Abuse of Symbolic Logic, and More

[Dan_Eastwood]

A drive-by troll in the queue this morning, left this little gem for us.

[quote]
(⊦∃{}') → ({}≡{}) → ({}={}) → ({}↔{}) → ({}→{}) → ({}:{}→{}) → ({}⊃{}) → ({}∻{})

({}≡{}) → (∀x∃x) → (∃!x∀t∀s)

\[(∃!x∀t∀s)∧({}⊃{})\] → (∀x⊃∃!x|∀t∀s)

\[(∃!x∀t∀s)∧({}∻{})\] → (∀x∻∃!x|∀t∀s) → (∃x∻∃!x|∀t∀s)

\[(∀x⊃∃!x|∀t∀s)∧(∀x∻∃!x|∀t∀s)\] → (∀W∈∃!x|∀t∀s)

(∑E=Ek+Ep) → (∃!x(E)|∀t)

(E=ħω/2) → (∃!x(E)|∀s)

\[(∃!x(E)|∀t)∧(∃!x(E)|∀s)\] → (∃!x(E)|∀t∀s)

E = E

∆E = ∆E

∆E(∆s/∆t) = ∆E(∆s/∆t)

∆E(∆s/∆t)(∆t/∆s) = ∆E(∆s/∆t)(∆t/∆s)

∆E = ∆E(∆s/∆t)(∆t/∆s)

∆E/∆t = ∆E/∆s(∆s/∆t)

∆W = ∆E/∆t, ∇E = ∆E/∆s, ∆v = ∆s/∆t

∆W = ∇E∆v

∫dW = ∫∇Edv

W = ∫∇Edv

\[(∃!x(E)|∀t∀s)∧(W=∫∇Edv)\] → (∀W∈E|∀t∀s)

So, I have established that there is an eternal, omnipresent, all-powerful, self-causal thing and that energy has these qualities. These qualities have been historically attributed to the notion of a god. Therefore according to the identity of indiscernibles God necessarily and factually exists.
[\quote]

And here is the AI deconstruction, which does a pretty good job of explaining it.

TL; DR: Someone used AI to write a bad proof.

[Rumraket (Mikkel R.)]

I can just agree to the proof. Energy is omnipresent and is required for all physical actions. This has nothing to do with God. It says nothing about having thoughts and emotions, whether there’s an afterlife, hating gays, wanting women to be silent and submissive, etc. etc.

[Dan_Eastwood]

@Dan_Eastwood

∀x∃x

It starts off with “∀x∃x”, “For All x There Exists x”, so I suspected circular logic from the start.

[Rumraket (Mikkel R.)]

I don’t so much care about that. To a person who doesn’t agree that something exists the argument begs the question in terms of assuming something exists. Okay, but… something exists, so I have no complaint there.

The real problem occurs here:

So, I have established that there is an eternal, omnipresent, all-powerful, self-causal thing and that energy has these qualities. These qualities have been historically attributed to the notion of a god. Therefore according to the identity of indiscernibles God necessarily and factually exists.

No. It just proves that energy is eternal, omnipresent, all-powerful (importantly, in the sense of being able to drive all physical actions), and self-causal.

It doesn’t prove the existence of God. The final step is the massive leap from energy to God. He says, basically, that if something has these properties it must be God. But he just proved energy has those qualities. He doesn’t prove God is energy.

[Gisteron]

Gotta love it when they just burst out some character string after doing bugger-all to even as much as clarify their notation (which, despite what someone full of their own notation might think, is not, in fact, universal, even within the bubble of their own field, let alone outside of it, where they hope to export the argument to for effect), and expect a “therefore God” to come out the other end…

At my most charitable, I am struggling to decipher what on earth the statements even are. Zero effort was put into disambiguating the meaning of common characters, whilst the more field-specific ones seem to be used in a proprietary manner, again, without declaring the form or referencing a work that does. It looks like an attempt to use an excess of symbols to appear less challengeable; meanwhile I have no grounds to suspect that there actually exists a form this gibberish complies with in the first place, much less that anything is actually being expressed in it.

[Dan_Eastwood]

I found the AI summary to be very helpful, and it caught the references to physics long before I would have (I wouldn’t have read that far either).

