Review: Beyond the Hoax: Science and Culture (Alan Sokal)

beyond the hoax – alan sokal

Much of the material is the same as in Sokal and Bricmont’s earlier book. But there is some new material as well. I especially found the stuff on hindu nationalism and pseudoscience interesting, and the stuff on pseudoscience in nursing. Never heard of that before, but it wasnt totally unexpected. All health related fields hav large amounts of pseudoscience. It is unfortunate that the most important fields are those most full of pseudoscience!

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Part III goes on to treat weightier social and political topics using the

same lens. Chapter 8 analyzes the paradoxical relation between pseudo­

science and postmodernism, and investigates how extreme skepticism can

abet extreme credulity, using a series of detailed case studies: pseudosci­

entific therapies in nursing and “alternative medicine”; Hindu nationalist

pseudoscience in India21; and radical environmentalism. This investigation

is motivated by my suspicion that credulity in minor matters prepares the

mind for credulity in matters of greater import — and, conversely, that the

kind of critical thinking useful for distinguishing science from pseudoscience

might also be of some use in distinguishing truths in affairs of state from

lies. Chapter 9 takes on the largest and most powerful pseudoscience of all:

organized religion. This chapter focusses on the central philosophical and

political issues raised by religion in the contemporary world: it deplores the

damage that is done by our culture’s deference toward “faith”, and it asks

how nonbelievers and believers can find political common ground based

on shared moral ideas. Finally, Chapter 10 draws some of these concerns

together, and discusses the relationship between epistemology and ethics as

they interact in the public sphere.

 

surely this is true.

 

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#115 The idea that theories should refer only to observable quantities is called operationalism.-, far

from being postmodernist, it was popular among physicists and philosophers of physics in the first

half of the twentieth century. But it has severe flaws: see Chapter 7 below (pp. 240-245) as well as

Weinberg (1992, pp. 174-184).

 

i thought this was a part of logiclal positivism, and it seems that it was. i knew about operational definitions.

 

plato.stanford.edu/entries/operationalism/

 

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When all is said and done, the fundamental flaw in Merchant and Hard­

ing’s metaphor-hermeneutics is not exegetical but logical. Let us grant for the

sake of argument that some of the founders of modem science consciously

used sexist metaphors to promote their epistemological and methodological

views (this much is probably true, even if Merchant and Harding have exag­

gerated the case). But what would that entail for the philosophy (as opposed

to the history) of science? Apparently the critics wish to claim that sexism

could have passed from metaphor into the substantive content of scientific

methods and/or theories. But if modem science does in fact contain sexist

assumptions, then surely the feminist theorists ought to be able to locate and

criticize those biased assumptions, independently of any argument from his­

tory. Indeed, to do otherwise is to commit the “genetic fallacy”: evaluating an

idea on the basis of its origin rather than its content.

 

Putting aside the florid accusations of rape and torture, the argument of

Merchant and Harding boils down to the assertion that the scientific rev­

olution of the seventeenth century displaced a female-centered (spiritual,

hermetic, organic, geocentric) universe in favor of a male-centered (ratio­

nalist, scientific, mechanical, heliocentric) one.21 How should we evaluate

this argument?

 

To begin with, one might wonder whether the gender associations claimed

for these two cosmologies are really as univocal as the feminist critics

claim.22 (After all, the main defender of the geocentric worldview — the

Catholic Church — was not exactly a female-centered enterprise, its adora­

tion of the Virgin Mary notwithstanding.) But let us put aside this objection

and grant these gender associations for the sake of argument; for the princi­

pal flaw in the Merchant-Harding thesis is, once again, not historical but log­

ical. Margarita Levin puts it bluntly: Do Merchant and Harding really “think

we have a choice about which theory is correct? Masculine or feminine, the

solar system is the way it is.”23

 

The same point applies not only to astronomy but to scientific theories

quite generally; and the bottom line is that there is ample evidence, indepen­

dent of any allegedly sexist imagery, for the epistemic value of modem sci­

ence. Therefore, as Koertge remarks, “if it really could be shown that patri­

archal thinking not only played a crucial role in the Scientific Revolution but

is also necessary for carrying out scientific inquiry as we know it, that would

constitute the strongest argument for patriarchy that I can think of!”24

 

true story :D

 

