Bravo! When I mentioned that I was well aware of the pitfalls of autodidacticism, that’s exactly the sort of thing I was talking about. Based on your information, I did some searching and stumbled onto this page. HOLY SHIT! The number of ways that S5 can be constructed fairly boggles the mind.
I’ve had many important discussion on the SDMB where I’ve learned something useful, and which have helped to alter aspects of my worldview. This is one of those. And I’ve ordered A New Introduction to Modal Logic (1996) by Hughs and Cresswell to help round out some of the foundational theory that I’ve obviously been missing.
I truly owe you a great deal of thanks for joining this discussion and then patiently and with great class, explaining your points. I imagine it helped that you already knew me, and knew what my shortcomings would be. It is my hope that you will join the community by subscribing. If finances are an issue with you, I will be honored to sponsor you.
The only thing that I would add to your introductory remarks about modal logic semantics is something that seems to be overlooked a lot. And that is that necessity is not a truth-functional operator (like negation). A does not depend for truth upon A being true.
If fields and forces aren’t real, then I struggle to conceive of anything which is. My entire sensoria is based on forces and fields (and their excitations), so I struggle to distinguish labelling them “just mathematical concepts” from plain old solipsism. (That’s not to say that solipsism can’t be true, of course.) If I were to repeat Rutherford’s gold leaf experiment, I would have to ask myself how I explain the visible scintillations on the screen if particles are “just mathematical constructs” and I’m afraid I simply could not. Forces, fields and excitations have directly observable consequences, and if “directly observable” and “just conceptual” are in any way synonymous, well, I don’t think I could really be said to understand anything.
I’ve said this to you before, but I think you sometimes unintentionally misrepresent physicists like Bohr and Heisenberg when you use their quotes here. Only particles we haven’t observed yet are characterised as probability functions. Once they have been observed, they are no longer distributions – they are spatially constrained like the plain old particles of our (and Democritus’) intuition. That’s the trouble with taking single quotes and trying to build them into huge syllogistic edifices such as “particles are just concepts” – they bypass a huge amount of context which is essential for genuine understanding. (Ultimately, I think your problem isn’t with particles, but with time – again, I’d be happy to explore the physics of time with you some … er … day.)
So no, quantum mechanics and wave-particle duality don’t bother me since I understand the Correspondence Principle between QM and my observations. Yes, there is an infinitessimal probability associated with observing, say, my coffee mug behaving as though it were “just a mathematical construct” (JAMC). But were I to sit here and observe it even for a Brahma lifetime, I would still have a negligible probability of actually seeing that happen. Similarly, yes, a tiny few of the particles that mug is made of do behave in a JAMC-like way even while I’m observing it right now. But the vastly (“Vastly” in Dennett-speak) overwhelming majority of those particles behave like, well, particles, not JAMC’s, and so my senses are swamped by decidely non-JAMC inputs and all is well with the Classical/Quantum World Correspondence.
In fact, I’m actually a little surprised that this was the only part of my post you picked up on since I also did my very best to respond to the OP as fully and candidly as I could. Of course I understand your time contraints, so I’ll just quickly mention the works of someone we both admire which you can Google at leisure (have you read this, by the way? I assure you, it will answer your questions of me much better than I could). Whenever he talks about Philosophical Zombies, old Dan admits that he really, really can’t conceive of them. When his opponent says “Oh hogwash, you’re just saying you can’t” he effectively replies “Actually, I believe that you’re just saying you can”. This, to me, is a beautiful summary of my conversations with theists. No matter how I might wish I could put all of the characteristics of this “God” entity together in my mind at once, I simply fail: it just ends up as a load of words or phonemes or, at best, a Photoshopped image. (I remember a thread here some time ago where someone asked people whether they could imagine in their mind’s eye a water wheel moving as though it was basically violating the laws of physics: some said they could, but I wondered whether they were “tricking” themselves somehow). For me to say that I can conceive of a thinking, intentional agent without any reference to forces, fields, stardust and biological evolution over billions of years, and that that entity is real (whatever that means), would just be wishful thinking on my part.
Actually (no pun intended), I believe that the cognitive science of modal logic will yield the biggest advance in philosophy this century: Lakoff and Nunez’ “Where Mathematics Comes From” is a promising first step.
You silly: it’s obvious that being bigger than something else is supremacy: therefore, if you appear in more universes than something else, you are superior.
