A Case Against Contemporary Theoretical Physics and Cosmology

The controversial American polemicist David Berlinski states that “contemporary cosmologists feel free to say anything that pops into their heads”. He also compares the Big Bang theory to Norse mythology. This essay discusses his claims.

(i) Introduction

(ii) Berlinski on Metaphysical Speculation

(iii) Berlinski on Lee Smolin’s Cosmological Natural Selection

(iv) Berlinski on the Big Bang Theory

(v) Berlinski on Alan Guth’s Inflationary Theory

David Berlinski is a well known and controversial writer and polemicist.

Berlinski rejects — or, perhaps, simply questions — the Big Bang theory, the theory of evolution and the cosmological inflationary theory. He also rejects (or simply questions) the existence of black holes, the multiverse, etc.

Perhaps Berlinski’s broader perspective on science is best expressed in his book The Devil’s Delusion: Atheism and its Scientific Pretensions (2008). More concretely, Berlinski is a signatory to A Scientific Dissent from Darwinism, which was a statement issued by the Discovery Institute in 2001.

One aspect of Berlinski’s critique of science is itself scientific (or perhaps philosophical) and the other part is almost purely sociological and political. (Berlinski writes: “If knowledge is power, then physicists have [] been given an enormous privilege.”)

Some commentators have stressed the fact that Berlinski has only a limited scientific background. The Wikipedia-like website RationalWiki goes further and basically claims that David Berlinski has no scientific credentials whatsoever. (It writes: “Although often referred to as a ‘mathematician’, Berlinski has done no research in mathematics.”) Yet the Discovery Institute (which Berlinski writes for) provides a biography of Berlinski which reads as follows:

“David Berlinski received his Ph.D. in philosophy from Princeton University and was later a postdoctoral fellow in mathematics and molecular biology at Columbia University. He is currently a Senior Fellow at Discovery Institute’s Center for Science and Culture. Dr. Berlinski has authored works on systems analysis, differential topology, theoretical biology, analytic philosophy, and the philosophy of mathematics, as well as three novels. He has also taught philosophy, mathematics and English at such universities as Stanford, Rutgers, the City University of New York and the Universite de Paris. In addition, he has held research fellowships at the International Institute for Applied Systems Analysis (IIASA) in Austria and the Institut des Hautes Etudes Scientifiques (IHES) in France.”

Do these credentials impress RationalWiki? Obviously not. That seems to be mainly because Berlinski hasn’t written any academic papers on physics or science generally. (RationalWiki also states: “It is worth noting that his books on mathematics are popular books.”)

As for theoretical physics and cosmology specifically (i.e., not the Darwinism Berlinski has a serious problem with).

The American biologist Jerry Coyne (who — to be a contrarian myself — has a Darwinian horse in this race) sums Berlinski’s general position up in the following manner:

“Science has no answers to ‘The Big Questions’ like ‘why is there something instead of nothing?’ (the answer that ‘it was an accident’ is fobbed off by Berlinski as ‘failing to meet people’s intellectual needs’, which of course is not an answer but a statement about confirmation bias); ‘where did the Universe come from?’; ‘how did life originate?’; ‘what are we doing here?’, ‘what is our purpose?’, and so on. Apparently Berlinski doesn’t like ‘we don’t know’ as an answer, but as a nonbeliever I’d like to know his answer! He has none; all he does is carp about science’s ignorance.”

Jerry Coyne’s words have just been quoted specifically because they more or less square with some of the positions which will be advanced in the following essay.

As stated, Berlinski seems to be primarily motivated by the (for want of a better term) sociology of science, politics and the defense of religion. This means that it’s hard — at least at first — to see why that would motivate him to be so strident when it comes to so much contemporary theoretical physics and cosmology.

Is this because Berlinski connects literally all contemporary theoretical physics and cosmology to atheism (which he certainly has a big problem with)?

So it’s deeply ironic that many other defenders of religion — or the belief in God — only ever mention physics or quote scientists when such mentions and quotes can be squared with (or connected to) their prior religious or “spiritual” views. Thus such people have written entire books or articles in which they cite scientific data which they believe doesn’t conflict with religious views at all — quite the opposite. Yet, even in these cases, science is hardly mentioned at all outside of their own personal religious or theistic contexts.

All that said, much has also be written about Berlinski’s contrarianism (i.e., not his scepticism) being an end in itself.

[See the critical article ‘Ode to the Contrarian’, which mentions Berlinski. This piece, however, lumps all supposed contrarians together and fails to distinguish those people who are — well — contrarian about a single scientific subject/issue from across-the-board contrarians like Berlinski himself.]

In the following essay, most of the quotes from Berlinski come from his ‘Was There a Big Bang?’. The subheading to that essay reads as follows:

“The universe, cosmologists affirm, came into existence in an explosion; but the evidence for this thesis is more suspect [].”

The essay ends with this paragraph:

“Like Darwin’s theory of evolution, Big Bang cosmology has undergone that curious social process in which a scientific theory is promoted to a secular myth. The two theories serve as points of certainty in an intellectual culture that is otherwise disposed to give the benefit of the doubt to doubt itself. [] Myths are quite typically false, and science is concerned with truth. Human beings, it would seem, may make scientific theories or they may make myths, but with respect to the same aspects of experience, they cannot quite do both.”

Now for a final introductory comment.

I can’t claim to be an expert on David Berlinski and I certainly haven’t read everything — or even much — that he’s written. So I’ve simply tackled his words and arguments as they’re expressed in his aforementioned essay on the Big Bang (as well as a spattering of his words from elsewhere). ‘Was There a Big Bang?’ is long. It’s almost 9,000 words in length — i.e., twice as long as my own response here. (That makes it slightly longer than the average academic paper.) What’s more, virtually every sentence within Berlinski’s essay is expressed in an extremely literary (or poetic) manner. (Berlinski calls his own writing style “rhapsodic and florid”.) And that may explain why some of it — to be honest, though not sarcastic — went over my head.

It also needs to be said here that when it comes to a lot of the scientific issues and theories discussed in this essay, I’m not completely on top of all the technical details. Put simply: I’m not a mathematical physicist…

Then again, I’m pretty sure that the very same thing can be said about David Berlinski himself.

Berlinski on Metaphysical Speculation

In his essay ‘Was There a Big Bang?’, Berlinski is often vague, rhetorical and very literary about the issue of speculation in theoretical physics and cosmology. However, he does actually cite various concrete examples. He also offers some technical detail.

For example, Berlinski writes:

“Unhappy examples are everywhere; absurd schemes to model time on the basis of the complex numbers, as in Stephen Hawking’s A Brief History of Time, bizarre and ugly contraptions for cosmic inflation; universes multiplying beyond the reach of observation; white holes, black holes, worm holes, and naked singularities; theories of every strip and variety, all of them uncorrected by any criticism beyond the trivial.”