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Of course, the feminist science-critics are not only archaeologists of

300-year-old science; some of their critique is resolutely modem, even post­

modern. Here, for instance, is what Donna Haraway, professor of the history

of consciousness (!) at the University of Califomia-Santa Cruz and one of

the most acclaimed feminist theorists of science, says about her research:

 

For the complex or boundary objects in which I am interested, the

mythic, textual, technical, political, organic, and economic dimensions

implode. That is, they collapse into each other in a knot of extraordinary

density that constitutes the objects themselves. In my sense, story telling

is in no way an ‘art practice’ — it is, rather, a fraught practice for narrat­

ing complexity in such a field of knots or black holes. In no way is story

telling opposed to materiality. But materiality itself is tropic; it makes us

swerve, it trips us; it is a knot of the textual, technical, mythic/oneiric,

organic, political, and economic.2

 

As right-wing critic Roger Kimball acidly comments: “Remember that this

woman is not some crank but a professor at a prestigious university and

one of the leading lights of contemporary ‘women’s studies.’ ”26 The saddest

thing, for us pinkos and feminists, is that Kimball is dead on target.

 

women’s studies is nearly completely trash. reminds me of the article about black studies in the US: chronicle.com/blogs/brainstorm/the-most-persuasive-case-for-eliminating-black-studies-just-read-the-dissertations/46346

 

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This theory is startling, to say the least: Does the author really believe

that menstruation makes it more difficult for young women to understand

elementary notions of geometry? Evidently we are not far from the Victorian

gentlemen who held that women, with their delicate reproductive organs,

are unsuited to rational thought and to science. With friends like this, the

feminist cause has no need of enemies.

 

the worst enemy of women: women.

 

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[after quoting Lacan]

Mathematicians and physicists are used to receiving this sort of stuff in

typewritten envelopes from unknown correspondents. Lacan’s grammar and

spelling are better than in most of these treatises, but his logic isn’t. To put it

bluntly, Lacan is a crank — an unusually erudite one, to be sure, but a crank

nonetheless.59

 

interesting. i will ask Sokal to expand on that theme.

 

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So, if we look critically at realism, we may be tempted to turn toward

instrumentalism. But if we look critically at instrumentalism, we feel forced

to return to a modest form of realism. What, then, should one do? Before

coming to a possible solution, let us first consider radical alternatives.

 

surprisingly true.

 

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[after quoting Plantinga]

Let us stress that we disagree with 90% of Plantinga’s philosophy; but if he is so eloquently on

target on this particular point, why not give him credit for it?

 

i was surprised they quoted him, but then, they make that comment. perfect play!

 

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Let me stress in advance that I will not be concerned here with explaining

in detail why astrology, homeopathy and the rest are in fact pseudoscience;

that would take me too far afield. Nor will I address, except in passing, the

important but difficult problems of understanding the psychological attrac­

tions of pseudoscience and the social factors affecting its spread.28 Rather,

my principal aim is to investigate the logical and sociological nexus between

pseudoscience and postmodernism.

 

footnote 28:

For a shrewd meditation on the former question, see Levitt (1999, especially pp. 12-22

and chapter 4). The latter question is indirectly addressed by Burnham (1987), in the context

of a fascinating history of the popularization of science in the United States in the nineteenth

and twentieth centuries.

 

For my own part, I have been struck by the fact that nearly all the pseudoscientific systems

to be examined in this essay are based philosophically on vitalism: that is, the idea that living

beings, and especially human beings, are endowed with some special quality ( “life energy”,

elan vital, prana, q i ) that transcends the ordinary laws of physics. Mainstream science has

rejected vitalism since at least the 1930s, for a plethora of good reasons that have only become

stronger with time (see e.g. Mayr 1982). But these good reasons are understood by only a tiny

fraction of the populace, even in the industrialized countries where science is supposedly held

in high esteem. Moreover — and perhaps much more importantly — the anti-vitalism charac­

teristic of modem science is deeply unsettling emotionally to most (perhaps all) people, even

to those who are not conventionally religious. See again Levitt (1999). Of course, none of these

speculations pretend to any scientific rigor; careful empirical investigation by psychologists

and sociologists is required.