[AllenWitmerMiller (Semi-Expired Professor & Minister.)]

@Dan_Eastwood

And here is the AI deconstruction

At age 71, I see Al’s deconstruction every time I look in a mirror.

(Yeah, sometimes I make ya work for it.)

[Gisteron]

I did skim through the summary you linked, I just struggle to find verification for some of its interpretations, and some I can say with some confidence are overly generous, if what overlap I noticed between the notation in logic on the one hand and maths on the other reflects common usage. I am careful not to call the poster’s usage incorrect – not least because I do not believe there is strictly incorrect use of language at all – but rather proprietary and insufficiently documented to be understood by someone who has received training in parsing such notation in its more common uses, like myself, to where I do have an expectation on the outset to understand most or all of it. The issue is not that it’s too technical for my lay eyes. The issue is that for my adequately trained eyes it appears like technically nonsensical. Here follows my own deconstruction, to illustrate what I mean. I shall where needed reference the AI’s interpretation as a base, because the original author’s actual intended meaning I could otherwise say far less about, obscure as it is to me with their proprietary notation.

• \vdash\exists\{\} The AI interprets this as something like “It is a given that something exists”. I am willing to grant this, but already notice a stark departure from common usages of these symbols. Also, the prime at the end of that statement is completely left unaddressed and I too have no clue what it means.
  • First of all, \exists is not a predicate, whether or not we allow ourselves to treat existence as one. The symbol may at times be translated to “there exists” in natural language, but it is commonly used as a quantifier. Another reading of it is, perhaps, “for some”, and all of a sudden the usage displayed here falls apart. If P is some unary predicate, such that for any individual constant x, Px or P\left(x\right) is a proposition, then \exists x:P\left(x\right), where the expression after the colon (which itself is omitted in some notations) is called that quantifier’s scope, translates to “There exists something that satisfies P”, or “P\left(x\right) evaluates to \texttt{TRUE} for at least one x”, or, in set-theoretical terms, “The set of things that satisfy P is non-empty”. If one simply wants to assert that some individual a exists, one would have to make a proposition of “a exists”, which is to say, one would need to introduce a predicate E such that E\left(a\right) evaluates to \texttt{TRUE}.
  • Secondly, \{\} usually is not a dummy individual constant, to my knowledge. What I would intuitively read this as is the empty set, commonly denoted also by \emptyset.
• Next follow a sequence of presumably implications (\to) of relations this object denoted as \{\} apparently has with itself:
  • \equiv is a fairly generic equivalence symbol, = is identity, which one could read as an equivalence in all applicable regards, though the identity of indiscernibles is apparently a daring philosophical commitment, to the defense of which I shan’t here speak.
  • \to is an implication, which maps two propositions p and q to a new one p\to q, which by definition is \texttt{TRUE} exactly when either the latter is \texttt{TRUE} or the former \texttt{FALSE}, and \texttt{FALSE} otherwise. But, of course, in order that \{\}\to\{\} can mean something (and a tautology would be all it means, in that case), it must be that \{\} is a proposition in the first place, which makes the very first statement not actually assert the existence of an object, but the existence of… a statement? Not truth itself, but trueness (what ever the difference is)?
  • \leftrightarrow is a propositional equivalence or bidirectional implication. p\leftrightarrow q maps to \texttt{TRUE} if and only if p\to q and q\to p do, i.e. when p and q map to the same truth-value under the same conditions, what ever they may be.
  • The AI next suggests that \{\}:\{\}\to\{\} is a type mapping, like how in mathematics a function. Well, in some sense, a mathematical function could be understood as the set of all tuples (x,y), where x is an element of the function’s domain, and y is an element of its codomain, such that f maps x to y, denoted most explicitly as x\overset f\longmapsto y, or oftentimes x\mapsto f\left(x\right)=y or even just f\left(x\right)=y for short. For this to make sense in the string we are working with, however, \{\}, which we already were suggesting is an individual constant on the one hand, and a proposition on the other, would also now on a third hand need to be a function, which not merely maps functions to other functions, but one that in fact somehow maps its own elements onto other elements of itself. This is highly recursive, of course, and I’m not positive that there exist model theory specialists who investigate the logical and algebraic structure of objects like this, or if they are even compatible with the Zermelo-Fraenkel set theory axioms.
    On the other hand, if \{\}\to\{\} continues to be a proposition (the tautology, at that), then it stands within something rather like the scope of \{\}, which only works if \{\} is not a proposition but merely a quantifier, in which case \{\}\to\{\} no longer means anything. It is a mess!
