Hence the suggestion of moving to temperature, which is less ambiguous. — Banno

Good. Should we say that temperature is (brute identity) molecular energy? Or better to say that temperature measures that energy? I don't know how a chemist would respond. As a philosopher, I'm slightly inclined to say that this is not a type of supervenience. But that raises a larger question -- what does the concept of "measure" involve? Is the measurement of a distance simply that distance, full stop? Something both right and wrong about that. After all, we can speak about a distance we haven't measured -- just not very precisely. And if this is a supervenience relationship, we'd need to specify what grounds what. I guess the (unmeasured) distance grounds the measurement of that distance, in that you can't have the latter without the former, but beyond that I'm not sure what to say. A measurement just doesn't seem like a feature or a property that can supervene . . . too "added-on" somehow.

As a philosopher, I'm slightly inclined to say that this is not a type of supervenience. — J

Pretty clear that $\langle E_k \rangle = \frac{3}{2} k_B T$ is an equivalence. The "=" bit.

Taking a measurement is a whole language game. There's quite a bit to say about such a simple task. Malcolm added to this with the other article mentioned, Kripke and the Standard Metre. At the heart of that article is whether a stipulation is necessary or contingent. Lots of material here. Do we go into all that?

My question is, if we make this change, does the objection you have in mind dissipate? Or are the problems that Malcolm suggests still there? — Banno

Where to begin? Let me take a stab at some Philosophy of Science and see where this goes.

Let us considered three "scientific equations":

1. E=Mc²

2. X = vt + Xi where v is average velocity and Xi is initial position.

3. Kinetic molecular theory is expressed as P = 1/3nMv^2/V and ideal gas law as P = nRT/V, we get the relationship between the two expressed as 1/2Mv^2 = 3/2RT

All three utilize the symbol "=", but should we assume all function as identity statements like the logician's "a = a"?

1. Examining E=Mc², does this express the idea that E is identical to Mc². Often physicists describe such a relationship as different forms of the same fundamental quantity that can be converted into each other. Strange to call this "identical" would you not agree? Yet there is an equal sign between the E and Mc². Seems to me that this symbol "=" means some fundamental quantity can be converted from one form to another and that is it. Can something be the same if they have different forms? I would say no. This is similar to the discussion with H2O and its different forms, steam, water, and ice. I would not say the water is identical with ice, or steam.

2. Is the final position of an object identical with the average velocity multiplied by time plus the initial position of the object? In the case, we are talking about differences in position, based on the initial position and the resulting final position, yet we use an "=" symbol to express such a relationship that an object has with space.

3. The Kinetic molecular theory equation is a theoretical mathmatical expression of the motion of molecules while the ideal gas law equation is more of expression of the actual experimental behavior of gas as measure by pressure, volume, and temperture. In this case, the "=" symbol is showing the proportionality of the average molecular kinetic energy to the absolute temperature is a conclusion drawn by comparing a theoretical expression with an empirical equation which summarizes macroscopic gas facts. As Malcolm says, a correlation is set up showing a relationship between getting hotter and rapid molecule motion.

My conclusion is that all three uses of the symbol "=" have different meanings in the aforementioned scientific equations. Additionally, these uses do not seem to reflect the logician's use in an expression such as "a = a". While I can see the application in Kripkes' examples of "table = table" or "Nixon = Nixon", its application to these so called "identity statements" discovered by scientist, well that is a bridge too far.

This may have no appeal for you, but I was quite pleased with the papers cited (by Chakravartty and Pincock) in the "Epistemic Stances . . . " thread. I thought those two philosophers did an excellent job making big issues clear within a smaller, manageable discussion. Would you be willing to read them, perhaps guided by some of the comments in the thread? At the very least, you'd see that the "either it's foundationally true or it's merely useful" binary is not the only stance available.

That makes sense. I think the problems brought up there are more serious than they might seem. Just for one example, an anti-realism that makes science a matter of sociology seems to be able to keep the door open on any attempt to specify "natural" good or a human telos. Indeed, a sort of anti-realism often underpins calls for major social engineering projects. If man has no nature, he can be molded to fit any ideal system (the Baconian mastery/engineering of nature). The popularity of transhumanism with today's oligarchs suggests this sort of thinking might make a comeback.

In particular, I think appeals to reasonableness outside the confines of reason per se tend to actually be relying on a sort of shared tradition and backcloth, a shared moral paradigm. But I think we are seeing such a shared paradigm collapse in real time these days. It's only held up so well because it was around for two millennia and had time to work its way into every aspect of culture and even into our very vocabulary, but other paradigms exist, and there is no reason to think the one undergirding the West will overcome the forces of decay through sheer inertia.

I think what bothers some people is that "true in a context" is seen as some inferior species of being Truly True. It's hard, perhaps, to take on board the idea that context is what allows a sentence to be true at all. If a Truly True sentence is supposed to be one that is uttered without a context, I don't know what that would be.