 

vitalism -.-

 

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Sokal mentions the en.wikipedia.org/wiki/Emily_Rosa experiment.

 

the proponents must really feel bad… even a child can disprove their beliefs. how study are they??? hopefully, it was only a fringe idea, right, right?

 

When I first heard about Emily’s experiment, I admired her ingenuity but

wondered whether anyone really took Therapeutic Touch seriously. How

wrong I was! Therapeutic Touch is taught in more than 80 college and uni­

versity schools of nursing in at least 70 countries, is practiced in at least

80 hospitals across North America, and is promoted by leading American

nursing associations.32 Its inventor claims to have trained more than 47,000

practitioners over a 26-year period, who have gone on to train many more.33

At least 245 books or dissertations have been published that include “Thera­

peutic Touch” in the title, subject headings or table of contents.34 All in all,

Therapeutic Touch appears to have become one of the most widely practiced

“holistic” nursing techniques.

 

sigh!

 

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cited from pseudoscience source:

[0]ur intuitive faculty is nothing other than a source of sound premises about the

nature of reality…. [T]here exists within us a source of direct information about

reality that can teach us all we need to know.

 

top #1 reason not to teach Plato’s nonsense.

 

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But of course, those who believe in Genesis or transubstantiation do not

consider these ideas to be crazy; quite the contrary, they think that they have

good reasons to hold their beliefs. Indeed, Harris argues convincingly that

whenever any person P believes any proposition X — at least in the ordi­

nary sense of the English word “believe” — this requires, first of all, that P

must believe X to be true, i.e. to be a factually accurate representation of

the world; and secondly, that P must think he has good reasons to believe

X, in the sense that he envisions his belief as caused, at least in part, by

the fact that X is true. As Harris puts it (p. 63), “there must be some causal

connection, or an appearance thereof, between the fact in question and my

acceptance of it.”

 

this kind of causal reliabilism will not work. cf. plato.stanford.edu/entries/platonism-mathematics/#EpiAcc

 

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Some quotes from Every Thing Must Go (Ladymann, Ross, and others)

every thing must go

 

Preface

This is a polemical book. One of its main contentions is that contemporary

analytic metaphysics, a professional activity engaged in by some extremely

intelligent and morally serious people, fails to qualify as part of the enlightened

pursuit of objective truth, and should be discontinued.We think it is impossible

to argue for a point like this without provoking some anger. Suggesting that

a group of highly trained professionals have been wasting their talents—and,

worse, sowing systematic confusion about the nature of the world, and how to

find out about it—isn’t something one can do in an entirely generous way. Let

us therefore stress that we wrote this book not in a spirit of hostility towards

philosophy or our fellow philosophers, but rather the opposite. We care a great

deal about philosophy, and are therefore distressed when we see its reputation

harmed by its engagement with projects and styles of reasoning we believe bring

it into disrepute, especially among scientists. We recognize that we may be

regarded as a bit rough on some other philosophers, but our targets are people

with considerable influence rather than novitiates. We think the current degree

of dominance of analytic metaphysics within philosophy is detrimental to the

health of the subject, and make no apologies for trying to counter it.

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1

In Defence of Scientism

The revival ofmetaphysics after the implosion of logical positivismwas accom-

panied by the ascendancy of naturalism in philosophy, and so it seemed obvious

to many that metaphysics ought not to be ‘revisionary’ but ‘descriptive’ (in Peter