  • Next we have \{\}\supset\{\}, and the AI correctly recognizes that the relation in question is, essentially, an implication. It is definitely an ordered relation, just like implication is. Seeing it with curly braces, and associating the latter with sets like I, and surely many of my peers, would, I should think that the statement is that the empty set is its own strict superset. That is false, of course. Being more generous, perhaps we are saying the empty set is just its own superset, and that’s at least true. How does it follow from anything previous is unclear, however. Now, if \{\} is a proposition, then we are dealing with an implication, and it is unclear why two distinct symbols (\to and \supset) are being used, or, again, how the statement follows from any priors.
• In the new line the AI is again being exceedingly charitable. Sure, if we read \exists x as “There exists x”, and refrain from approximating the symbol in any other manner, then it may be fair to interpret \forall x\exists x as “Everything exists”, as utterly absurd as such a statement sounds evenso. But, again, \exists and \forall are quantifiers. They serve a structural function, not just as a shorthand to package English words into. Translate it as “For all x it is the case that for at least one x” and it becomes exceedingly obvious how the expression is far too incomplete to qualify as anything that can be reasonably judged true or false.
  The line continues with asserting that there exists exactly one thing “… of which it is the case that for all t and for all s”, continuing the grammatically unfinished gibberish.
  Again, one can be charitable and allow that the symbolic expressions are mere shorthand for what should have been expressed in natural language, and that this is simply a case of proprietary use of form. In that case, we can focus on the actual argument itself, which states that “Everything exists, and hence there exists exactly one thing at all times and at all locations”. So this “charitable reading” shifts the mess from being one of grammatical incompleteness to one of a blatant and laughable non sequitur incompleteness of logic. The author is welcome to voice which of the two they’d rather continue with.
• In the next three lines the AI interprets \exists!x\,|\,\forall t\forall s as "that unique entity which exists at all times and in all places. I shall grant this interpretation for the sake of the argument, but point out that once again, since quantifiers are not predicates, there was not established an individual constant, much less a symbol defined for it for later reference. Why not just give it a symbol and call it God for the rest of the argument? I couldn’t tell. This is not the only issue with these lines, however:
  • Of all the uses I am familiar with of the vertical bar symbol, this is none.
  • x is of course an individual constant/variable in these expressions. The author would mean by \forall x\supset\exists!x|\forall t\forall s something like “all things point to the unique thing that exists at all times and in all places”, but even setting aside the merits of the statement and all the formal issues discussed hereto, the x in the leading quantifier is not meant to be the same entity as the one paired with the unique existence quantifier. The author treats \forall x as a literal substitute for the English phrase “all things”, rather than the logical quantifier that is meant to cycle through all things and then assert a specific proposition for all of them. A second symbol should have been used in either the former or the latter quantifier.
  • Line 5 in particular is most egregious about this, introducing the new individual variable W in a quantifier, but continuing immediately with \in, the symbol denoting that what ever item left of it is an element of the set right of the symbol. Of course \forall W is not an entity, but a quantification, and to the right of it should follow a full proposition, but we’ve been over this. The God-entity is arguably also not a set, but such theological concerns I shall leave with the author. A more common way to formalize “All work is within God” would be something like \forall x:\left(W\left(x\right)\to\left(x\in G\right)\right), i.e. “For any thing x, if x is an instance of work, then x is an element of God”.
    I should point out, that as much as some freshly trained formal logicians in philosophical circles may be confused by it, mathematicians have more patience with a slightly different notation that does allow for \in to follow a quantifier, because they work with sets all the time. In their notation one could make the same expression in this manner: \forall x\in W:x\in G, meaning “For all x that are elements of W (the set of all instances of work, say), x is also an element of G”, or more naturally “All elements of W are elements of G”, or “W is a subset of G”, for which there is a much more efficient expression: W\subseteq G.
    Lastly, I believe the AI is making a mistake interpreting W as work. More on that later.