Berlinski seems to take the extreme and (to use his word) absurd position that all speculation — and indeed all hypothesising — in theoretical physics (perhaps all physics) and cosmology is beyond the pail. Yet if such a position on speculation were ever (as it were) made law, then that would have destroyed all physics from day one.

Berlinski also seems to be ignorant of the history of science (or simply one aspect thereof) when he uses phrases such as “there is [] no evidence whatsoever in favour of” various contemporary theories in theoretical physics and cosmology. He should — and probably does — know that all sorts of theories which began life as hypotheses — or even straight speculations — were later backed up by observations, tests, experiments, data, etc. All this was true of Maxwell’s kinetic theory, Paul Dirac’s postulation of an “anti-electron”, Murray Gell-Mann’s “quark model”, etc. There are, of course, many other examples. Indeed it can be assumed that physicists themselves could provide a list that’s as long as their collective arm…

Unless, that is, Berlinski rejects all these theories and entities too.

As it is, it’s hard to know what precise technical problems Berlinski has with using “complex numbers”, the “bizarre and ugly contraptions for cosmic inflation”, “worm holes”, “naked singularities”, etc. So perhaps this has nothing to do with Berlinski’s own technical problems with such arcana. Perhaps Berlinski has purely aesthetic, religious, political and/or philosophical problems with these theories and speculations.

Alternatively, perhaps Berlinski’s contrarianism-as-an-end-in-itself is at the heart of the matter.

So the question is whether Berlinski has a problem with what may be called pure speculation. Or to ask a simpler question:

Is Berlinski ruling out all future observational and experimental backup for all speculations in theoretical physics and cosmology a priori?

Take the American theoretical physicist and cosmologist Alan Guth (1947-), whose inflationary theory is targeted by Berlinski (see later section).

The American theoretical physicist Lee Smolin (who’s also targeted by Berlinski) argues that “the theory of inflation predicts that omega should be equal to one.” He continues:

“Therefore the inflationary theory is subject to experimental tests, observational tests. These tests are going to occur in the next ten of fifteen years.”

And, lo and behold, that’s what happened!…

Well, not quite.

It’s true that the basics of inflationary theory (if there are such things) are accepted by most physicists. That’s primarily because many of Guth’s predictions have been confirmed by observation. More specifically, Guth’s theory accounts for the homogeneity of the observable universe. It also accounts for the observed flatness. Indeed, since Guth’s early work, much of his theory has received further confirmation. This is especially the case when it comes to the detailed observations of the cosmic microwave background made by the Planck spacecraft.

However, an important minority of scientists have serious problems with Guth’s inflationary theory. And that, in a strong sense, is both a good and a bad thing (as Popperians would argue) for theoretical physics and cosmology . To Berlinski, on the other hand, all such disagreements (or anomalies) are portrayed as being deeply profound and disturbing. And that’s precisely why he uses such disagreements as weapons against contemporary science.

Berlinski goes on to write:

“What are discovering is that many areas of the universe are apparently protected from our scrutiny, like sensitive files sealed from view by powerful encryption codes.”

Now that passage could be about the multiverse theory, the extra dimensions and branes of string theory and God knows what else. Yet it must be said here that such critical and sceptical words have also been uttered by some well-known and high-ranking physicists themselves (even if their prose styles are not at all like Berlinski’s own).

For example, much has been written by (ironically) Lee Smolin about the purely mathematical and speculative nature of string theory. (The main claim is that string theory suffers from an “absence of falsifiable predictions”; and what predictions it does offer aren’t “unique”.) Smolin even wrote the following words (i.e., in his book The Trouble With Physics: The Rise of String Theory, the Fall of a Science, and What Comes Next) about string theory:

“The feeling was that there could be only one consistent theory that unified all of physics, and since string theory appeared to do that, it had to be right. No more reliance on experiment to check our theories. That was the stuff of Galileo. Mathematics [alone] now sufficed to explore the laws of nature. We had entered the period of postmodern physics.”

Another example is theoretical physicist Brian Greene’s (non-literary and non-rhetorical) take on the idea of a multiverse. He states:

“The danger, if the multiverse idea takes root, is that researchers may too quickly give up the search for such underlying explanations. When faced with seemingly inexplicable observations, researchers may invoke the framework of the multiverse prematurely — proclaiming some phenomenon or other to merely reflect conditions in our own bubble universe and thereby failing to discover the deeper understanding that awaits us.”

And, finally, the British astrophysicist and cosmologist Martin Rees says more or less the same thing Brian Greene in the following:

“If people believed that some features of the universe were not fundamental but just accidents, resulting from the particular way our domain in the meta-universe cooled down, then they’d be less motivated to try to explain them.”

If we return to pure speculations.

Are such speculations (i.e., from theoretical physicists and cosmologists) automatically “metaphysics” simply because there’s no observational and/or experimental evidence for them? Indeed would the metaphysical status of such speculations automatically be a bad thing if, at least in principle, future findings, tests, observations, experiments, etc. would turn them (as it were) non-metaphysical?

So what does Berlinski himself believe?

He believes the following:

“This scrupulousness has been compromised. The result has been the calculated or careless erasure of the line separating disciplined physical inquiry from speculative metaphysics. Contemporary cosmologists feel free to say anything that pops into their heads.”

Some readers may think that a person like Berlinski (i.e., as a strong critic of contemporary science and the social/political — his word — “power” of physicists) would have some time for metaphysics — if not also for “speculative metaphysics”. (It has been said that all metaphysics is speculative.) Who knows. Perhaps Berlinski does have time for metaphysics; just not when it’s carried out by those scientists he has no time for.

In any case, Berlinski singles out Lee Smolin’s cosmological natural selection in which (to use Berlinski’s own words) “the Big Bang happened within a black hole”.

Berlinski on Smolin’s Cosmological Natural Selection

Berlinski writes:

“There is, needless to say, no evidence whatsoever in favour of this preposterous theory. The universes that a bubbling up are unobservable. So, too, are the universes that have bubbled up and those that will bubble up in the future. Smolin’s theories cannot be confirmed by experience. Or by anything else. What law of nature could reveal that the laws of nature are contingent?”

Of course quarks and all the other particles are (to use Berlinski’s own word) “unobservable” too. Strictly speaking, the four forces of physics are unobservable — even if their effects aren’t. So too is the past, the future, other minds, the earth’s core, numbers, etc.

[The line between what’s observable and what’s not is vague and the issue is complicated. See ‘The Image of Observables’ by Valerie Gray Hardcastle.]