But I think it is the case. Let’s call omni-knowledge K and omni-power P. The only reason a bi-omni God cannot know K is if it contradicts P, and the only reason He cannot do P is if it contradicts K. But then, the same holds for any other agent because of the relation between K and P. Knowledge is epistemlogical power, and power is metaphysical knowledge.
I know what I know not just because I’ve been exposed to it synthetically, but because I have the power to comprehend it analytically. Likewise, I can do what I can do not just because I am strong enough, but because I know how. An agent who has looked at Godel’s theorems but cannot read is at no advantage over an agent who is blind. And an agent with strong arms who knows nothing about screws and levers has no advantage over the agent with weaker arms who knows how to construct a jack.
And so an agent who knows what will happen but cannot cause it has no advantage over an agent who knows what will happen and can cause it. The latter agent, in fact, is causing the former agent to have knowledge — knowledge the former agent would not have if the latter agent did not have power. There are contradictions between K and P regardless of agency.
The supremacy is in the union of possibilities, where U is the union of elements from sets K and P.
Well, sure. But another way to look at it is that it is no longer an inequality, but is now an equation. It’s still just a mathematical construct.
I don’t think I’m taking those people out of context. Rather, I think that people who use quantum mechanics (or for that matter, any physics equations) to make decisions about reality are taking things out of context. I mean, it’s nice to know that f=ma, but what’s real about it? If one’s skull is smashed by a baseball bat, what does the formula tell us aside from trivial information about the rearrangement of already existing mass and the discharging of already potential acceleration? Of much greater significance, in my view, is why the bat was swung. Why did Jones bash Smith? Whatever is compelling Jones to violence is the reality; the things around him which may be accelerated are merely obeying trivial rules over which they have no control.
Yes, and every natural number almost certainly has a successor. I am as confident as you that the coffee cup will not disappear and reappear on the moon. I am also confident that I will not win a lottery, and so I don’t buy tickets. Nevertheless, just because a probability emerges into a certainty (Ms. Brown wins the lottery), I’m no better off. My ass right now is suspended on an electromagnetic field (my chair seat) that is deteriorating as gravity inexorably tugs at it and entropy inevitably rots the fibers that hold it together. It is a temporary solution to a temporary problem. Why would something temporary be real? The statement, “My chair exists” is true only for a little while, was not true some time ago, and won’t be true sometime in the future. If that sort of truth is real, then what’s the point of formulating all this philosophy about physical things (a la Dennett)? What assurance do you have that what you derive today will be true tomorrow? And if there are nontemporal truths, then why are they trumped by temporal ones?
I do appreciate your responding to the OP, partly because so few people have, but mainly because it is you. I’m delighted you’re here, and if you search my posts in this thread, you will see that I have highlighted your mental brilliance and your social grace. But I’ve been particularly interested in the points being made by Indistinguishable because they were taking me into unfamiliar territory, and you know how I am about learning something new. It was a matter of timing, not slight. I hope you know that.
I take your point, but I hope you realize that I can both admire a man and disagree with him. Daniel Dennett has no advantage over you in that regard. And I hope you understand that I don’t think you’re bluffing about conceptualizing anything. We just simply think differently. Incidentally, one trick that might help the physicalist visualize the renegade water wheel is simply to assign it a different physics. Surely, you understood f=ma upon first seeing it without having to derive it for yourself. One advantage of humanity is the abilitity for one generation to learn the hard way and then pass knowledge on to the next. And so if you’re used to seeing only circles with pi ratios, you need only imagine a different kind of plane to see circles differently.
One question - what is the truth value of* <>P1 + <>P2 +…+<>Pn* -> <>(P1 + P2 +…+Pn) to you, Liberal? It seems, in my readings so far, to pop up in several objections to the possibility premise.
It looks like the converse of the S2 axiom to me, and so I’m not sure I buy it. If it is possible that Jim is 5 feet tall, and it is possilbe that Jim is 6 feet tall, that doesn’t mean it is possible that Jim is both 5 feet tall and 6 feet tall. Unless I misunderstand what it’s saying.