• Next come the “physics” lines, and here we introduce the notion that the vertical bar, that served earlier to identify the unique question whose existence was asserted by the existence quantifier in place of an actual predicate, does not serve a function after all. Because here \exists!x\left(E\right)\,|\,\forall t (or \ldots\forall s) translates to “There exists a single value of E that applies to all t (or s, as it were)”. Once again, setting merits aside, this is highly proprietary notation. If the AI’s interpretation of the author’s meaning is correct, a much more efficient and clear way of expressing it would have been E\left(t,s\right)=E_0=\text{const} or something like that, just say that the value of the function E does not vary with the values of s and t.
  • If indeed E_k and E_p are supposed to be the kinetic and potential energy of some system, then it is only the case that this is the system’s total energy, if one cheats and just dumps all energy forms but kinetic into the “potential” bucket. The conservation of energy, likewise, is a statement about a specific class of physical systems, and it is not an unqualified universal truth. A system’s potential energy is an antiderivative of what ever conservative forces operate in it. If the system is subject to non-conservative forces, like drag or friction of some form or another, then its total energy, insofar as such forces are treated as external to the system, is not in fact conserved. Also, once again we are dealing with proprietary symbol use. One could give the total energy just the name E. It would already be a sum of its constituent parts, there is no need to put a sum symbol ahead of it. The sum notation \sum_km_k is used to shorten addition expressions consisting of many items of a kind that can be conveniently indexed through some index set, often times a finite or infinite counting.
  • \frac{\hbar\omega}2 is not “the” zero-point energy, but specifically the ground state energy of a quantum harmonic oscillator, an example problem that is very similar to many quantum mechanical problems where the potential energy of a system has some local minimum point, when considering the behaviour of the system in vicinity of such a point. Unlike the classical harmonic oscillator, the quantum mechanical one’s lowest possible energy is this by just a hair width greater than the value of the potential at its minimum. Qualitatively explaining why the difference is not zero may be achieved by referencing Heisenberg’s uncertainty principle, but a derivation of the actual value would require actually solving
    E\cdot\varphi\left(x\right)=-\frac{\hbar^2}{2m}\cdot\varphi''\left(x\right)+\frac m2\omega^2\left(x-x_0\right)^2\cdot\varphi\left(x\right)
    for possible energies E and their corresponding eigenstates \varphi and identifying the lowest value the former can take (one could do this also in multiple dimensions, or in momentum space, or by quasi-algebraic methods using ladder operators, but let’s keep things basic, I thought). The point here is to say that this is not a universal value. It is the solution of a specific problem, and there are plenty problems in quantum mechanics that cannot be adequately modeled by the quantum harmonic oscillator near a point of symmetry, and that do not have the same ground state energy. The hydrogen atom is a prime example, and one whose importance to our understanding of all atomic physics and chemistry can hardly be overstated. At any rate, it may at first glance appear fair to say that a system’s total energy does not depend on its location or on any location within it, but just a line earlier the author argued that the total energy is in fact the sum of its kinetic and potential energy, the latter of which most definitely depends on the location of the system’s parts and/or the system as a whole (depending on whether it is subject to an external potential ontop of internal interactions or not). Neither the affirmative nor the negative, at any rate, follows as a general inference from the mere existence of a non-zero ground state energy of the harmonic oscillator, even just from the fact that not all problems are the harmonic oscillator.
• Lastly, as to what the AI calls the “calculus framework”, and assuming all the common usages of the letter-like symbols, this whole section contains a bunch of technical inaccuracies the AI was happy to ignore. For instance, mean velocity over some time interval is the ratio of displacement over said time, i.e. v=\frac{\Delta s}{\Delta t}, but the change in velocity \Delta v is a change of that quantity. In this and other examples the author just puts greek letters all over their equations because that’s what they remember from seventh grade science class, but why we do, and when we do not seems not to have been so well retained.
  • Something, meanwhile, that the AI seems to not have retained is that work, in fact, is a transfer of energy, and has therefore the same units/dimensions as energy. Work is not in fact energy divided by either time or distance, but just the difference in energy between one state and another, whether these states are separated by time or space.
  • This last suspiction that the AI may have mistaken the symbol W for work – admittedly a common usage – is consistent with its own earlier interpretation of the line when it first came up. Perhaps in actuality the author meant power, something of which it would make sense to say that all of it is concentrated within God. Power is indeed the rate through time of energy transfer, and the W symbol may have been used for it from remembering that its SI unit is the Watt.