Strawson’s terminology, 1959). That is, rather than metaphysicians using ratio-

nal intuition to work out exactly how the absolute comes to self-consciousness,

they ought instead to turn to science and concentrate on explicating the deep

structural claims about the nature of reality implicit in our best theories. So, for

example, Special Relativity ought to dictate the metaphysics of time, quantum

physics the metaphysics of substance, and chemistry and evolutionary biology

the metaphysics of natural kinds. However, careful work by various philosophers

of science has shown us that this task is not straightforward because science,

usually and perhaps always, underdetermines the metaphysical answers we are

seeking. (See French 1998, 93). Many people have taken this in their stride and

set about exploring the various options that are available. Much excellent work

has resulted.⁹ However, there has also been another result of the recognition that

science doesn’t wear metaphysics on its sleeve, namely the resurgence of the kind

of metaphysics that floats entirely free of science. Initially granting themselves

permission to do a bit of metaphysics that seemed closely tied to, perhaps even

important to, the success of the scientific project, increasing numbers of philoso-

phers lost their positivistic spirit. The result has been the rise to dominance of

projects in analytic metaphysics that have almost nothing to do with (actual)

science. Hence there are now, once again, esoteric debates about substance,

universals, identity, time, properties, and so on, which make little or no reference

to science, and worse, which seem to presuppose that science must be irrelevant

to their resolution. They are based on prioritizing armchair intuitions about the

nature of the universe over scientific discoveries. Attaching epistemic significance

to metaphysical intuitions is anti-naturalist for two reasons. First, it requires

ignoring the fact that science, especially physics, has shown us that the universe

is very strange to our inherited conception of what it is like. Second, it requires

ignoring central implications of evolutionary theory, and of the cognitive and

behavioural sciences, concerning the nature of our minds.

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1.2.1 Intuitions and common sense in metaphysics

The idea that intuitions are guides to truth, and that they constitute the basic

data for philosophy, is of course part of the Platonic and Cartesian rationalist

tradition.¹⁰ However, we have grounds that Plato and Descartes lacked for

thinking that much of what people find intuitive is not innate, but is rather a

developmental and educational achievement. What counts as intuitive depends

partly on our ontogenetic cognitive makeup and partly on culturally specific

learning. Intuitions are the basis for, and are reinforced and modified by,

everyday practical heuristics for getting around in the world under various

resource (including time) pressures, and navigating social games; they are not

cognitive gadgets designed to produce systematically worthwhile guidance in

either science or metaphysics. In light of the dependence of intuitions on species,

cultural, and individual learning histories, we should expect developmental and

cultural variation in what is taken to be intuitive, and this is just what we find. In

the case of judgements about causes, for example,Morris et al. (1995) report that

Chinese and American subjects differed with respect to how they spontaneously

allocated causal responsibility to agents versus environmental factors. Given

that the ‘common sense’ of many contemporary philosophers is shaped and

supplemented by ideas from classical physics, the locus of most metaphysical

discussions is an image of the world that sits unhappily between the manifest

image and an out of date scientific image.¹¹

 

While contemporary physics has become even more removed from common

sense than classical physics, we also have other reasons to doubt that our common

sense image of the world is an appropriate basis for metaphysical theorizing.

Evolution has endowed us with a generic theory or model of the physical world.

This is evident from experiments with very young children, who display surprise

and increased attention when physical objects fail to behave in standard ways. In

particular, they expect ordinary macroscopic objects to persist over time, and not

to be subject to fusion or fission (Spelke et al. 1995). For example, if a ball moves

behind a screen and then two balls emerge from the other side, or vice versa,

infants are astonished. We have been equipped with a conception of the nature

of physical objects which has been transformed into a foundational metaphysics

of individuals, and a combinatorial and compositional conception of reality that

is so deeply embedded in philosophy that it is shared as a system of ‘obvious’

presuppositions by metaphysicians who otherwise disagree profoundly.

 

This metaphysics was well suited to the corpuscularian natural philosophy of

Descartes, Boyle, Gassendi, and Locke. Indeed, the primary qualities of matter

which became the ontological basis of the mechanical philosophy are largely

properties which form part of the manifest image of the world bequeathed to

us by our natural history. That natural history has been a parochial one, in the

sense that we occupy a very restricted domain of space and time. We experience

events that last from around a tenth of a second to years. Collective historical

memory may expand that to centuries, but no longer. Similarly, spatial scales of

a millimetre to a few thousand miles are all that have concerned us until recently.

Yet science has made us aware of how limited our natural perspective is. Protons,

for example, have an effective diameter of around 10−15m, while the diameter of

the visible universe is more than 1019 times the radius of the Earth. The age of

the universe is supposed to be of the order of 10 billion years. Even more homely

sciences such as geology require us to adopt time scales that make all of human

history seem like a vanishingly brief event.