Physicists postulated atoms, particles and other fundamentals of physics primarily via theory and mathematics and only then did experiments and (indirect) observations save the day. Indeed pure speculation has often been what got the scientific ball rolling.

However, it’s not being argued here that Smolin’s theory of cosmological natural selection is in exactly the same ballpark — and in every respect — as, say, Murry Gell-Mann’s quark model (i.e., as it was before any experimental confirmation) and other well-known cases.

What’s more, even if a claim or theory is indeed speculative, then does that automatically mean that it must have simply (as Berlinski puts it) popped into the head of the speculator — especially if that speculator is a theoretical physicist or cosmologist?

Ironically, it’s possible that Berlinski has (as it were) borrowed some — or even all — of his (sceptical/contrarian) criticisms of theoretical physics and cosmologists from physicists — as the quotes above show. So perhaps his alternatives (although he rarely — if ever — states them) might be borrowed from physicists too.

Take the English cosmologist, theoretical physicist and mathematician John D. Barrow (who died in 2020).

Barrow himself seemed to be referring to Smolin’s theory — and, perhaps less directly, to the idea of a multiverse — when he wrote the following words:

“There has grown up, even amongst many educated persons a view that everything in Nature, every fabrication of its laws, is determined by the local environment in which it was nurtured — that natural selection and the Darwinian revolution have advanced to the boundaries of every scientific discipline.”

Berlinski on the Big Bang Theory

Despite the lack of details for some wild statements — and the lack of any alternatives — in his essay ‘Was There a Big Bang?’, Berlinski does offer a fair amount of technical detail when he discusses the case against the Big Bang. His main (or indeed only) technical point is that the redshift isn’t conclusive evidence — or evidence at all — for the Big Bang. He cites the work of the American astronomer Halton Arp (1927–2013) to back up his own position. Alternatively put: perhaps Berlinski’s case against the Big Bang theory is entirely due to Arp’s work.

[Arp was a critic of the Big Bang theory who advanced what’s called a non-standard cosmology — see here.]

In any case, Berlinski main weapon against contemporary theoretical physics and cosmology is to stress disagreements among theoretical physicists and cosmologists and then draw hugely negative conclusions from them (as well as failing to realise — or simply note — that most physicists embrace anomalies).

Berlinski also questions the Big Bang metaphor of the switching on of a light and the subsequent creation of time itself. Yet he also rejects the existence of the multiverse, which could provide an answer to his questions. Indeed so too could Lee Smolin’s cosmological natural selection, which he calls “preposterous”.

Yet, as already stated, there is some substance (underneath the literary rhetoric) within Berlinski’s words. Take the following passage:

“[T]he image of the fundamental laws of physics zestfully wrestling with the void to bring the universe into being is one that suggests very little improvement over the account given by the ancient Norse in which the world is revealed to be balanced on the back of a gigantic ox.”

The fact is that some theoretical physicists and commentators have also stated as much — even if Berlinski’s comparison with Norse mythology is cheap and rhetorical. That is, some theoretical physicists themselves have seen the problems here. (Again, Berlinski might have actually borrowed these arguments from such physicists.)

Here’s another passage from Berlinski:

“The image of a light switch comes from Paul Davies, who uses it to express a miracle without quite recognizing that it embodies a contradiction. A universe that has suddenly switched itself on has accomplished something within time; and yet the Big Bang is supposed to have brought space and time into existence.”

Berlinski must know that there are many answers (if not necessarily correct or acceptable answers) to this issue in theoretical physics and cosmology. The problem is that he doesn’t like any of these answers either.

So now take these words from Lee Smolin (again):

“But if time does not end, then there is something there, happening. The question is, What? This is very like the question about what happened ‘before the Big Bang’ in the event that quantum effects allow time to extend indefinitely into the past.”

The problem here is that this passage also includes references to Berlinski’s unobservables. (Is Berlinski a 19th-century positivist or Machian?) So Berlinski wouldn’t like Smolin’s alternative either. This effectively means that Berlinski doesn’t like the idea of time suddenly being switched on… And he doesn’t like any of the alternatives either.

So perhaps Berlinski should just “put up or shut up” instead! (To requote Jerry Coyne: Berlinski “has none” of the answers. “All he does is carp about science’s ignorance.”)

All that said, some physicists can be adopted (or co-opted) to express Berlinski’s problems and worries.

Take the the physicist John Archibald Wheeler and Berlinski’s (now repeated) words

“the image of the fundamental laws of physics zestfully wrestling with the void to bring the universe into being”.

Wheeler had (kinda) already expressed Berlinski’s own position when he provided a good riposte to (for want of a better term) Pythagoreanism in physics.

The fairly-well-known story is that Wheeler used to write many obscure and technical equations on the blackboard and then stand back and say to his students:

“Now I’ll clap my hands and a universe will spring into existence.”

[According to Pythagoreans, however, the equations are the universe.]

Then Stephen Hawking (a physicist Berlinski also criticises) outdid Wheeler with an his even-better-known passage. He wrote:

“Even if there is only one possible unified theory, it is just a set of rules and equations. What is it that breathes fire into the equations and makes a universe for them to describe?”

Yet the science writer Kitty Ferguson offers a (possible) Pythagorean answer (as already hinted at) to Hawking’s question when she says that “it might be that the equations are the fire”. Alternatively, could Hawking himself have been “suggesting that the laws have a life or creative force of their own?”.

Again, is it that the “equations are the fire”?

This hint at Pythagoreanism is expressed by both the friends and the foes of contemporary theoretical physics and cosmology.

For example, this is how a non-scientist friend of science puts it:

“While some cosmologists are speculating that the laws of physics might explain the origin of the universe, the origin of the laws themselves is a problem so unfathomable that it is rarely discussed [] Is there a way in which the universe may have organized itself?”

So Berlinski could now legitimately ask theoretical physicists and cosmologists this question:

What, exactly, “breathes fire into the equation to make a world”?

Alternatively, we could ask Berlinski himself that very same question! (Berlinski, please put up or shut up!)

Berlinski on Alan Guth’s Inflationary Theory

As partially stated in the introduction, I don’t know all the technical details on this specific issue…

But does David Berlinski?

It may be tempting to assume that Berlinski is missing something when it comes to the Big Bang and the parallel something-from-nothing scenario (which is not from Norse mythology). Alternatively, perhaps Berlinski has simply misinterpreted (or simplified) this scenario in the haze of his flamboyant prose.

All that said, surely Berlinski’s statements are broadly legitimate. Or to put that in a weaker way: Surely non-experts (as well as experts themselves) are right to ask the questions which Berlinski asks.