Well, the idea that 'truth' is primarily a property of sentences appears to be a core step in the path that leads towards deflationism and relativism. I would imagine rejecting this premise itself is more common. Utterances are signs of truth in the intellect, but truth is primarily in the intellect.

We might ask, what is the "context" you refer to? A "game?" A formal system? I would argue that the primary context of truth is the intellect (granted we can speak of secondary contexts). My take would be that analytic philosophy has gravitated towards "truth is a property of sentences," and "justified true belief" precisely because they are analytically tractable and open to more formal solutions. But to my mind, this is a bit like looking for the keys under the streetlight because "that's where the light is." When these assumptions lead to paradox, we get "skeptical solutions" that learn to live with paradox, but I'd be more inclined to challenge the premises that lead to paradox.

I think Borges story the Library of Babel is an excellent vehicle for thinking through the implications of the idea that truth is primarily "in" strings of symbols, although the idea of a truly random text generator that outputs every finite string of text over a long enough time works well too. The fact is that these outputs are never "about" anything from the frame of communications.

To see why meaning cannot be contained within external signals, consider a program that randomly generates any possible 3,000 character page of text. If this program is allowed to run long enough, it will eventually produce every page of this length that will ever be written by a person (plus a vastly larger share of gibberish). Its outputs might include all the pages of a paper on a cure for cancer published in a medical journal in the year 2123, the pages a proof that P ≠ NP, a page accurately listing future winning lottery numbers, etc.¹¹

Would it make sense to mine the outputs of such a program, looking for a cure to cancer? Absolutely not. Not only is such an output unfathomably unlikely, but any paper produced by such a program that appears to be describing a cure for cancers is highly unlikely to actually be useful.

Why? Because there are far more ways to give coherent descriptions of plausible, but ineffective treatments for cancer than there are descriptions of effective treatments, just as there are more ways to arrange the text in this article into gibberish than into English sentences.¹²

The point of our illustration is simply this: in an important sense, the outputs of such a program do not contain semantic information. The outputs of the program can only tell us about the randomization process at work for producing said outputs. Semantic information is constructed by the mind. The many definitions of information based on Shannon’s theory are essentially about physical correlations between outcomes for random variables. The text of War and Peace might have the same semantic content for us, regardless of whether it is produced by a random text generator or by Leo Tolstoy, but the information theoretic and computational processes undergirding either message are entirely different.

A funny thing happens here. The totally random process is always informative. Nothing about past outputs every tells you anything about future ones. It is informative as to outcomes, and wholly uninformative as to prediction. Nothing that comes before dictates what comes after. Whereas the string that simply repeats itself forever is also uninformative, although one always knows what future measurements will be (it is perfectly informative vis-a-vis the future). There is a very Hegelian collapse into oppositional contradiction here, a sort of self-negating. Spencer Brown's Laws of Form have a lot of neat stuff like this too. Big Heg has a funny relationship to electrical engineering :rofl: .

. . . the "Epistemic Stances . . . " thread. I thought those two philosophers did an excellent job making big issues clear within a smaller, manageable discussion. Would you be willing to read them, perhaps guided by some of the comments in the thread?

That makes sense. — Count Timothy von Icarus

Great. I'll watch for any comments you may post to that thread.

truth is primarily in the intellect. — Count Timothy von Icarus

I don't really understand that. It's a metaphor, yes? So, truth is "in" the intellect, in the same way that ___ is in ____? Could you fill it out? Also, sorry, but what is "the intellect"? Faculty of reason, perhaps?

"If a Truly True sentence is supposed to be one that is uttered without a context, I don't know what that would be." - J

We might ask, what is the "context" you refer to? A "game?" A formal system? — Count Timothy von Icarus

I think "game" is overused, and can be misleading, but interpreting it charitably, then yes, a game could be a context, and so could a formal system. Really, though, I mean "context" in the good old-fashioned way. Sentences are spoken or written. This has to occur somewhere, done by somebody, in some sort of intersubjective discourse, etc. That's the context. Can you write a sentence for me that is free of context?

the Borges story, the Library of Babel — Count Timothy von Icarus

Glad to know you're a Borges fan! His story, "Funes the Memorious" would be very pertinent to the ongoing thread about memory. And "Pierre Menard, Author of the Quixote" may be the best philosophical short story ever written.

Pretty clear that ⟨Ek⟩=2/3kBT is an equivalence. The "=" bit. — Banno

Pardon my math deficiencies, but I assume this means we can isolate T on the right side of the equation, giving a description of temperature in terms of kinetic energy?

An excellent reply. "=" is used in different ways in these examples, so one can argue that such equations as these do not use "=" in the way that it is being used by logicians doing modal logic. If this is so then Kripke apparently overreaches in claiming the necessity of such equivalences. Following this line of thought, the relation between mean kinetic energy and temperature is not one of metaphysical identity.