[Puck_Mendelssohn]

I always find these excursions people take into philosophy and logic strange. That which exists surely exists; but what is just as certain is that reality itself is where one tests reality. No mere form of words ever demonstrates that a thing certainly exists or certainly does not exist.

I think it is a frustration, a fatigue of sorts, with evidence. To be asked for evidence for a cherished belief, and to find oneself so completely bereft of evidence, is undoubtedly frustrating. And that which a person assumes to be true without the involvement of evidence is liable to seem, to him, as though it is so much a part of the fabric of reality itself that its truth or falsity can be accessed by incantations of this sort, without the pesky, elbow-dirtying task of finding evidence for its truth or falsity.

But, spirit-summoning is a tricky bit of business. And where a pentagram won’t do, one can indeed always sketch a buttload of symbolic logic, but it tends to be just as futile. Even a completely sound argument which consists only in reasoning, without evidence, is going to be about as valuable as the lack of evidence would have been had the reasoning been omitted.

[Gisteron]

@Puck_Mendelssohn

That which exists surely exists; but what is just as certain is that reality itself is where one tests reality. No mere form of words ever demonstrates that a thing certainly exists or certainly does not exist.

There is an argument to be had here, as to whether “existence” is all that one-dimensional. It is easy enough to agree that no amount of deep thinking into an arm chair will yield any information about “the natural world out there”, what ever its bounds are exactly. And of course, those who insist that their gods are real enough with respect to the world to be able to interact with it in some way, from creating things on the outset all the way to performing miracles in the here and now, may come to frustration trying to justify a belief about something so presumably tangible and observable without any actual empirical evidence to point that way.

Still, there is merit to pure reason in principle, if not for synthetic matters such as statements about nature. When the mathematician investigates with pure logic whether or not there “exists” a prime integer within some specified range, or a function that satisfies a particular differential equation, they might end up proving or disproving such existence, but at no point does anything other than axioms and definitions feed into their reasoning. Likewise, no amount of putting rulers to lengths will ever prove with an appropriate rigor any theorem of geometry, though it may help make it intuitively believable, and perhaps spark an idea as to how a rigorous proof could be constructed.

This would of course be a different kind of “existence”, so much so, that one is tempted to suggest calling one or the other by some other name altogether, to avoid the inevitable equivocation. Alas, tradition has it that we do use much the same vocabulary for both kinds of existence, and none of us will do ourselves any favours by adopting an alternative vernacular just to avoid a mistake so easily corrected.

Point is, it depends on exactly what is at issue. The “greatest of all conceivable things”, or the “ground of all being” is of course not the fatherly ghost who magics puppies and bunnies out of his sheer will, or the bodies of saints out of their graves, but still I think one ought to be careful dismissing arguments about the existence of things which are rooted in logic alone on the grounds that (other kinds of) evidence alone can ever substantiate “existence”. That term can mean several things, and there is an entire class of things whose “existence”, for lack of a better word for it, can in fact only be truly demonstrated by logical argument and not by any amount of (empirical) data. These over-philosophized, irrecognizably abstract descriptions of God would, I am willing to grant, fall into that category, and at that point the arguments (at least until they assert any existence beyond the merely abstract, of course) may need to be parsed for their merit, rather than dismissed as unfit for purpose as a matter of principle.

[Puck_Mendelssohn]

All true and fair enough. I tend to think of mathematics as an abstraction which corresponds to the real world in ways that are extraordinary enough that it is a really useful method of reasoning about “reality” in the particles-and-forces sense. I’d still say that “four” doesn’t exist, but as a concept it characterizes the number of legs on a sheep so well that it’s not unreasonable to call the abstract sense of “four” a part of “reality,” and to conclude that just as two of 'em make eight, the number of legs to be counted on a pair of sheep is also likely to be eight. But, as you point out, once one does that, there are indeed aspects of “reality” which can be accessed almost through reasoning alone. I say “almost” because all mathematics still depends upon postulates, and we accept some set of postulates mostly because it is agreeable to the physics of our world.