So it may help readers when Berlinski actually offers some technical details here. Berlinski writes:

“Having entered a dark logical defile, physicists often find it difficult to withdraw. Thus, Alan Guth writes in pleased astonishment that the universe really did arise from ‘essentially… nothing at all’: as it happens, a false vacuum patch ‘10⁻²⁶ centimetres in diameter’ and ‘10⁻³² solar masses’.”

He concludes:

“It would appear, then, that ‘essentially nothing’ has both spatial extension and mass. While these facts may strike Guth as inconspicuous, others may suspect that nothingness, like death, is not a matter that admits of degree.”

It does — again — seem that Berlinski has a point…

But that’s only if he’s characterised Alan Guth’s position correctly. (It could of course be the case that Berlinski’s quotes from Guth are artfully out of context.)

Yet, on the surface at least, it does seem that Berlinski has (more or less) expressed Guth’s position correctly.

So here’s Guth himself on the “false vacuum”:

“[A] ‘false vacuum,’ which is the driving force behind inflation. We discovered that a large enough region of false vacuum would create a new universe, which, as I described earlier, would rapidly disconnect from ours and become totally isolated.”

More relevantly:

“Since the mass density of the false vacuum is approximately 10⁶⁰ times larger than the density of an atomic nucleus, it would certainly not be easy.”

Guth then admits to a degree of speculation when he concludes:

“Nonetheless, one can speak about the physics of universe creation as a matter of principle, and I find it a very interesting question.”

It’s worth noting here that Guth’s position is now almost standard among many theoretical physicists and cosmologists. For example, take the words of Marcelo Gleiser (1959-), a Brazilian physicist who states the following words:

“We plow ahead, proposing tentative models that join general relativity and quantum mechanics where the universe pops out of nothing, no energy required: All is due to a random quantum fluctuation.”

It may be wondered if Berlinski is conflating a vacuum (or a false vacuum) with nothingness. After all, in the last quote above Guth doesn’t even use the word “nothing”. (Gleiser does!) In any case, it’s crystal clear that the two notions of a vacuum and a false vacuum (in physics) aren’t even meant to be cases of literal nothingness — at least not the nothingness which has often been discussed by philosophers, theologians and others.

Yet, despite that last sentence, let’s still ask this obvious question:

How can nothing have “both spatial extension and mass”?

It may be relevant here that, even according to Berlinski’s own first quote, Guth does prefix his word “nothing” with the word “essentially”. It can now be argued that the words “essentially nothing” actually mean not quite nothing. So perhaps this is an odd and uncareful use of the word “essentially”. And no doubt Guth, as a physicist, would have a problem with such pedantry here…

[The word “pedantry” is used because physicists often do have a problem with philosophers and other people nit-picking the words they use. See my ‘Why Richard Feynman (the Superstar Physicist) Hated Philosophy and Philosophers’.]

But that’s too easy.

It’s too easy because it’s surely acceptable to ask what Guth means by “essentially nothing”. After all, if there is a difference — even a big difference — between nothing and essentially nothing, then that will have a profound impact on the nature of the Big Bang. In other words, the (possible) pedantry above is simply a means of clarifying the actual physics. Many physicists, of course, will argue that only better mathematics and clearer physics can do any of the clarifying which needs to be done…

Finally, perhaps David Berlinski believes that Alan Guth (qua physicist) is playing God. That is, in the best-selling book The Inflationary Universe (published one year before Berlinski’s own ‘Was There a Big Bang?’), Guth speculated as to whether or not it would be possible to create a new universe in his own basement laboratory!

Professor Donald Hoffman’s Idealist Take on Brains and Volleyballs

Donald Hoffman states that when it comes to a brain or a volleyball, “if you don’t look, it’s not there”. He also believes that “a volleyball no more has a position or momentum when it’s not observed than does an electron”. All this is basically a 21st-century update of Bishop Berkeley’s 18th-century idealism (as Hoffman more or less admits in various places).

“[P]articles are vibrations not of strings but of interacting conscious agents.”

— Professor Donald Hoffman

It’s worth putting Professor Donald Hoffman’s position on volleyballs and brains in its larger context.

Firstly, Hoffman isn’t modest about his “interface theory of perception” (more broadly and philosophically, his idealism). For example, he states that

“[i]t consumes decrepit ontology, preserves methodological naturalism, and inspires exploration for a new ontology”.

Hoffman also compares what he’s doing to what Alan Turing did (see here). What’s more, Hoffman believes that his idealism (or what he calls conscious realism) is a

“vehicle sufficiently robust to sustain the next leg of our search for a theory of everything”.

Now it may not be altogether clear to all readers (from that short quote alone) whether or not Hoffman actually believes that his own idealist philosophy will be that “theory of everything”. Alternatively, is Hoffman simply (or only) claiming that his idealism could be (or actually is) a “vehicle” of such a grand enterprise?

That said, it can easily be shown that the former option is far more likely.

That’s the case because in Hoffman’s philosophy, consciousness must ground any theory of everything. (That will include any theory which will be offered in the future by high-ranking theoretical physicists and/or cosmologists.) After all, Hoffman has explicitly argued that his idealism will “boot up space, time and matter” as well as literally everything else.

The clincher, however, can be found in Hoffman’s following words:

“Spacetime is doomed. It, and its particles, cannot be fundamental in physical theory, but must emerge from a more fundamental theory.”

Hoffman believes that this “more fundamental theory” is, of course, his very own conscious realism — aka, his “scientific” idealism.

Hoffman on Brains

Donald Hoffman is an idealist (or conscious realist) who’s stated that “brains and neurons do not exist unperceived”. That isn’t a claim that our perceptions don’t (as Hoffman puts it elsewhere) “resemble” whatever it is that gives rise to them. It’s a straight claim that brains and neurons don’t exist when unperceived.

Hoffman was at his most Berkeleyan when he wrote this simple line about a brain:

“If you don’t look, it’s not there.”

Yet if you don’t look at what is defined as (to use Hoffman’s word) “phenomenal”, then of course it’s not there when no one is looking at it. That’s true by definition.

Here’s a definition of the word “phenomenon” (i.e., if only as used in philosophy and science):

“A phenomenon is an observable event. [] In modern philosophical use, the term phenomena has come to mean things as they are experienced through the senses and processed by the mind as distinct from things in and of themselves (noumena) [].”

In addition:

“In scientific usage, a phenomenon is any event that is observable, including the use of instrumentation to observe, record, or compile data.”

Hoffman doesn’t have much time for physicalism (or materialism), yet a physicalist and even a naïve realist can accept most — or even all — of the definitions above. (They may even accept Hoffman’s use of the word “phenomenal”.) That is, they will accept that a phenomenal brain is only there when someone is looking.

[Naive realism has just been mentioned. Hoffman seems to believe that all positions on “reality” which aren’t his own — or which aren’t idealist — are examples of naïve realism.]