The implication for Kripke is a weakening of the apparatus he uses to argue for a posteriori necessity and doubt cast on his argument against the identity of mind and brain.



One possible reply is that there is something in common to equations, since in each case they use the "=" to state that the value on the left will be the same as the value on the right; that it is this value that is rigidly designated, not the items in the equation. So in E=mc2, what is rigidly designated is that the value of E is the very same as the value of mc², and so on for each example. This would be to agree with you that in physics "=" does not always assert an ontological identity, but that if the use of "=" is to make any sense, it must assert the identity of the two values it equates.

On this account, the identity here is not between ontological entities but between their values within the structure put together by doing science. This would considerably weaken the applicability of Kripke's system.



A second possibility is that the historical use of "=" back to Russell's attempt to ground arithmetic in logic, does show that the "=" in physics is the same as the "=" in logic. They are both uses of the identity relation set out in Begriffsschrift, and that all arithmetic equations are grounded in that logical interpretation. It's just what "=" means. So the mean kinetic energy $\langle E_k \rangle$ just is $\frac{3}{2} k_B T$.

This is a pretty dogmatic response, stating that the reason we can write such equations at all is that their effectiveness is dependent on or justified by the logic of identity, that accepting your argument would be tantamount to claiming that identity signs in physics are ambiguous and equivocal. Pretty harsh. My response to suffered from something like this, and perhaps Tim might say something similar. Are physical equations really that precise?



A third approach might be to take on board what has been said, and go back to the basics to reassess how our modal logics work.

In propositional logic, one can substitute any proposition for any other provided that they have the same truth value. In predicate logic, one can substitute any individual variable for another provided that they designate the same individual. In modal logic, this fails: while two propositions may both be true in a given world, it does not follow that they are true in every possible world. Truth is evaluated not only by what individual is designated, but also by which world the evaluation takes place in.

However, at the level of possible worlds semantics, modal logic is extensional: formulas are assigned sets of possible worlds as their extensions, and modal operators like necessity (□) are interpreted as quantifying over those sets. That is, □A is true at a world w if A is true in every world accessible from w. Because substitution of formulas with identical extensions preserves truth across all worlds in the model, the possible worlds interpretation is extensional.

☐p is true in w iff p is true in every world that is accessible from w.

We also have that in S5 and elsewhere that it is valid that a=b→□(a=b). It is the consequences of this simple theorem that Kripke is teasing out. The salient bit is that we may find out only a posteriori that a is indeed equal to b. This is what leads to the conclusion that so many find objectionable, that there are necessities that are discovered by looking around at how things are rather than understood a priori.

In the simplest case, that a=b means that a and b are the very same individual. And becasue of the extensionality involved, with some standard considerations we have it that if some expression is true for a, it will also be true for b. There is no obvious reason that this analysis can't be somewhat extended, including to kinds. So if we find, as seems to be the case, that every animal that has a heart also has kidneys, then extensionally, the set of animals with hearts and the set of animals with kidneys are the very same set, and we can substitute "animals with hearts" for "animals with kidneys" while preserving truth.

So if, whenever we pick out an animal that has a heart, we also thereby pick out an animal that has a kidney, then necessarily, if an animal has a heart then it has kidneys. If they are extensionally equivalent in every possible world, then necessarily, if an animal has a heart is has kidneys.

We might do this if, for instance, we were to insist that if we were to come across some animal that appeared to have a kidney but no heart, what appears to be a kidney is not a kidney, but has been misidentified.

The third response, then is to note that Kripke's move treats identity statements as extensional, and not in the intensional fashion seen in Malcolm. These rigid designators refer to the same entity or set in all possible worlds. Substitution of such identical entities is permitted at a modal semantic level, so when we find that a=b a posteriori, we might stipulate this as a metaphysical necessity, and reject counter instances as errors of identification.




What we have here is an at least apparent conflict between two quite different approaches. Folk might be tempted to suppose, somewhat simplistically, that either one or the other must be true, and the other must be false. Is it the case that we must either adopt the extensional approach and Kripke, or the intensional approach of Malcolm? Or are they talking past each other.

It might be interesting to look at Malcolm's approach through the lens of one of the formal intuitionist logics. Perhaps relevance logic would be informative.

This post has taken a few hours to put together, so thanks for the challenge. I hope you find it as interesting as I do.

My conclusion is that all three uses of the symbol "=" have different meanings in the aforementioned scientific equations. Additionally, these uses do not seem to reflect the logician's use in an expression such as "a = a". While I can see the application in Kripkes' examples of "table = table" or "Nixon = Nixon", its application to these so called "identity statements" discovered by scientist, well that is a bridge too far. — Richard B

I agree here -- which is why I began to think that the lecturn lectern example might be better because it gets us out of thinking about how the science relates to the metaphysics, which is a whole ball of wax, and starts to focus on an object which we take as real, and then Kripke demonstrates how we might still be able to have necessary relationships after the fact and so a kind of "essence" might still hold good.

Excellent response.