I’m not quite sure how we digressed into talking about formulae rather than the objects and processes my definition of the universe specified, but the point I think you’re missing is that physics can also be used to describe (and, in evermore complex networks, explain) systems such as decision-making neural networks. (Note that I said explains rather than predicts – just because physics explains the weather doesn’t mean it can tell you whether it will rain on your birthday). After all, it may well be that we are merely obeying (stochastic) “rules”, and control is an illusion! Even the judgement over what is trivial and what is salient might one day be well understood in terms of outputs from computational “judgement modules” which are every bit as physical as the devices which judge whether a car is speeding or not.
I would personally go as far as to say there are no nontemporal truths, since “truth” itself did not exist for 13.6 billion years – it being, again, the output of a biological computer the like of which simply wasn’t around while galaxies were forming, planets cooling, and molecules self-replicating: Everything is temporary, even physical laws (since all bets are off in the Planck era!), and indeed one can’t be certain about anything (“certainty” itself being merely a … yes, you guessed it!.. output of a blah blahdy blah). In fact, your point about chairs reinforces what I said earlier about the pre-humanity intuition pump. We must all offer an opinion about whether we ourselves, and all our conceiving, statement-making and truth judging, existed for those billions of years, and whether we will exist for billions of years in future. I find the proposition that “I” existed in a universe comprising only hydrogen and helium absurd, and so I seek an explanation of how a conceiving machine might evolve from gas. That is the point of formulating a physicalist philosophy.
Of course – in fact, I apologise for sounding even slightly slighted.
Fair enough, but a word of advice – do endeavour to pinpoint where exactly you disagree with him if you have time. Breaking the Spell and Freedom Evolves are particularly relevant to the points you’ve made in this thread.
I guess we drop off here, then. It may well turn out this way and it may well turn out that way. But right now, I’m just as confident that entropy will continue to increase as I am that the coffee cup won’t fly to the moon. An equation is just as much a mathematical construct as an inequality (or probability). And I don’t see how something real can emerge from something that isn’t real.
I don’t know why you need physicalism for that. A conceiving machine can evolve without regard to a physicalist framework. In fact, given that there is so much uncertainty afoot just as you describe, you might well miss something very important if you prefilter what you examine. I very much agree with Arthur Eddington, who said, “What we are observing is not nature herself, but nature exposed to our type of question.”
I haven’t read the books, so I can’t address them specifically. But wherever my points conflict with his, they would be where I disagree. I would buy the books on your recommendation alone, but I’ve just bought and committed to examining a book foundational modal logic theory. I wish I were twenty again!
Okay. I spent much of last evening (whilst doing other things) working myself into a tizzy, trying to understand not just how modal logic works, but the purpose thereof. (If one looks at it crosswise it begins to appear that there is not a distinction between necessariness and truth…which is bad. Also not correct, but if it were correct it would unfold the entire thing into a scam.)
So, having thoroughly confused myself yesterday, I did some digging today (on the reliable source the internet of course) and found this site. (Specifically the three connected pages of it.) In reading this, I came to understand something. (If I’m still wrong, anybody, feel free to correct me.)
It’s the case in modal logic that a statement can be true, but not necessarily true. Coming from a non-modal logic background, this didn’t make a lick of sense. Truth is Truth is Truth! Nothing is more ultimate than truth! Well, on reading, this appears not to be so in modal logic. The way that site explained it clicked something in me, so that I now understand the following:
Modal logic is for making formal proofs about the impossible. Specifically, it’s for making speculations. “Germany lost WWII” is true, so the statement “if Germany didn’t lose WWII, German would be the dominant world language” can’t even be reasonably discussed in ordinary formal logic. It’s always true, purely on the virtue of having a false premise. Which has nothing do with the question the statement asks. To formal-logically discuss theoretical or alternate scenarios, you need the ability to suspend knowledge of actual reality; for this we have modal logic.
So, just because a statement is true, it’s not necessary. What then does it mean to be necessary? Based on my newfound (and possibly grossly incorrect) new understanding, to be necessary means it can’t even be imagined to be false. We can imagine a scenario, a ‘possible world’ wherin Germany didn’t lose the war; ergo the assertion that it did isn’t necessary. The same goes for any bald fact.
What use then is necessitute? Well, given certain assumptions, others must be true. If we accept that all integer numbers have an integer successor of greater value, then it must be true that there is no highest number. There is no possible world -even a theoretical, or an imaginary one!- where successorship doesn’t imply infinity. So, you could reasonably assert (Succ -> ~MaxNum), since a logically consistent world where that was not the case can’t even be imagined.
