide justification for that unsubstantiated claim, and you have repeatedly repeated it without giving any justification whatsoever. — Tristan L

Simply look up the word "idea" in the dictionary. But perhaps you think that what we call ideas aren't ideas at all.

Yes, if a fact about x actually exists (which it does), or if a false or undetermined proposition about x actually exists (which it also does), then x actually exists. I don’t see where the problem lies. I can perfectly maintain a distinction between info and propo. Can you?

By your logic, if my broken leg possibly exists, then my broken leg actually exists
— Luke

No; “Luke’s broken leg” in not a technically right noun-phrase. On the other hand, “that Luke’s leg is broken” is a right name-phrase, and it refers to the proposition that Luke’s leg is broken. This proposition actually exists, though it is false. Its negation, the proposition that Luke’s leg isn’t broken, also exists, but is true. Aren’t you mixing truth up with actual existence again? — Tristan L

All of the above implies that my broken leg actually exists. My leg isn't broken! I don't have a broken leg that could exist anywhere.

What we call “existence on Earth” isn’t existence at all; — Tristan L

"What we call existence isn't existence at all"? If you don't see a problem with this, then there's not much left to say.

I've been thinking more about this and I think the creative idea ("Hold on, guys, I have an idea!") encapsulates all three elements of a guided search in optimisation algorithms exactly, consistent of:

1. An intelligent approximation (e.g. based on prior experience of searches, prior experience of outcomes and/or theoretical knowledge) as to where to begin a search;
2. An approximate characterisation of the goal (e.g. a tonal quality);
3. A search method.

These are more or less constrained in each case. The instruments at hand, for instance, constrain (3) heavily.

One tries a trial solution based only on the initial approximation (1) and compares to the known character of the optimal solution (2). Then one amends the trial solution according to the difference based on a method of incremental improvement (3).

A random or brute force search only constitutes (3), and badly, since it is independent of (1-2).

All ideas are discovered. It is only through discovery, as a unique articulation, that it (discovery) becomes the INVENTION. We are continuum of the endless variation of the one word (UNI-VERSE)...

Simply look up the word "idea" in the dictionary. — Luke

See here (1.), for instance. This gives you the original meaning of the word “idea” and its philosophical definition, and it’s therefore the one we’re interested in.

All of the above implies that my broken leg actually exists. My leg isn't broken! I don't have a broken leg that could exist anywhere. — Luke

I don’t know how much crystal clearer I can be in order to help you understand this very simple matter. The proposition that your leg is broken has actual existence, but it doesn’t have truth. Truth is not the same as existence. Has it become clear now?

"What we call existence isn't existence at all"? If you don't see a problem with this, then there's not much left to say. — Luke

There would not be much left to say indeed, but not here, but rather in the point before if you still can’t see the gaping difference between existence and truth.

Regarding this point, let’s look at another example. When we say “The number 3 exists in that room”, we mean that there is a group of three items, such as three humans, three balls, or three ants, in the room. What we mean, of course, in not really the existence of the number 3, but a particular way of manifesting in the room. The same goes for “existence on Earth”. For example, when we say “Such and such genome exists on Earth”, we mean that it manifests as a physically articulated sequence of physical base-pairs. But the genome itself obviously exists regardless of that – it’s an abstract string and therefore corresponds one-to-one with a natural number.

You seem to have suddenly changed your definition of the phrase “actual existence”... or did you really think that I was arguing for the manifestation of unicorns on Earth in flesh and blood?

:up: I think that you might have the same general understanding of the matter as I. In short, mine goes like this: For every idea EID, EID itself exists as an abstract entity, and so can only be discovered. However, if someone S discovers EID by his or her own free will, he or she invents a piece of information belonging to a certain proposition about EID, which he or she thus causes to be true, namely the proposition that S thinks about EID at some point in his or her life.

If I perceive something directly with my senses, that must form a first-order idea. Over time, I perceive many horses, and I build up an idea in my brain of 'horse-ness', or things that are 'horsey'. Mostly this helps me identify from my senses what I am currently perceiving, and potentially some action that I ought to take (like step out of the way of the running horse).

The reason I might want to step out of the way is because the idea of horses has combined with some other perceptions I've had of people being run down by running bulls, so I create a second order idea that combines 'the danger of large animals running' and 'horses are large animals' in order to draw a conclusion that 'a running horse could cause me danger'.

The idea of a horse is an abstract entity as it resides in my head. And I could just as well embellish it with other first-order ideas that I also have, created as a result of perception, such as 'horns' and 'rainbow colours' to create an idea of a unicorn. But this would be a second-order idea, not a first-order one. I've never actually seen a unicorn (except for that time when I drank that green liquor, but I 'saw' many other odd things then too).

If you created those ideas, then how come you can’t change them at will? Can’t a creator do with his or her creations what he likes? Why can’t you make your supposed creation horsehood be such that you can blow horses away like dandelions? Why can’t you make the number 8 odd?

The idea of a horse is an abstract entity as it resides in my head. — Roy Davies

That can’t really be the case, for abstractness lets not-mentalness follow by definition: to be abstract is to be not-physical, not-mental, not-spatial, not-tidesome (non-temporal), and onefold (simple).

Yes. Now let us hypothesise a zeroeth order: an underlying object that is as it is whether perceived or not. What would we expect of a word in which horses we perceived also had objective realities? One thing we would expect is great similarity in first-order impressions. How can we detect this? In similarities between my vocalisations regarding horses and those of others, such as having both an impression of a horse that is beautiful and an impression of someone saying, 'Oh, what a beautiful horse'.

If we agree on our impressions of horses and that therefore horses have objective realities, my second-order idea of 'horse' is likely to be very similar to your second-order idea of 'horse', such that I may vocalise my second-order idea and have an impression of you making a very similar vocalisation. We would be able to speak of this idea as if it were real, maybe even fall under the illusion that it had primacy over first-order impressions and zeroeth order extrapolations.

I like the logic there. I don't think it proves a zeroeth order, but it is a logical and sensible hypothesis that matches the observations and can easily be tested, so in the manner of theories it serves well.