Good laying out of positions and replies -- I just finished it so nothing to substantive to say, but wanted to give kudos for a well thought out response on the topic.

This post by way of pointing out how our own conceptions on what constitutes philosophy are different, so we are talking past one another.

Okay, sure. Water cannot be divisible and indivisible. This is a true contradiction. Yet this is the first time I've seen you presenting Aristotle as a proponent of indivisibility. Earlier you were talking about teleology. — Leontiskos

The purpose of using names isn't to demonstrate what I've read and understood, but to refer to a shared body of knowledge between speakers. So when I say "Aristotle", I presume you understand Aristotle well enough and modern science well enough to be able to put together the dots that teleology and modern science, especially of the enlightenment era, are in conflict.

I switched to divisibility because the example is as good as the teleological one -- namely, I don't know if Lavosier, on a personal level, might have believed there was some kind of teleology behind water, but the whole enlightenment project basically rejects teleology in favor of efficient causation for its mode of explanation -- this is one of the primary reasons people reject Enlightenment era materialism and go in various ways.

There is no strict division between philosophy and science. Aristotle is generally referred to as a scientist, perhaps the first, and yet this does not disqualify him as a philosopher. — Leontiskos

I agree. My inclination to using examples is to overcome this -- we don't have to define things in terms of their necessary and sufficient conditions, but can instead use paradigmatic examples to show what we mean: definition by ostension.

So there are three names that we've been using, and with those names I'll draw some differences:

Aristotle is an ancient scientist and philosopher
Lavoisier is a modern scientist
Kripke is a modern philosopher.

Because I'd draw a distinction between ancient and modern science -- they don't operate the same. And Kripke counting as modern because of the scope of the question which utilizes Aristotle.

Right... I guess I would need you to set out the thesis that you believe to be at stake. I wrote that post with your emphasis on falsehood in mind. You have this idea that Lavoisier must have falsified something in Aristotle. The whole notion that we can grow in knowledge presupposes that we have something which is true and yet incomplete, and which can be built upon. — Leontiskos

I think all it takes to grow in knowledge is to plant seeds and see what happens. And what had been can die, and what is will stop being.

But noting here: even our notions of "falsification" are at odds. So perhaps we cannot appeal to falsification in our back-and-forth, because even this is being equivocated in our dialogue.

I assure you that by my understanding of falsification that Lavasioer does not falsify Aristotle, and that this is pretty much just another rabbit whole to jump down before getting to the topic "What is real?"

To say what's at stake: I don't think science delineates what is real. I also think that the project towards finding essences using the sciences is doomed to fail -- the big difference between Aristotle's and our day is the sheer amount of knowledge that there is. In Aristotle's day it probably seemed like a reasonable project to begin with the sciences and slowly climb up to a great metaphysical picture of the whole.

But any one scientist today simply can't have that perspective. Looking at https://pubmed.ncbi.nlm.nih.gov/ their tagline on the front page states "PubMed® comprises more than 38 million citations for biomedical literature from MEDLINE, life science journals, and online books."

Aristotle could review all the literature that was in his day and respond to all his critics and lay out a potential whole. But he didn't have so many millions of papers or forebears to deal with. And I'd be more apt to look to the Gutenberg Press to explain this difference.

But this is only if we treat metaphysics as exactly the same as science, too. That was Aristotle's goal, but it need not be metaphysics goal. I'm more inclined to think that these metaphysical ways of thinking are ways of dealing with the sheer amount, the multiplicity, that one must consider to make a universal generalization. The generalizations, rather than capturing a higher truth, is a way of organizing the chaos for ourselves.

So what's at stake -- the usual stuff. The relationship between science, philosophy, and whether science can or ought to have or how much they ought to have a say in "What is real?"

It is odd to say that it is false. If it is "good enough" to begin understanding, then it simply cannot be wholly false. If it is wholly false then it is not good enough to begin understanding. — Leontiskos

Another terminological difference. I tend to think attributions of "not wholly false" or "not wholly true" can be reduced to a set of sentences in which the name is sometimes the predicate and sometimes not the predicate, and so we need only refer to the conditions for each. "False" doesn't admit of degrees in a strict sense, I don't think, though it's a common way of parsing the world in our everyday reasonings.

If I know something about water, and then I study and learn more about water, then what I first knew was true and yet incomplete. It need not have been false (although it could have been). Note, though, that if everything I originally believed about water was false, then my new knowledge of water is not building on anything at all, and a strong equivocation occurs between what I originally conceived as 'water' and what I now understand to be 'water'.

For Aristotle learning must build on previous knowledge. To learn something is to use what we already know (and also possibly new inputs alongside).

I agree that Aristotle would accept and expect this -- but I don't think he'd predict what's different.
— Moliere

Right. He knows that there is more to be learned about water even though he does not know that part of that is H2O.