 

As LewisWolpert (1992) chronicles,modern science has consistently shown us

that extrapolating our pinched perspective across unfamiliar scales, magnitudes,

and spatial and temporal distances misleads us profoundly. Casual inspection

and measurement along scales we are used to suggest that we live in a Euclidean

space; General Relativity says that we do not. Most people, Wolpert reports, are

astounded to be told that there are more molecules in a glass of water than there

are glasses of water in the oceans, and more cells in one human finger than there

are people in the world (ibid. 5). Inability to grasp intuitively the vast time scales

on which natural selection works is almost certainly crucial to the success of

creationists in perpetuating foolish controversies about evolution (Kitcher 1982).

The problems stemming from unfamiliar measurement scales are just the tip of

an iceberg of divergences between everyday expectations and scientific findings.

No one’s intuitions, in advance of the relevant science, told them that white

light would turn out to have compound structure, that combustion primarily

involves something being taken up rather than given off (Wolpert 1992, 4), that

birds are the only living descendants of dinosaurs, or that Australia is presently

on its way to a collision with Alaska. AsWolpert notes, science typically explains

the familiar in terms of the unfamiliar. Thus he rightly says that ‘both the ideas

that science generates and the way in which science is carried out are entirely

counter-intuitive and against common sense—by which I mean that scientific

ideas cannot be acquired by simple inspection of phenomena and that they

are very often outside everyday experience’ (ibid. 1). He later strengthens the

point: ‘I would almost contend that if something fits with common sense it

almost certainly isn’t science’ (ibid. 11). B. F. Skinner characteristically avoids

all waffling on the issue: ‘What, after all, have we to show for non-scientific or

pre-scientific good judgment, or common sense, or the insights gained through

personal experience? It is science or nothing’ (Skinner 1971, 152–3).

 

Lewis famously advocated a metaphysical methodology based on subjecting

rival hypotheses to a cost–benefit analysis. Usually there are two kinds of cost

associated with accepting a metaphysical thesis. The first is accepting some kind

of entity into one’s ontology, for example, abstracta, possibilia, or a relation

of primitive resemblance. The second is relinquishing some intuitions, for

example, the intuition that causes antedate their effects, that dispositions reduce

to categorical bases, or that facts about identity over time supervene on facts

about instants of time. It is taken for granted that abandoning intuitions should

be regarded as a cost rather than a benefit. By contrast, as naturalists we are

not concerned with preserving intuitions at all, and argue for the wholescale

abandonment of those associated with the image of the world as composed of

little things, and indeed of the more basic intuition that there must be something

of which the world is made.

 

There are many examples of metaphysicians arguing against theories by

pointing to unintuitive consequences, or comparing theories on the basis of

the quantity and quality of the intuitions with which they conflict. Indeed,

proceeding this way is more or less standard. Often, what is described as intuitive

or counterintuitive is recondite. For example, L. A. Paul (2004, 171) discusses

the substance theory that makes the de re modal properties of objects primitive

consequences of their falling under the sortals that they do: ‘A statue is essentially

statue shaped because it falls under the statue-sort, so cannot persist through

remoulding into a pot’ (171). This view apparently has ‘intuitive appeal’, but

sadly, ‘any counterintuitive consequences of the view are difficult to explain

or make palatable’. The substance theory implies that two numerically distinct

objects such as a lump of bronze and a statue can share their matter and their

region, but this ‘is radically counterintuitive, for it seems to contradict our usual

way of thinking aboutmaterial objects as individuated by theirmatter and region’

(172). Such ways of thinking are not ‘usual’ except among metaphysicians and

we do not share them.

 

Paul says ‘[I]t seems, at least prima facie, that modal properties should super-

vene on the nonmodal properties shared by the statue and the lump’ (172).

This is the kind of claim that is regularly made in the metaphysics literature.