Part of why that works so well is of course the compact simplicity of numbers. They represent a solitary aspect of the thing they represent, and they do it so simply that four stars are “four” in exactly the same way that four sheep legs or four phases of fermentation are. And this compact simplicity makes them uniquely manipulable in logic.

When we reach out to “big” concepts linguistic ambiguity takes over and the incomplete, not-fully-stated, complex character of things makes a muddle of it all. You can’t move “god” around like a chit on a gameboard or an element of a logical problem the way you can move “four” around. Real entities outside the domain of abstraction tend to be ragged and incompletely knowable, and the language we use to describe them – which the amateur logician is so often tempted to treat like so many As, Bs, Cs and fours, to be inserted into formulae and equations – is even worse. The practice of law teaches one that that linguistic component of the thing is devilishly complicated, in part because the attempt to render verbal terms unambiguous has a maddening tendency to introduce new deeper ambiguities. Not only is it turtles all the way down, but the very meaning of “turtles” and “down” may be at issue.

[Dan_Eastwood]

Wow! I no expectation of anyone putting any real effort into this, much less what you have done . Here … have a badge.

@Gisteron

A system’s potential energy is an antiderivative of what ever conservative forces operate in it. If the system is subject to non-conservative forces, like drag or friction of some form or another, then its total energy, insofar as such forces are treated as external to the system, is not in fact conserved.

Which leaves us to wonder whether or not God is a conservative force.

[Gisteron]

Thank you kindly!

These days it makes me giggle how some unironically begin their argument with “Energy cannot be created nor destroyed.” only to follow it up immediately with “So where did it come from?”. Best if they grin smugly, too.

[AllenWitmerMiller (Semi-Expired Professor & Minister.)]

[Roy (34-year veteran)]

@Dan_Eastwood

Which leaves us to wonder whether or not God is a conservative force.

As opposed to a liberal one?

[Gisteron]

The opposite of a conservative force in mechanics is a dissipative one. Not really sure what a god is, but (some overcommitting forms of) religiosity would certainly seem to siphon a lot of energy out of people and radiate it out into uselessness, so…

[Dan_Eastwood]

Since we are in the midst of the summer doldrums, I am repurposing this thread to bring you the worst of what comes into the moderation queue. I am reserving this for the obvious drive-by posts. New members presenting themselves as humans will not get this treatment.

[Dan_Eastwood]

[Our next entrant …]

I would like to intoruduce you all to Time Dilation Cosmology (TDC) if you are not already aware of it.

TDC originates the universe within the mind of the Creator and resolves all the conundrums in current astrophysics models.

It also demonstrates how we are all One Life, the Creator, and how the universe is also actually unfolding from within us as we, all living things, are what the Creator is doing to escape Its eternal loneliness and pass Its eternity.

The model is now well known within the astrophysics, quantum physics and theological universities down to the PHD student level throughout the English-speaking world.

TDC describes an eternally evolving, perceptually infinite, holographic universe. It first became popular with the astrophysics community when the velocity formula, v = c*sqrt(dRt), where dRt = the difference in the rate of time, was published in 2021 as it demontrates that all gravitationally induced velocities are merely compensation for the slower rate of time at any coordinate point in the universe.

Nine papers have been published to date and a 10th is under review. The papers are in 2 journals but links to all of them can be found in the Time Dilation Cosmology volume in the Journal of Cosmology, where there is also a link to a new video for the layperson at the bottom of the page.

The model is also getting a lot of attention from the Whiteheadians.

[link to predatory nonsense journal redacted]

[Dan_Eastwood]

AI search says this is just Physics Spam.

The provided text is a promotional statement by independent author Joseph H. (Cass) Forrington, with similar content found on alternate physics sites and the Journal of Cosmology. A specialized volume on the Journal of Cosmology hosts Forrington’s papers, which blend theological, metaphysical, and physics concepts. The works are also published on the open-access platform viXra.org, an alternative to mainstream e-print repositories.

I have reason to think it may have been Forrington himself who posted this. Had he introduced himself first, I might not have immediately dealt with him as a Spammer.

Which goes to show just how little effort Spammers are willing to put forward.

[Puck_Mendelssohn]

I have a Time Domain Reflectometer. Can I use that to see God? Right now I use it to test Ethernet cables.