So what I see is that skepticism, rather than security, is the basis of knowledge. Jumping out into the unknown and making guesses and trying to make sense of what we do not know is how new knowledge gets generated -- if we happen to find some connections to what we thought we knew down the line that's a happy accident.

The emphasis on security, I think, leads one to complacency. Rather than testing where we are wrong we defend when we are right.

Right, good. Let's just employ set theory with a set of predications about water:

Aristotle: Water: {wet, heavy unlike fire}
[Call this AW]
Lavoisier: Water: {wet, heavy unlike fire, H2O}
[Call this LW]

On this construal Lavoisier's understanding of water agrees with Aristotle in saying that water is wet and heavy unlike fire, but it adds a third predication that Aristotle does not include, namely that water is composed of H2O.

What is the relation between AW and LW? In a material sense there is overlap but inequality. Do Aristotle and Lavoisier mean the same thing by "water"? Yes and no. They are pointing to the same substance, but their understanding of that substance is not identical. At the same time, neither one takes their understanding to be exhaustive (and therefore AW and LW do not, and are not intended to, contradict one another).

Now the univocity of the analytic will tend to say that either water is AW or else water is LW (or else it is neither), and therefore Aristotle and Lavoisier must be contradicting one another. One of them understands water and one does not. There is no middle ground. There is no way in which Aristotle could understand water and yet Lavoisier could understand it better.

If one wants to escape the problematic univocity of analytical philosophy they must posit the human ability to talk about the same thing without having a perfectly identical understanding of that thing. That is part of what the Aristotelian notion of essence provides. It provides leeway such that two people can hit the same target even without firing the exact same shot, and then compare notes with one another to reach a fuller understanding. — Leontiskos

I think your construal of AW and LW is such that they look like they agree more than they do not agree. Maybe, but note this is why the historical method is more interesting than stipulated definitions.

I'd go back to the distinction in this post I made between Aristotle, Lavoisier, and Kripke.

Aristotle's concern is philosophical and scientific, and he lives in an era where his project is feasibly both philosophical and scientific. He has a much wider theory of water that conflicts with the enlightenment, mechanistic picture of H2O which Lavoisier is credited with determining. I think of hisLavoisier's work primarily as a scientist because his work as a scientist was in improving analytic methods, and it was due to his care towards precision that he was able to demonstrate to the wider scientific community the ratio of Hydrogen to Oxygen you get with electrolysis. So maybe there's some philosophical work of his I do not know, but I'd say this work fits squarely within the scientific column, even if we don't have strict definitions to delineate when is what.

And, likewise, Kripke is making a point about whether essences can be made viable in the 20th century after they had been largely abandoned by contemporary philosophy (even if there are other traditions which keep them). So he's a philosopher, but if science turns out to be wrong about the whole H2O thing his points will still stand(EDIT:or fall) regardless. So he's not a scientist, in this particular instance.

This is a pretty dogmatic response, stating that the reason we can write such equations at all is that their effectiveness is dependent on or justified by the logic of identity, that accepting your argument would be tantamount to claiming that identity signs in physics are ambiguous and equivocal. Pretty harsh. My response to ↪J suffered from something like this, and perhaps Tim might say something similar. Are physical equations really that precise? — Banno

Yeah, that was the direction of my wondering, but I'm definitely out of my depth when it comes to how chemists and mathematicians regard questions of identity, so I'll continue to follow your discussion with @Richard B.

Thank you.

So what I see is that skepticism, rather than security, is the basis of knowledge. — Moliere

Excellent phrase.

There's a risk, in focusing on second reply, of watering down the response to the other two. But it;s interesting, so...

I gather, or at least supose, that mathematicians and physicist see a continuity between their use of "=" in 1+1=2 and in $\langle E_k \rangle = \frac{3}{2} k_B T$. Philosophers are the sort of people who question such things. Let's look at the three examples provided.


makes the point that E=mc² can be considered as showing how we convert matter into energy, and that's a valid way to understand it. But others will say that it shows an equivalence such that matter and energy are different forms of the same thing. Need we insist that one of these views must be the correct on? I don't see why.

X = vt + Xi is a pretty direct bit of maths. If you start at 5m and travel at 1m/s for three seconds, you will be at 8m. Is that final position identical to "1m/s x 3s +5m"? That's just 3m + 5m, so yes, it is.

$\langle E_k \rangle = \frac{3}{2} k_B T$ was derived form first principles rather than from the results of experiment. Interestingly the 3/2 comes from $E = \frac{1}{2}m(v_x^2 + v_y^2 + v_z^2) = \frac{1}{2}mv^2$, the energy in each dimension added together. in kinetic theory, temperature is a measure of average kinetic energy. In this model, the concepts are interdefinable—we can understand temperature through motion and vice versa.

We are indeed doing quite different things with each equation. However there is a pretty strong case for claiming that despite this, the "=" fulfils much the same role in each.

That word - interdefinable - may well be seen as about a metaphysical stipulation.