So. Presuming <> to approximately mean “it can be imagined to be the case that”, and to approximately mean “it cannot be imagined not to be the case that” , what does this mean for the premises of The Ontological Argument?
Version 1: (Defining G to mean “God exists”.)
P1: <>G: It can be imagined to be the case that God exists.
P2: G -> G: If God exists, then it cannot be imagined to be the case that God does not exist.
Uner this argument, with nothing else at all implied by the term ‘God’ but ‘thing’, I can accept P1 readily enough. “A thing called God might exist.” Sure, sure.
However I reject P2. There’s nothing that exists that I can’t imagine not to exist, absent other presumptions that might contradict such an assumption. In fact, the only way I could possibly accept P2 would be if God was presumed or defined to necessarily exist.
Which brings us to the other version of the argument:
Version 2: (Defining G to mean “God, which exists necessarily”, aka “God, which cannot be imagined to not exist, exists”.)
P1: <>G: It can be imagined to be the case that God, which cannot be imagined not to exist, exists.
P2: G -> G: If God, which cannot be imagined not to exist, exists, then it cannot be imagined to be the case that God, which cannot be imagined not to exist, does not exist.
Well, under this argument P2 is darned near a tautology. However, P1 has now become unacceptible. I can’t even imagine something that cannot be imagined not to exist. Anything can be imagined not to exist, absent other presumptions.
So, I regect P1 if you explicitly include necessary existence into the definition of God, and I reject P2 if you don’t explicitly include necessary existence into the definition of God. Therefore, under all possible definions of God, I cannot accept all of the premises of this argument; ergo, I find it to be unsound, proving nothing. Q.E.D.
(Unless there’s something I’ve seriously misunderstood about the premises or how modal logic is used, anyway.)
Wow, thanks. That’s a very kind offer, but I’m happy enough to have just helped someone learn something new. Besides, (if I choose to stick around) I imagine I could suck it up and pay out of my own wallet.
Also, though I’ve never read it myself, people seem to say a lot of good things Hughs and Cresswell, so it will probably be an enjoyable read (though it uses an unusual L and M notation for the alethic operators, rather than the more conventional square and diamond). Checking it out a little, it seems the points I’ve been making are mostly found in the last section, Part Three.
Ah, yes, this is a good point, and you’re right that this deserves stress in an introduction to the subject. In some sense, this is the essence of what it means for an operator to be modal, and the reason that modal logic is sometimes referred to as “intensional logic” (as opposed to “extensional logic”; in general, the extension of a term is the “object” it refers to, while the intension of a term is the specific … way in which it makes that reference.).
I think your set theory is rusty - as you have outlined it, U is the intersection of sets K and P, not the union.
It seems to me you’re kind of saying God is in the possibility space where the commonality of various positive attributes intersect. I see where that might be the case, but that doesn’t say “supreme being” to me. Add enough incompatible positive attributes in there (e.g the incompatibles of Absolute Mercy and Absolute Justice, see below) and your God-space becomes so claustrophobic that even a particularly good and pro-active human fits the bill.
No, that’s about right - like I said, it’s the symbolic representation of the problem many philosophers have with the “possibility premise” - “a supreme/perfect being is possible”. The premise assumes that sum of possible positive attributes implies possibility of the sum of those attributes, and that’s relatively simple to show as false.
I can’t believe you haven’t come across this objection to the MOP before, but you sound like that formulation is news to you. Just my casual reading in trying to keep up turned up this
article specifically dealing with the problem of incompatible attributes.
Yeah, thanks. Not rusty. Just thinking faster than I typed. But that’s right, it’s the intersection.
Various maximal or perfect attributes. I’m not sure how “positive” would be defined.
Given that “supreme” is a superlative, I don’t know what else perfection could be but supreme.
I don’t buy quite much of the protests about incompatibilities. The mercy versus justice arguments, for example. To make them incompatible, they are presented as opposites when in fact mercy can sometimes be just and justice can sometimes be merciful.
It’s also a strawman. The premise assumes no such thing, especially in the MOP where the only attribute under examination is the attribute of existence.
I really don’t keep up much with the stuff from Infidels, which as I understand it, is where the old Usenet atheists got together on the web. The world is still reeling from Usenet’s “you can’t prove a negative” monstrosity. People actually believe it, and even use it in arguments against each other. It has become a meme. I think some of what is found there is the Jack Chick of atheism.