However, such people will not also accept that that the physical brain is only there when someone is looking.

Of course Hoffman collapses this distinction — but at least it should be made clear.

Hoffman on Volleyballs

Hoffman makes his Berkeleyan position even clearer in the following passage:

“The phenomenal volleyball isn’t there when you don’t look, so it isn’t off-white or any other color. Nor is it round or soft or leathery.”

Then he immediately adds the following contemporary scientific gloss on his idealist position:

“The relational volleyball is circuits and software, and it isn’t literally off-white either. There may be portions of the software whose intent is to spray photons on your eyes such that you will construct an off-white phenomenal volleyball. But this software isn’t any color at all. And the color of the circuits is irrelevant to the color of the phenomenal volleyball[].”

Again, if even a physicalist can accept Hoffman’s term “phenomenal volleyball”, then what he wrote will be true by definition.

The reader will have noted Hoffman’s use of the words “circuits” and “software” in the passage above.

Hoffman often — very often — uses technical terms taken from the world of computers or from computer science. (One can even say that Hoffman is hooked on such technical terms.) So perhaps it’s the case that these technical terms from computer science tie Hoffman up in various philosophical knots.

Firstly, does Hoffman use such terms as “circuits”, “software”, “icons” and “interface” analogically or metaphorically?…

No; he doesn’t.

After all, when Hoffman writes “[t]he relational volleyball is [my italic] circuits and software”, that statement isn’t meant to be an analogy or a metaphor. Hoffman is arguing that the relational volleyball literally is circuits and software. (Note that Hoffman isn’t referring to a computer-generated image of a volleyball on a computer screen. He’s referring to a real volleyball which one can literally kick.)

So let’s take a specific example of Hoffman’s fixation on terms from computer science.

Hoffman often refers to the “icon interface on your computer” as a means to get his idealist point across about the icons in human consciousnesses.

Yet the icon interfaces of computers have all been designed by human persons to “guide” human users. No one has ever claimed — or even believed — that an icon of a trashcan is identical to — or even resembles — the “unseen circuits and software” found inside a computer.

So Hoffman’s position basically amounts to arguing that only x is x. (Or: Only x can be x.)

More accurately, the upshot of Hoffman’s argument is that only experience x can be like (or “resemble”) experience x. (This argument is taken directly from Bishop Berkley.) That is, only that which is phenomenal can also be phenomenal.

But who’s ever argued otherwise?

Another way of putting this is to say that a “phenomenon” is by definition something that only belong to minds or to conscious experiences. That’s essentially how that word was defined by Immanuel Kant some 240 years ago. More clearly, in Kant’s scheme we have phenomena and we also have a noumena. So obviously phenomena aren’t noumena.

But no one has ever claimed otherwise.

[Of course that’s if readers — and others — accept these Kantian terms and philosophical distinctions at all.]

This means that if a volleyball is entirely defined as a phenomenal volleyball, then by definition it can’t exist as a volleyball if no one is looking at it. Unless, here again, Hoffman simply means phenomenal volleyball by the single word “volleyball”. If Hoffman does mean that, then his claim is true by definition.

Hoffman then compares a “phenomenal volleyball” to an electron.

Hoffman Compares a Volleyball To An Electron

To give a flavour of where Hoffman is going with all this, it’s worth noting that Hoffman’s position on a volleyball must be — at least partly — a result of a position he expressed in the following (to be rhetorical for a moment) almost meaningless, jargon-infested passage:

“We show that one particular object, the quantum free particle, has a wave function that is identical in form to the harmonic functions that characterize the asymptotic dynamics of conscious agents; particles are vibrations not of strings but of interacting conscious agents.”

It’s also important to note here that Hoffman began using mathematics — or mathematical technical terms — on a large scale and as an seemingly essential part of his philosophy when he started working with the mathematician Chetan Prakash. And, from then on, Hoffman began using copious mathematical terms (i.e., in his idealist philosophy) as if they were round shapes being pushed into square holes.

In direct relevance to an electron, Hoffman writes:

“A volleyball no more has a position or momentum when it’s not observed than does an electron. Only in the act of observation do you construct a phenomenal volleyball with a position, motion, color, and shape. Similarly, only in the act of observation is an electron constructed with a position, or momentum, or other dynamical properties. All phenomena are constructed by observation, whether quantum phenomena or volleyball phenomena.”

There’s a severe problem with comparing a volleyball to an electron.

Even if we accept that a phenomenal volleyball is, well, a phenomenal volleyball, then Hoffman’s comparison to an electron is not at all accurate.

It’s true that a phenomenal volleyball needs to be perceived. However, arguably it still exists as a physical object when not perceived. Yet when it comes to an electron, the situation is very different indeed.

According to the Copenhagen interpretation (as well as most other interpretations) of quantum mechanics, nothing (much?) can be said about an electron when it’s not being indirectly observed or when it’s not part of an experimental setup. Indeed the experimental setup largely determines what the electron is taken to be (or what is said about it). This essentially mean that if an electron isn’t part of any experimental setup, then it isn’t really anything at all. (What is this electron that exists apart from an experimental setup and all indirect observations? Tell me something about it.)

On the other hand, much can be said about any given volleyball even when it isn’t being observed.

For a start, one can still know (or have a good guess) where it still is. One can also know that it must have the same shape, size and weight as it did when observed.

Of course all these properties can also be deemed to be phenomenal — at least on Hoffman’s Berkeleyan reading.

[Hoffman mentions and quotes Berkley’s idealist position favourably — see here and here. For example, he writes: “Resemblance between the phenomenal and relational realms: I argue that there need be no resemblance. But Berkeley has an ingenious argument that goes much further, and is probably valid.”]

But isn’t there still some x which is in a place and which has a given weight, shape and size?

In terms of the “off-white” colour mentioned by Hoffman, however, the volleyball may not have that colour when not observed. (Some will say that it does. Others will say that it doesn’t. Yet virtually no one offers idealist reasons for either position.) But should we go as far as Bishop Berkeley (1685–1753) and say the same things about location, weight, shape and size (see here)?

Hoffman does.

Now in order to make more sense of Hoffman’s position on brains and volleyballs, it will help to tackle his notion of an “arbitrary representation”.

Hoffman on Arbitrary Representations

One central point which Hoffman advances is that even though he accepts that we have (what he calls) “representations” of this volleyball, those representations need not — and indeed do not — resemble anything in the “objective world”. Or, more accurately, they don’t resemble whatever it is that (as it were) underpins this volleyball in what Hoffman calls “the relational realm”.