All very good, thoughtful posts :up:

, Leon


Much as I dislike the present infection of Aristotelian thinking, I have to agree with this:

A very recent book aiming at summarizing the philosophers’s doctrines concludes the chapter on Aristotle’s physics with the words: “We can say that nothing of Aristotle’s vision of the cosmos has remained valid.” From a modern physicist’s perspective, I’d say the opposite is true: “Virtually everything of Aristotle’s theory of motion is still valid”. It is valid in the same sense in which Newton’s theory is still valid: it is correct in its domain of validity, profoundly innovative, immensely influential and has introduced structures of thinking on which we are still building. — Carlo Rovelli, Aristotle’s Physics: a Physicist’s Look

Does this roughly correspond to your point, Moli?

Roughly, yes.

I love that paper so much.

The "correct in its domain of validity, profoundly innovative, immensely influential and has introduced structures of thinking on which we are still building" bit might have less of a rhetorical influence with respect to chemists though.

This is a pretty dogmatic response, stating that the reason we can write such equations at all is that their effectiveness is dependent on or justified by the logic of identity, that accepting your argument would be tantamount to claiming that identity signs in physics are ambiguous and equivocal. Pretty harsh. My response to ↪J suffered from something like this, and perhaps Tim might say something similar. Are physical equations really that precise?

There are a lot of questions there, the relation of the equations of the current discipline of physics to physical reality, the indeterminacy of measurement, etc. Yet even on the mathematical side we might allow that:

6+7 = 13 = 13 - 3, and yet these are not the same computations, and this becomes obvious when one considers something like a large input Hamiltonian path problem where it might take until every star in the sky has burned out for the fastest super computer to finish processing the computation, and yet the input is said to "be the same thing" as its output.

Barry Mazur has an interesting paper on "When One Thing is Equal to Some Other Thing". However, one has to also consider what mathematics is and its application to the "material world" it has been abstracted from. The Scandal of Deduction, for instance, comes because no distinction is made between the virtual, potential, and actual, and the way in which physical computation always involves communications (which occurs over some interval).

So we agree that the second response seems inadequate*? Cool.

Making a deduction is a process, something we do, rather than something sitting passively waiting to be noticed. This goes for rationality in general, as can be seen by the presence of irrationality. If we had no choice but to be rational, there wouldn't be so much fuss about being irrational. Adding six and seven and realising that doing so gives the same value as adding nothing to 13 is not quiescence.

This leads to another point relating to mathematics. Making a calculation requires effort. Performing a deduction makes explicit what was previously hidden. And physically, doing this require work - energy over time.

There's also the interesting fact that not all Hamiltonian path problems have an answer. That is, some of them are not equal to any value. It’s not accurate to say that “the input is the same thing as its output” in a Hamiltonian path problem when there is no path. The input does not implicitly contain a path if there isn’t a path. The input is not the same thing as the output.


*added: Is that your opinion? There is no explicit conclusion in your post.

This post has taken a few hours to put together, so thanks for the challenge. I hope you find it as interesting as I do. — Banno

Interesting and stimulating, it has put my mind in such a state of agitation.

Response nonetheless:

"116 When philosophers use a word - "knowledge", "being", "object", "I", "proposition", "name" - and try to grasp the essence of the thing, one must always ask oneself: is the word ever actually used in this way in the language-game which is its original home?- What we do is to bring words back from their metaphysical to the everyday use." Wittgenstein, PI

In this spirit, along with my reaction to your's and others feedback, I believe I need to take a little more creative approach. I like to borrow, roughly, an approach Quine performed in Word and Object around his treatment of time. In previous post I presented three scientific equations:

1. E = Mc²
2. X = vt + Xi
3. 1/2Mv^2 = 3/2RT

Special attention was given to the symbol "=" that I believe gave way to talk of "identity" and "equivalence". After much thought, I started thinking this symbol was creating some problems. One, it was leading one to think there must be some similarity to logicians use of "a = a". Two, this symbol was distracting the actual meaning of these scientific expressions. Lastly, and obviously, its persistent use in mathematics may lead one to think this may be the ultimate meaning of these equations, "numeric value" is equal "numeric value".

Given these concerns, I think it best to leave behind the symbol "=" and use another, "⇔"

1. E ⇔ Mc²
2. X ⇔ vt + Xi
3. 1/2Mv^2 ⇔ 3/2RT

This different symbol is to emphasize what the relationship between both side of the equation. Let's take the simpler of the three equations, #2.

What is this scientific equation trying to express: For experimentally determine values of variables v, t, and Xi, where v is average velocity, t is duration of time, and Xi is the initial object's position, the object's final position is determined by v multiplied by t plus Xi. So, if you determine v, t, and Xi, you can predict X. Consider, equation #3, if you determine the temperature, you can predict the kinetic energy of the gas, or vice versa if you determine the kinetic energy of the gas, you can predict the temperature of the gas. Notice, there is no need to call these expressions as some kind of identity statement. This is just to introduce some metaphysical baggage that is not needed for these equations to function.