I’ve never seen that particular construct in any discussion of the MOP, probably because as the converse of S2, it is a logical fallacy. And why would it even apply since the axiom that is actually used is completely the other way around: <>(A + B) -> <>A + <>B?
You do realise it’s smaller than the union, right? You’re reducing perfection to less than either of its partakers
I thought you already had defined it as an aesthetic judgment? Positive = Good, Negative = Bad is my understanding.
But God’s not perfect if he doesn’t partake of the entire sum of his attributes, is he? A being who is less than the sum of his parts would be imperfect.
You can, of course, come up with an example or two, right? Just saying you don’t buy it doesn’t refute anything
I disagree. Strongly! Godel’s formulation of the MOP definitely assumes it. So does Plantinga’s with “Maximal excellence”. God is defined in both as a collection of positive/excellent properties, and the implicit assumption is that these are both consistent definitions (not paradoxical). If this were not the case, it breaks down to “A God is not possible”, and the MOP is not a sound argument.
Of course you haven’t seen it, because it’s one of the major weaknesses - but it is certainly implicit in any conflation of Gödel’s Definition 1 and Axiom 3 (from Stanford):
Definition 1: x is God-like iff x has as essential properties those and only those properties which are positive
Axiom 3: The property of being God-like is positive
I’m sorry, but that’s exactly what’s being said here - the sum of all positive properties (being God-like) is positive.
You do reailze that the partakers are knowledge and power, not God1 and God2, right?
As I’ve said repeatedly, aesthetics is subjective: one man’s heaven is another man’s hell.
Even granting you that (for no particular reason), the attributes aren’t possibilities. What you strung together were possibilities.
Suppose you harmed me in some way. Suppose further that I am a pacifist, and believe that a man who harms me should be forgiven, and so I forgive you. The merciful thing for God to do is forgive you. The just thing for God to do is forgive you. Otherwise, he slights me.
The argument is called ontological because it deals with the atribute of existence. That’s what the “O” in MOP is for. Existence is the only attribue the argument examines.
Certainly no more than your “you do realize don’t you?” crap.
[quote]
The article in question is from a professional philosophical journal.But the article in question has nothing to do with ontology. It has to do with allegedly competing attributes other than existence. Philo typically publishes contrary articles. Did Infidels include it?
First of all, I am aware of the weaknesses of the MOP, and competing attributes isn’t one of them. Second, Godel’s version is not even valid and isn’t being discussed here. Third, it is ludicrous to objectivize positivity. Light can be the absence of darkness, or darkness can be the absence of light.
Practice what you preach: give an example of any statement from the MOP (modern, not Godel) that addresses any attribute other than existence.
I’m glad you’ve begun to acquaint yourself with modal logic, begbert2, and have realized the distinction between contingent truths (those which are true, but not necessary) and necessary truths. However, I have some small points to make about what appears to be your understanding of modal logic.
First of all, it is a common misconception to think that modal logic is just about necessity and possibility. Modal logic is brimming with all sorts of operators beyond those two. Things like “Person P believes that”, or “The theory T proves that”, or “At some point in the past, it was true that”, or “It is very probable that” are also modal operators as well. In general, a modal operator M is one that is non-truth-functional; i.e., such that the truth status of M(A) is not determined by the truth status of A alone. Knowing whether something is true or false doesn’t tell you if it’s necessary, if someone believes it, if it’s provable in some system, etc.
The particular part of modal logic dealing with necessity and possibility is called alethic logic. However, there are various sorts of alethic logics as well. In general, the alethic systems posit a multiverse of “possible worlds” (“possible worlds” is a technical term, don’t read anything into it), and also that some of these worlds can “see” other ones. A statement is considered necessary in some world W if it holds in every world W can see, and considered possible in world W if it holds at some world W can see. You seem to be thinking that alethic logic forces us to take a statement to be possibly true if there’s some logically consistent, conceivable state of affairs where it holds, and to be necessarily true if it holds in every logically consistent, conceivable state of affairs. This is a “plenitude principle” (of “possible worlds”), corresponding to taking the set of “possible worlds” to be every logically consistent, conceivable state of affairs, and saying that each one of these worlds can “see” all the other ones. (“plenitude” basically means we don’t leave anything out; we add in everything we can grab). That’s certainly one natural and intuitive system to formulate in alethic logic (incidentally, since every world can see every other world in that system, it’s called an S5 system), but it’s not the only way. Alethic logic is capable of handling subtler notions of necessity and possibility as well. Depending on the particular notion of necessity and possibility you want to capture, you can set the alethic logic up differently (i.e., with a different conception of the multiverse of “possible worlds” and the “sight” relation between them). Hopefully, my post #439, where I discuss the semantics of alethic logic in more detail, may be of some use to you.