We have no idea whether it is true, and we reject the idea that such claims can

be used as data for metaphysical theorizing. Paul summarizes the problem for

the advocate of substance theory as follows: ‘This leaves him in the unfortunate

position of being able to marshal strong and plausible commonsense intuitions

to support his view but of being unable to accommodate these intuitions in

a philosophically respectable way’ (172). So according to Paul, metaphysics

proceeds by attempts to construct theories that are intuitive, commonsensical,

palatable, and philosophically respectable. The criteria of adequacy for meta-

physical systems have clearly come apart from anything to do with the truth.

Rather they are internal and peculiar to philosophy, they are semi-aesthetic,

and they have more in common with the virtues of story-writing than with

science.

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In 1.1 we announced our resistance to the ‘domestication’ of science. It would

be easy to get almost any contemporary philosopher to agree that domestication

is discreditable if the home for which someone tries to make science tame is

a populist environment. Consider, for example, the minor industry that seeks

to make sense of quantum mechanics by analogies with Eastern mysticism.

This is obviously, in an intellectual context much less rigorous than that of

professional philosophy, an attempt to domesticate physics by explaining it in

terms of things that common sense thinks it comprehends. Few philosophers

will regard the gauzy analogies found in this genre as being of the slightest

metaphysical interest. Yet are quantum processes any more like those described

by Newtonian physics than they are like the temporal and spatial dislocations

imagined by mystics, which ground the popular comparisons? People who

know almost no formal physics are encouraged by populists to find quantum

mechanics less wild by comparing it to varieties of disembodiment. Logically,

this is little different from philosophers encouraging people who know a bit

of physics to make quantum accounts seem less bizarre by comparing them

to what they learned in A-level chemistry.²⁸ We might thus say that whereas

naturalistic metaphysics ought to be a branch of the philosophy of science, much

metaphysics that pays lip-service to naturalism is really philosophy of A-level

chemistry.

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and then i got bored with the next parts.

 

Time travel: reading material

I am taking a metafysics class1 and last lectur’s topic was time travel. That is an issu i sort of like but i dislike the way people discuss it, in general. Ther is a widespred lack of clarity and lack of training in the relevant logics (that is, modal logics: alethic logic and temporal logic). A fine example of that is the first essay below.

John M. E. Mctaggart – Time Is Not Real

David Lewis The Paradoxes Of Time Travel

The followup essay (2nd abov) is certainly better than the first but not quite clear enof to my taste. I do generally agree with Lewis tho. I advice people interested in the subject to lern alethic logic (S5) and read the following materials.

www.sfu.ca/~swartz/time_travel1.htm

www.sfu.ca/~swartz/beyond_experience/index.htm Chapter 8.

And for those who like fiction about time travel and wants to see som fiction with time travel that seems to be non-contradictory.

Robert A. Heinlein – Time enough for love_ the lives of Lazarus Long

Robert A. Heinlein – All You Zombies

Notes

1Well, tecnically, i signed up for it but never turned up so far. I blame the timing. They put it at 0900, and even on the same day as another class (filosofical logic) altho not the same time. But it still implys that if i want to attend both lectures, then i hav to spend a lot of time on the university in one day. But i disfeel like spending that much time, unless ther is alcohol involved. :)

Propositions, cross-world identity and truth values

1. There is a thing, x, such that it is a contingent proposition.

∃xCx

2. For any thing, x, if x is a contingent proposition then there is a possible world, w, where x is true, and there exists a possible world, w’, where x is false.

∃xCx→∃x∃w∃w’Pxaw∧Pxbw’

3. Thus, there is a thing, x, and there is a possible world, w, and there is a possible world, w’, such that x has the property true in world w and x has the property false in w’.

⊢ ∃x∃w∃w’Pxaw∧Pxbw’ [1, 2, MP]

4. For any thing, x, and for any possible world, w, if x has the property true or has the property false in w, then x exists in w.

∃x∃wPxaw→∃x∃wExw

5. Thus, there is a thing, x, and there is a possible world, w, and there is a possible world, w’, such that x exists in w and x exists in w’ and

⊢∃x∃w∃w’Exw∧Exw’∧Pxaw∧Pxbw’ [3, 4, MP]

6. For any thing, x, for any possible world, w, x has the property true iff x does not hasve the property false.

∀x∀w(Pxaw↔¬Pxbw)

7. For any thing, x, and for any thing, y, for any possible world, w, and for any possible world, w’, if x exists in w and y exists in w’, then (x and y are identical iff for any property, z, if x has it in w, then y has it in w’).