Historically, scientists established these equations well before the creation of S5 modal logic. What exactly is Kripke's value in calling them identity statements? That when we of talking about object's initial position and final position, we, by metaphysical necessity, must be talking about the same object. But this seems to be a troublesome expectation. What if the final position is not as we predicted, should we, as you say, "reject counter instances as errors of identification." No, we should proceed as scientists would do in these cases, see if we made some error in measuring, or maybe the instrumentation malfunctioned. But could you not say that you made an error by measuring the incorrect object? Sure, but I also could have measure the wrong object and found the position to be what was expected, and this just demonstrates that this has nothing to do with metaphysical necessity.

"124 Philosophy may in no way interfere with the actual use of language; it in the end only describe it." PI 124

Interesting and stimulating, it has put my mind in such a state of agitation. — Richard B

I'm sorry for the agitation. I hope I can show you that there is no need for such disquiet, and at the same time take us back to the theme of this thread. I want to assure you that I agree with you that Malcolm has the better handle on language as a whole, and that Kripke has taken steps too far in applying his logic. I think we can be fairly precise as to where and how, and bring this back to the discussion of what is real and what is not real.

We started to talk about essences because some folk here suppose that in some way it is the essence of a thing that decides if it is real or not; or perhaps the other way around. It has been difficult to obtain a clear explanation of how we are to fill this all out.

Now the Wittgenstein of the Tractatus may well have had a view along these lines, since we can read amongst the changes between that work and the Investigations a change in Wittgenstein's approach to both logic and to essence. For the Wittgenstein of the Tractatus - and here I must ride rough-shod over the detail - the essence of a thing is implicit in the logical form that sets out the nature of that thing. This reflects a kind of logical essentialism: the structure of reality (and language) is essential and necessary, and it defines the limits of meaningful discourse.

But by the Investigations, much of this had become unacceptable. The assumptions that had held this view firm were rejected. Where in the Tractatus each meaningful term had a strict definition, in the Investigations we were admonished to look instead at what we are doing with words and see that this vast variety of uses can and must not be understood in such a simple and fixed fashion. Doing so greatly misunderstands and misrepresents the variety of language. The notion of a family resemblance is important here, but is not alone.

At around the same time, Quine was proffering another influential critique of essences, one more within the constraints of formal logic. Quine's argument shows that when someone uses a name - "gavagai" there may be no fact of the matter as to what that might be referring to. There are two aspects of this, the first that it need not be necessary to fix the referent perfectly in order to get your rabbit stew. The second, that no statement is true or false only as it stands, but that they are true or false as a part of the whole web of belief. Extensionally, to supose "gavagai" refers to the same thing as "rabbit" is to suppose that each element of the set "rabbit" is an element of the set "gavagai" - that's setting out what it would be for "gavaga" to mean "rabbit" in a way that does not rely on the intentionality of speaker meaning or web of belief. But that some individual is a member of the set "gavagai" or "rabbit" is of course open to referential opacity. If reference wasn't fixed, so much the worse for essence.

Historically, these and other considerations led to a pretty widespread consensus in around the 1950's that essences were a bit useless, an anachronistic hangover form Medieval logic with which we could safely do without.

The spurning of modality had much to do with the great success of predicate calculus and other advances in formal logic after Russell that seemed to have left the formalisation of modality behind. This changed dramatically when a kid from Nebraska showed how to construct a semantics and demonstrate completeness for S5.

At the centre of this formalisation is a simple idea, restored from Leibniz. Modal language is pretty every-day. It comes about when we consider how things might have ben different - what if that table had been in the other room, or had been red instead of blue. In using such language we are asking about how the world would be if things had been a bit different - perhaps if the table were in the other room, the young people could play their board game on the table in there while we old folk dance in here... or whatever - we have interesting parties. The suggested way to understand such utterances is wondering what would be different in a world in which the table were in the other room. That's all a possible world is - a way of giving a firmness to such utterances by stipulating a difference and inferring the consequences.

The formal version gets a bit complex, of course, but that's the basic idea. The formal stuff is what gave the idea respectability - here we had a way of using modal talk that we could be assured was coherent and complete, and that for many was intuitively familiar.

And along with this comes a way of thinking about essences that shares in this coherence and completeness. Essence could be considered as being those properties that belong to a thing in every possible world in which that thing exists. Or, if you prefer, the properties without which we'd be talking about something else.

It's worth paying some attention to how this works. A typical example is that Nixon was necessarily Human, and so that in every possible world in which Nixon exists, Nixon is human. Now it remains that perhaps the Nixon who was impeached might have been an alien. In that case, we are not talking about Nixon, but some alien who has replaced Nixon. Our Nixon is necessarily human.

The point Id like you to see here is that the specification that Nixon is necessarily human is not a restriction on Nixon so much as a restriction on how we can make use of the word "Nixon". We might use the word "Nixon" to refer to something other than Nixon - to the alien. But doing so does not make Nixon an alien.