Hoffman himself writes:

“If ‘well adapted’ doesn’t mean ‘resembles,’ then what does it mean? It means a systematic but arbitrary relation. Our perceptual experiences are well adapted to the relational realm because they provide a systematic but arbitrary guide to those aspects of the relational realm that are critical to our needs and our survival — just as the icon interface on your computer is well adapted because it provides a systematic but arbitrary guide to the computer’s unseen circuits and software.”

Sense now has to be made of Hoffman’s word “arbitrary”.

[“Arbitrary” = df. “existing or coming about seemingly at random or by chance or as a capricious and unreasonable act of will”. Or: “arbitrary” = df. “not fixed by rules, but left to one’s judgment or choice; discretionary”.]

Even if the word “arbitrary” simply means could have been otherwise (or something similar), then it still seems to be too strong. That is, if the relational realm might have been represented (or whichever the correct word is) differently, then does that still automatically mean that all representations are arbitrary?

If Hoffman simply means (as discussed above) that that what is phenomenal can’t also be relational (by definition and an idea Hoffman takes from both Bishop Berkeley and Immanuel Kant), then, in that strict sense, x can’t be y. But simply because x can’t actually be y, then why does it follow that this relation (whatever it is) between x and y should also be arbitrary?

Take this loose comparison.

When I put a sandwich in the freezer, it freezes. The sandwich and the freezing process aren’t the same thing . However, the relation between the sandwich and the freezing process (in the freezer) certainly isn’t arbitrary.

Similarly, a phenomenal representation of something that isn’t itself a phenomenal representation needn’t be arbitrary simply because the representation and the represented aren’t one and the same thing.

In addition, there may be many reasons as to why the represented x is represented (in the way it is actually represented) by y. Those good reasons would still hold even though representation y isn’t the same thing as the represented x.

In terms of Hoffman’s example of a volleyball. There may be other reasons (other than what is conducive to survival) as to why members of the species homo sapiens represent this volleyball the way they do.

So Hoffman really gives the game away when he uses the word “resembles”. He writes:

“If ‘well adapted’ doesn’t mean ‘resembles,’ then what does it mean? It means a systematic but arbitrary relation.”

The words “systematic but arbitrary relation” can’t possibly mean well adapted. If a systematic but arbitrary relation is anything, then it’s a single characterisation of something that’s merely connected to being well adapted — it isn’t its meaning.

So we still need to why this supposedly arbitrary relation also leads to being well adapted (more of which later).

In addition, of course the word “resembles” doesn’t mean identical to. That is, if y resembles x, then that doesn’t also mean that y is identical to x.

However, Hoffman may be right to argue that the idea of resemblance doesn’t work at all in his case of some given x in the relational realm and its representation in the phenomenal realm. Indeed Kant and Kantians — long before Hoffman — have deemed the notion of any resemblance between anything noumenal and anything phenomenal to be confused.

Hoffman also makes much of successful adaptation not (always?) coming alongside what he calls “truthful perceptions”.

Perceptual Adaptation and Truth?

Hoffman writes:

“Our perceptual experiences are well adapted to the relational realm because they provide a systematic but arbitrary guide to those aspects of the relational realm that are critical to our needs and our survival.”

This question now needs to asked:

How are our perceptual experiences “well adapted” to the world at all?

How does that adaptation work without what Hoffman calls resemblance? It’s certainly the case that resemblance may not be required. However, we need to know how our perceptual experiences are well-adapted in ways which don’t involve “reality”, “truth”, “resemblance”, accuracy, etc. In other words, what is the precise relation between our perceptual experiences and Hoffman’s relational realm?

Hoffman only seems to answer that question negatively.

The argument is that the relation between our perceptual experiences and “reality” needn’t be — or actually isn’t — one of resemblance, truth, correspondence, accuracy, etc. Instead, Hoffman focusses on filtering out superfluous data in order to survive. Yet this hints at the idea that the perceptions or representations which are left (i.e., after the filterings) may still be of a non-idealist reality. Indeed doesn’t the very idea of filtering assume a non-idealist reality?

But, again, what is the precise relation?

Even if perceptual experience x doesn’t resemble y, then why does it have the character that it does have? Indeed what evolutionary role does perception x not resembling y have? (Again, Hoffman explains all this is terms of the evolutionary disadvantage of, basically, sensory overload.) And why does perception x have the character it does have in the first place?

Another way of putting all this is to argue that if our perceptual experiences are only (as Hoffman puts it) “critical to our needs and our survival”, then how and why are they so? That is, how is such survival brought about without any resemblance, correspondence, truth. accuracy or whatever?

So Hoffman tells us that all species don’t need truth when it comes to perception. But we are left in the dark as to what species do need. We can’t simply be happy with phrases like

“[p]erception guides adaptive behavior; it does not estimate a preexisting physical truth”

without also being informed as to why we have given perceptions and what their precise relation is to… what? Reality? The physical world. Hoffman’s (non-physical) relational realm?

Hoffman then writes:

“More information requires, in general, more time to obtain and process. But in the real world where predators are on the prowl and prey must be wary, the race is often to the swift. [] So natural selection tends to favor perceptual systems that, ceteris paribus, take less time. One way to take less time is, again, to see less truth, especially truth that is not informative about fitness.”

Interestingly, there’s an (implicit) acknowledgement of the (for want of better words) external world (i.e., something outside consciousness) in that passage. Indeed Hoffman’s phrase “less truth” implies some truth. That is, the truth that is left may well be conducive to survival — even if the complete truth isn’t. And surely that works against Hoffman’s idealism (or his conscious realism).

[See my ‘A Contradiction in Donald Hoffman’s (Idealist) Fitness-Beats-Truth Theorem’. This essay tackles Hoffman’ implicit acceptance of a non-idealist physical world.]

Hoffman seems to be aware of this counterargument when he quotes the psychologist James J. Gibson in the following manner (as expressed in Gibson’s ‘The Ecological Approach to Visual Perception’):

“[I]n Gibson’s ecological theory of perception, our perceptions primarily resonate to ‘affordances,’ those aspects of the objective world that have important consequences for fitness [].”

Yet Hoffman believes that there are no affordances — at least not if they’re based on any “resemblances” to, truths about, accuracies in relation to, etc. what Hoffman calls the “objective world”. Alternatively put: perceptions can “resonate to affordances” without any need for resemblance, truth, accuracy, etc. In the idealist picture, then, affordances need have no relation at all to anything outside consciousness.

Yet despite his book title, rhetorical statements about “reality”, etc., Hoffman actually does believe in the objective world. It’s just that Hoffman’s objective world isn’t what he believes most people take it to be. (Hoffman nearly always takes his opponents to be naïve realists.) To Hoffman, objective reality is, in fact, an idealist reality.