∀x∀y∀w∀w’(Exw∧Eyw’)→(x=y↔(∀zPxzw↔Pyzw’))

This set is inconsistent (5∧6→¬7)1. But it seems clear to me that we ought to give up 7.

Notes

1I thought about giving the proof tree but it would be awfully long. Until I have an automatic way of doing this, I won’t prove such complex argument beyond formalizing them.

Sentence theories of truth, meaningless sentences and untrue sentences

By sentence theory I just mean a theory of truth carriers that implies that some sentences are true or some are false. Not necessarily a monist sentence theory (=theory that implies that sentences are the only kind of truth carriers) or a theory of sentences as primary truth carriers (=theory that implies that sentences are the primary truth carriers). For more about these terms, see my earlier writings on the subject.

Anyway, I read the newest post on my favorite logic blog (Blog&~Blog). It dealt with the sentences which I have given incredibly clever names (in footnotes):

For all sentences, if it is not the case that it is meaningful, then it is not the case that it is true.

NMNT.1 (∀S)(¬M(S)→T(S))

For all sentences, if it is not the case that it is meaningful, then it is not the case that it is false.

NMNF.2 (∀S)(¬M(S)→F(S))

With the obvious interpretation keys.

This seems like plausible sentences to many when faced with sentences such as the Chomsky:

C. Colorless green ideas sleep furiously.

Which Ben, btw, got wrong as he forgot the first word.

Let’s also agree that:

1. It is not the case that C is meaningful.

¬M(C)

However, this along with some other sentences is inconsistent (=implies a contradiction). First sentence bivalence:

SB.3 For all sentences, it is either true or it is false.

(∀S)(T(S)∨F(S))

The contradiction is easy to derive here:

2. ¬T(C) [from 1, NMNT, MP]

3. ¬F(C) [from 1, NMNF, MP]

4. T(C) [from 3, SB, DS]

5. T(C) ∧¬T(C) [from 2, 4, conj.]

Contradiction! So this doesn’t work. Here I told Ben (author of the blog) that I would drop SB.4 However that apparently doesn’t work either.

Say hi to the T-schema, or the semantic theory of truth:

TS1. For all sentences, iff it is true, then it is the case.

(∀S)(T(S)↔S)

TS2. For all sentences, iff it is false, then it is not the case.

(∀S)(F(S)↔¬S)

Now these are obvious to most people. Not something is that plausible to deny unless the alternatives are really bad. However from these one can get their contra-positional versions:

TS1-CP. For all sentences, iff it is not the case, then it is not the case that it is true.

(∀S)(¬S↔¬T(S))

TS2-CP. For all sentences, iff it is not the case that it is not the case, then it is not the case that it is false.

(∀S)(¬¬S↔¬F(S))

And from these, we can derive their converses (and we can do that because these are bi-conditionals that can be conversed without problems). Do the same for TS1 and TS2:

TS1-CP-C. For all sentences, iff it is not the case that it is true, then it is not the case.

(∀S)(¬T(S)↔¬S)

TS2-CP-C. For all sentences, iff it is not the case that it is false, then it is not the case that it is not the case

(∀S)(¬F(S)↔¬¬S)

TS1-C. For all sentences, iff it is the case, then it is true.

(∀S)(S↔T(S))

TS2-C. For all sentences, iff it is not the case, then it is false.

(∀S)(¬S↔F(S))

And these actually need to be simplified too before I can use them, but I’m too lazy to do that, so I’ll just add a simp. step. No big deal.

Now:

6. ¬C [from 2, TS1-CP-C, simp., MP]

7. F(C) [from 6, TS2-C, simp., MP]

8. F(C)∧¬F(C) [from 3, 7, conj.]

Contradiction. And I didn’t need to use double negation to get it though one could do that too with TS2-CP-C, and of course I didn’t use SB either. It seems to me that this is terrible and the best way out of the contradiction is to deny NMNT and NMNF, and believe instead that sentences like C cannot even meaningfully be said to be true or false, nor can they meaningfully be said to be not true or not false. Any complex sentence with a meaningless part is itself meaningless.5

There is a tendency for people to conflate denial of properties with the denial of the meaningful application of these properties to things. This seems to be the case here too. So instead of saying things like:

Meaningless sentences are not true.