Notice here the shifting of the burden from ontology to language. That's really quite important. Kripke can be understood as sneaking metaphysics in in the guise of logic. And at time he does appear to be guilty of this sin. But there is also a way of treating possible worlds as setting out for us a way to talk coherently about modal problems, without, or at least with minimal, metaphysical implications.

Following this path, we treat possible worlds not as metaphysical entities but as stipulated language games within which we can evaluate the truth of particular propositions, of how things might otherwise have been. And essential properties are not discovered, nor the attributes of Platonic Forms, but are decided by virtue of keeping our language consistent. They are a thing we do together with words.

There's a lot more that can be said here, but I have to go do other things, an there is enough here for now. The Law of Diminishing Returns applies, too. Is any one reading this?

Following this path, we treat possible worlds not as metaphysical entities but as stipulated language games within which we can evaluate the truth of particular propositions, of how things might otherwise have been. And essential properties are not discovered, nor the attributes of Platonic Forms, but are decided by virtue of keeping our language consistent. They are a thing we do together with words.

There's a lot more that can be said here, but I have to go do other things, an there is enough there for now. The Law of Diminishing Returns applies, too. Is any one reading this? — Banno

I am sir.

I'm glad to see your explicit rendition of possible worlds, because that was my fuzzy notion but you've made it explicit.

I will let you have the last word for now. I am sure our paths shall cross again about this topic.

Following this path, we treat possible worlds not as metaphysical entities but as stipulated language games within which we can evaluate the truth of particular propositions, of how things might otherwise have been. And essential properties are not discovered, nor the attributes of Platonic Forms, but are decided by virtue of keeping our language consistent. They are a thing we do together with words. — Banno

If philosophy becomes merely a matter of keeping our language games internally consistent, then it risks becoming a kind of syntax-policing—about saying what can or can't be said, not about what is or must be. That’s a long way from asking what is real and how it might be known.

I would have thought that the existence of necessary truth, and questions as to what that implies, or why they are necessary, are fundamental philosophical questions, about more than simply 'what we can say'.

I am sir. — Moliere

Good to know.

I am sure our paths shall cross again about this topic. — Richard B

Sure. I still haven't responded to the points you made in your previous. Will do so later.


Perhaps. But at the very least philosophical theories ought be internally consistent, so there is a point to the process of working out what that looks like. If it doesn't matter what can be said then anything goes.

If the whole ambit of philosophy is human experience and judgement then is it not always a matter of "what can (coherently and consistently) be said? So, the Op question reframed would be not "how do we know what is real?" but "how do we decide what counts as real?"

If the whole ambit of philosophy is human experience and judgement then is it not always a matter of "what can (coherently and consistently) be said? — Janus

What can be said is a start. What can be shown might be more important. That's part of what is problematic about mysticism. If it is showing stuff rather than saying stuff, it's not actually false. But when it says stuff, it is almost invariably false.

So, the Op question reframed would be not "how do we know what is real?" but "how do we decide what counts as real?" — Janus

I still prefer "How do we use the word real?"

What can be said is a start. What can be shown might be more important. That's part of what is problematic about mysticism. If it is showing stuff rather than saying stuff, it's not actually false. But when it says stuff, it is almost invariably false. — Banno

When it says stuff is it false or merely inapt?

I still prefer "How do we use the word real?" — Banno

The word is used in many ways obviously. Usage presumably cannot determine whether something is real, but rather whether it should be counted as real. A theist might say "God is real", does it follow that God might be counted as real, as opposed to, say, imaginary?

I still prefer "How do we use the word real?"

Charles Pierce claimed that the term “real” was invented by scholastic philosophers to signify “that which is not a figment”, in order to close the debate around the problem of universals. I’m not sure if that is true or not, but I thought it was neat. Before then the word “real” already had its use in “real property”, something like “immovable property”, which we know today as real estate.

Is any one reading this? — Banno

Yes. I'm getting a lot from what you and @Richard B and your interlocutors are discussing.

. . . fundamental philosophical questions, about more than simply 'what we can say'. — Wayfarer

I'm plucking this phrase out of its context because of what I think it implies. One version of what a "fundamental philosophical question" is would claim that such a question is about something that might be inexpressible in words. Another version would limit the idea of a "fundamental philosophical question" to what can be said in a language, on the grounds that philosophy must not be misunderstood as the gatekeeper of all truths, all things "fundamental." Philosophy is limited to discourse, and so must be the subjects of its questions. Yet a third version would insist on a distinction between "answer" and "subject": thus, we can answer a philosophical question within the realm of philosophical discourse, but that doesn't mean that the subject of such discourse is also necessarily linguistic.

I think you mean to stake out the first territory, yes? That there are truths -- answers to fundamental philosophical questions -- that cannot be uttered? Or is it closer to the third version, with all truths utterable but not all subjects being linguistic?