In fact Hoffman repeatedly uses the term “objective reality” (which few contemporary philosophers and scientists use — at least not in their technical work) without ever really telling us what he means by that term. Here’s another example:

“[T]he idea is that natural selection has not shaped our perceptions to be insights into the true structure and causal nature of objective reality, but has instead shaped our perceptions to be a species-specific user interface, fashioned to guide the behaviors that we need to survive and reproduce.”

This, again, is Hoffman acknowledging objective reality without telling us what he takes it to be. Perhaps that’s because if he did so, then his idealism would have to embrace something outside consciousness (or consciousnesses) and thus render it contradictory.

So how can an a idealist (or conscious realist) accept any objective reality at all? That is, how can any idealist accept an objective reality if that reality is meant to be something outside consciousness or consciousnesses?

Of course it may be that to Hoffman objective reality is his “relational reality” (which is very similar to Kant’s noumenal realm). But Hoffman hardly ever explicitly states that. And even if he did, then he would be using the term “objective reality” in a way that hardly any scientist, philosopher or layperson uses it. Hoffman may be very happy with that fact. And of course he’s free to use an old term in his own new way. Indeed since Objective Idealists and other idealists have used the term “objective reality” to refer to something that is an exclusive matter of consciousness, consciousnesses, Cosmic Consciousness, Geist or whatever, then that may actually be what Hoffman is doing.

Hoffman also tells us that the cognisance — or experience — of the (to use a philosophical phrase) Kantian manifold (or Hoffman’s “every bit of information”) has led to species-death. (How could this be known anyway?) Yet we aren’t told about the truth-remainder (which Hoffman implicitly accepts) and its relation to… what?

So here again it can be said that even though perceptual experiences can’t be identical to what they are experiences of, then that doesn’t also mean that they are arbitrary.

Hoffman goes into more detail when he writes that

“[e]xperiences need not resemble the relational realm to be well adapted, they need only be a useful guide for behaviour”.

Why are such experiences “useful”? And useful in which respects?

One obvious riposte to Hoffman’s statement above is to argue that experiences of volleyballs, brains or anything else are a “useful guide for behaviour” precisely because they do “resemble”… something outside consciousness.

[The existence of a relational realm needn’t be accepted here. Bear in mind that the term “relational realm” is Hoffman’s own.]

So all anyone needs to argue is that his/her perceptions (or experiences) of a volleyball, a brain or anything else must have strong connections to things (whatever they are) outside consciousness — or things outside a collective of what Hoffman calls conscious agents.

Of course Hoffman, as an idealist, must reject that claim.

****************************

Note: See also my ‘A Contradiction in Donald Hoffman’s (Idealist) Fitness-Beats-Truth Theorem’, ‘Donald Hoffman’s Philosophy of Consciousness and Reality: Conscious Realism’ and ‘Donald Hoffman’s Long Jump From Evolutionary Biology/Theory to Highly-Speculative Philosophy’.

A Platonist Take on the A Priori and the Analytic?

The philosopher Anthony Quinton expressed an “anti-conventionalist” (or Platonist) position on the analytic when he wrote: “There is a non-conventional identity of concepts which would still exist even if no means of expressing the concepts had ever been devised.”

Anthony Quinton (1925 — 2010) was a British philosopher. He was educated at Christ Church, Oxford University, where he obtained a first-class honours in Philosophy, Politics and Economics. He was President of Trinity College, Oxford from 1978 to 1987; and a chairman of the board of the British Library from 1985 to 1990. Quinton was also the president of the Aristotelian Society from 1975 to 1976.

Quinton once presented the BBC Radio programme, Round Britain Quiz.

Axioms

It’s often argued that axioms don’t need to be true. That is, axioms can — and do — have a purely formal or syntactic role. What follows from axioms, however, must do so according to strict logical rules. This basically means that different geometrical and mathematical systems can be — and are — constructed on axioms which needn’t be taken as being true. ( As a result of various findings in geometry, this largely came to be seen to be the case in the late 19th century.)

Of course all this depends on how the word “true” is taken.

Anthony Quinton (in his 1963 paper ‘The A Priori and the Analytic’) saw axioms very differently. He argued that

“axioms only confer truth on theorems if they are true themselves”.

So how is the truth of axioms established?

Generally speaking, axioms are seen as “assumptions”. Alternatively, it has been argued that axioms can be “taken to be true” — but only in order to (as it were) get the ball rolling. (Axioms have also been seen as being evident or even self-evident.)

It’s worth stressing here that the term “axiom” is defined differently when used in mathematics, logic, and, indeed, philosophy. In philosophy, an axiom has traditionally been seen to be a statement that’s evident or simply well-established. In modern logic, axioms aren’t treated this grandly. They’re simply seen as being the starting points for reasoning. In mathematics, axioms are often taken to be statements which are often taken to be true — but only within the logical systems they define or generate.

So the word “axiom”, in this case at least, needs to be seen within the context of Anthony Quinton’s discussion of the a priori and the analytic — both terms hardly used outside philosophy. Indeed the term “analytic” only became widely discussed in analytic philosophy in the1930s. (For example, with the logical positivists and others; though such philosophers did work on Gottlob Frege’s ideas — see here.)

According to Quinton, a “formally sufficient axiom will be materially adequate only if it is intuitive”. This means that an axiom’s truth is discovered (or seen) intuitively.

This reliance on intuition (see also here) here must also mean that there’s no other way to see (or discover) the truth of axioms precisely because they’re so basic. In other words, they can’t be shown to be true by other axioms, the world, evidence, data and certainly not by theorems.

Remember also that axioms are used as the starting-points of systems or chains of reasoning. This means that axioms can’t rely on anything else. And that must explain why Quinton believed that their truth is seen intuitively. His position has the consequence that there’s no alternative to that position.

Still, what is meant by truth here? How are axioms true at all?

Philosophers of mathematics have often asked if it’s even meaningful to state (or believe) that axioms are true. (See Penelope Maddy’s paper ‘Believing the Axioms’.)

For example, the French mathematician Henri Poincaré expressed what has been called a conventionalist view. Poincaré’s use of non-Euclidean geometries showed him that the axioms used in geometry should be chosen not for their truth, but for what they can produce. What’s more, axioms shouldn’t be chosen (at least not exclusively) for their (supposed) coherence with human intuitions about the world.

Does all this mean that axioms aren’t about — or derived from — the world at all? And, presumably, do this also means that axioms aren’t about — or derived from — other axioms or theorems either?

So, again, why are axioms deemed to be true? Why can’t they simply be taken syntactically or even as simple scribbles on a page?

Analytic Statements

Anthony Quinton tied the intuitive truth of axioms to the intuitive truth of analytic statements. He wrote:

“According to the analytic thesis, an a priori truth is intuitive if its acceptance as true is a condition of understanding the terms it contains.”