That having been said, the particular system of alethic logic you are concerned with (the “possible worlds” being all conceivable states of affairs, and with all of them being able to “see” all the rest) is important, because it is the only real way to justify some of the premises in the modal ontological argument, and your analysis of the problems with this argument’s premises is pretty spot-on. I’ll just comment on them a bit more:
Yes, I basically agree with you here, although, I should note, I think P2 should be (G -> G), or else the ontological argument doesn’t work. If P2 is just G -> G, then we can satisfy both premises by taking God to be something which doesn’t exist in reality (thus satisfying P2 by making the antecedent false), but which could possibly exist (thus satisfying P1). So I’m going to carry on discussion assuming P2 was meant to be (G -> G).
There’s no good reason for us to accept <>G except via the plenitude of “possible worlds” principle: whatsoever is conceivable is possible. If we interpret G as something conceivable, we see that G is possible. But this PoPW principle also commits us to accepting the existence of a “possible world” in which nothing at all exists, and thus forbids us from simultaneously accepting the second premise (that it be logically demanded that if G is true at all, then G can’t be conceived to be false). So, as you say, there’s no good reason to accept both premises here.
Again, you’re pretty much on here. P2 is a tautology in this formulation, and thus we must admit it (it needn’t even be a premise, it can be proved from the definition of God in this formulation). However, P1 is unsupported now; we might want to get P1 through the PoPW principle, saying if we can conceive G, then we should derive <>G. But can we conceive G? Well, G says that God exists necessarily. Can we conceive of God existing necessarily? Well, you may be tempted to say yes, but don’t forget that we’ve adopted the PoPW principle to get this far, and thus need to remember what we mean by necessarily: logically/conceptually demanded. Can we conceive of God’s existence as conceptually demanded? No, certainly not (since, again, it’s easy to conceive of a world in which nothing exists). And thus we have no reason to accept premise P1.
Now, for my wholly own thoughts on the argument.
Basically, what the apparent soundness of the argument comes down to, I think, is a sleight of hand, where we find P1 reasonable under one interpretation of necessity/possibility, but not the right one to make the argument go through, but are tricked into conflating the two interpretations. P1 (it is possible that God exists necessarily) seems reasonable on some sort of plenitude-based account: certainly, we could imagine a world W which was part of a multiverse M such that God happened to fall into every “possible world” of M. But if that multiverse M isn’t the full multiverse F of things visible from our actual world (which our commitment to a plenitude-based account of possibility tells us should contain all consistent states of affairs), then God’s necessity in W is entirely dependent upon W being unable to see any worlds outside of M (in particular, W can’t see the conceivable worlds in F where God doesn’t exist). Thus, we are committed to saying that some worlds may be hidden from other worlds if we want to obtain P1 on a plenitude account. Specifically, the manner in which we allow worlds to hide from each other corresponds to something no stronger than an S4 system (worlds can see themselves, and sight is transitive, but sight won’t always be symmetric). The modal argument will go through fine and get us <>G (we can see some world which can only see worlds where God exists), but we won’t be able to move from <>G to G (and thus to G) without the full system S5 (which adds the symmetry condition on sight). So that is the problem with the argument: in order for us to convince ourselves of the truth of the premise <>G, we use a plenitude principle whose validity is based on an understanding of alethic logic as allowing asymmetry in the sight relation between possible worlds; however, to then, later in the argument, move from <>G to G and then G, we must use a logic which demands symmetry on the sight relation.
What I’ve said above may be all rather dense and unclear, so I’d be happy to explain it further, but it is late and I really must sleep.
(One point to note: I’ve used the evocative term “sight” many times above, and in previous posts on modal logic, but the usual term for this concept is the more dull sounding “accessibility”).
It was a matter of timing, not slight. I hope you know that.