To state the obvious: analytic statements are very unlike (simple) axioms. Most of the oft-quoted analytic statements (such as “All bachelors are unmarried”) contain predicates about — and references to — worldly items. Axioms are usually nothing like that. (Quinton himself gave no examples in his paper.)

It can of course be argued that we (as it were) see the truth of the statement “All bachelors are unmarried” intuitively. However, that only means that we understand the concepts or words involved and see that they are synonyms. Surely that can’t be said of individual axioms.

Indeed it’s tempting to think that analytic truths — along with tautologies — are pretty pointless if they really are only about words (or symbols) and their synonymy. Moreover, if they’re all about conventionality, synonymity or analyticity (see W.V.O Quine’s own ‘Two Dogmas of Empiricism’), then the world (or reality) seems to completely drop out of the picture. (Of course analytic truths — as written down, spoken or even thought about — must still be part of the physical world.)

All that said, Quinton did make a distinction between analytic sentences and the (as he put it) “propositions they express”.

Propositions

Quinton argued that

“the conventionality principle fails to distinguish sentences from the propositions they express”.

This is a clear commitment to abstract propositions. Or, at least for now, a commitment to propositions.

In other words, Quinton must have believed that it’s the words (or sentences) used in analytic statements which abide by the rules of convention. However, the “propositions they express” have nothing at all to do with such rules.

So take the following sentence:

“All bachelors are unmarried men.”

Clearly, that’s a sentence because it occurs within quotation marks (among other things).

But we also have this:

All bachelors are unmarried men.

Is that a proposition?

It’s of course the case that the the (?) about bachelors directly above is again expressed by a sentence. However, when we take away the inverted commas, it (to put it ironically) suddenly becomes a proposition… Or does it? Isn’t proposition still expressed by a sentence even if the quotation marks have been taken away! And, without sentences (as well as minds), what purchase can we have on these supposedly abstract propositions?

Moreover, even if I write

The state of affairs of bachelors being unmarried men.

or more simply

Bachelors being unmarried.

they are still two sentences.

In any case, these linguistic expressions simply seem to be about facts or states of affairs (or the philosophers’ truth conditions). Yet propositions aren’t deemed to be worldly or concrete things. That is, propositions have often been seen (from Frege to Quinton) as being abstract entities which don’t belong to time and space and which have no causal relations with the world.

So how do human minds gain access to these abstract propositions?

Concepts

Quinton moved on from using propositions as an argument against mere conventionality (or mere analyticity) to arguing exactly the same thing about concepts.

(Wikipedia defines concepts as “abstract ideas”. Yet an abstract idea is an abstraction that needn’t itself be taken to be an abstract object.)

So now it’s concepts which are seen as being non-conventional and, therefore, abstract entities. (To be more accurate, Quinton was putting the position of what he called the “anti-conventionalist”.) Quinton wrote:

“[T]he anti-conventionalist maintains that there is a non-conventional identity of concepts, lying behind the conventional synonymy of terms, which would still exist even if no means of expressing the concepts had ever been devised.”

It’s not really a surprise that anti-conventionalists (or Platonists) should move from propositions to concepts because, on Frege’s picture, senses are the non-spatial and non-temporal parts of non-spatial and non-temporal propositions. In Frege’s own words:

“[T]houghts are neither things of the outer world nor ideas. A third realm must be recognized.”

To use Frege’s own terms, senses are (non-spatial) parts of what he called Thoughts. And both senses and Thoughts are “eternal” (see here). In that case, again, a sense (though not identical to a concept in Frege’s philosophy) is simply an abstract part of a larger abstract entity — a proposition.

[See Frege’s own ‘The Thought: A Logical Inquiry’, from 1918. Also bear in mind here that propositions and Thoughts aren’t deemed to be identical in Frege’s philosophy.]

Yet problems remain.

If we can’t make sense of abstract propositions, then perhaps we can’t make sense of abstract concepts (or even senses) either.

For one, it seems utterly bizarre that Quinton should have argued that the concepts (to use Quinton’s spatial metaphor) “behind” the terms “bachelor” and “unmarried man” are actually “timeless and objective”. Really? Perhaps it can provisionally be accepted that an abstract, timeless and objective number lies behind the symbol, say, “2”. However, can we really say the same about the concepts behind the words “bachelor” and “unmarried man”? Surely not.

For one, the words “bachelor” and “unmarried man” have only existed since the institution of marriage began. And therefore the concepts themselves (if expressed by different words in different languages) must have only begun to exist when the first words about (or even institutions of) marriage existed. So surely none of these things are timeless, atemporal or objective.

[It must be assumed here that Quinton used the word “objective” to refer to those words which had abstract objects — in this case, abstract concepts — as their referents.)

Perhaps it can be accepted that the concept [bachelor] is both objective and abstract. However, is it also timeless? That’s unless it’s believed — and it often is — that timelessness must necessarily always come along with being abstract and also with being objective. Yet if abstractness and objectivity do come along with timelessness, then the concept [bachelor] may not be abstract or objective either…

Conventionalism

In the philosophy of mathematics, and even in mathematics itself, a link was made — roughly from the 17th century to the 19th century — between the conventionality of mathematics and the fact that mathematical statements are true simply because they assert identities. (See here for the basic mathematical position on identities or equalities.) In other words, the identities of mathematical statements (according to Quinton’s conventionalists) follow from the fact that mathematics is about symbolic conventions — not truth. This was — very broadly speaking — the position advanced by David Hume (see here), Henri Poincaré (see here) and then Ludwig Wittgenstein in his Tractatus (see here). (See also ‘Tautology’.)

However, perhaps mathematical conventionality and identities don’t go together. Alternatively, perhaps conventionality and the importance of identities can both be rejected.

According to Quinton:

“Leibniz knew to much about mathematics to regard it as conventional.”

However, it seems that

“he did not know enough about it to realise that its propositions were not identities”.

So, according to Quinton, Leibniz believed that mathematical statements — indeed truths — were (mere?) identities. That is, he believed that both sides of the equality sign state the same thing — though in different ways.

This can be seen as a deflationary view of mathematics and it has been almost universally rejected. (The rejection largely set in the early 20th century; though perhaps before.)

Quinton even touches on Kant’s “synthetic a priori truths”.

If mathematical statements aren’t identities, then does that mean that they’re synthetic a priori truths? That is, truths that are neither mere identities nor determined by the meanings of the symbols on both sides of the equality symbol.

It is still argued that such truths too can be known a priori. However, that’s not because they’re identities or simply because both sides of the equation state the same thing. Yet such truths can still be known — according to Kant — without (further) experience.