Cars are not true.

We should say things like:

Meaningless sentences cannot meaningfully be said to be true.

Cars cannot meaningfully be said to be not true.

Maybe some people sometimes, confusingly, use the first versions as a shorthand for the second. If they do and really mean what the second ones mean, then they should use them.

In a web of beliefs approach one could set up an inconsistent set of sentences and see which one is the least plausible. I figure that my readers can do that in their heads without I needing to write it out in this case. Maybe the readers will agree with me that NMNT and NMNF are the least plausible ones in the set.

Notes

1Not meaningful not true.

2Not meaningful not false.

3Sentence bivalence.

4Because, seen as a set of inconsistent sentences, this one is the least plausible to me.

5One can formulate clever sentences for this principle. I’ll do that in another essay quickly to follow this one.

Monist sentence theory and modal truths

1. For all things, that it is a truth carrier logically implies that it is a sentence.

2. There exists a thing such that it is a truth carrier and that it is logically necessarily the case.

Thus, 3. There exists a thing such that it is a sentence and that it is logically necessarily the case. [from 1, 2]

4. For all things, that it is a sentence logically implies that (that it is logically necessarily the case logically implies for all possible worlds, that sentence is the case in that possible world).

Thus, 5. For all possible worlds, there exists a sentence such that it is the case in that possible world. [from 3, 4]

6. For all possible worlds and for all things, that a thing is a sentence logically implies (that that a thing is the case in that possible world logically implies that that thing exists in that possible world).
Thus, 7. For all possible worlds, there exists a thing in that possible world such that it is a sentence. [from 5, 6]

8. There exists a possible world, such that it is not the case that there exists a thing such that that thing is a sentence.

Proof of inconsistency

Readers who do not doubt that the above set is inconsistent may skip this section, as it is a technical proof of the inconsistent of the above.

The numbered formulas here are formalization of the above sentences.

Interpretation keys

Domain x ≡ things

Domain w ≡ possible worlds

Tx ≡ is a truth carrier

Sx ≡ is a sentence

Formalization

1. (∀x)(Tx⇒Sx)

2. (∃x)(Tx∧□x)

⊢ 3. (∃x)(Sx∧□x) [from 1, 2, Simp., MP, Conj.]

4. (∀x)(Sx⇒(□x⇒(∀w)(xw)))

⊢ 5. (∀w)(∃x)(xw) [from 3, 4, Simp., Simp., MP,)

6. (∀w)(∀x)(Sx⇒(xw⇒(∃xw)))

⊢ 7. (∀w)(∃xw)(Sx) [from 5, 6, MP]

8. (∃w)¬(∃xw)(Sx)

(7) and (8) are inconsistent. I don’t know if I got the names of the inferences right, I need to read up on that at some point. It should be intuitively clear to anyone that studied predicate logic that the set is inconsistent.

The formalization could have been simplified if I had introduced more domains that were connected to a predicate, such as a domain of sentences. Then I could have avoided the implications inside another implication and could simply have written “for all sentences”.

Discussion

I also think that the above set is minimally inconsistent, by which I mean that if one removed a single sentence, it would no longer be inconsistent. The interesting thing about such minimal inconsistent sets is that the set of all except truth carrier logically implies the negation of the last truth carrier. From such a set the last truth carrier can be constructed a valid argument. Thus, a good deal of arguments can be constructed from the above list.

Suppose a person finds himself believing all the above truth carriers. Which should he stop believing? One might take it as an argument against monistic sentence theory (1), or an argument against a fundamental part of possible worlds semantics, (4), or the additional premise about existence of sentences in the relevant possible world, (6), or as evidence that there are no possible worlds where there isn’t a sentence, negation of (8), or that there are no necessarily the case truth carriers (2). It is very hard to make the decision.

Generally, a rational agent ought to reject the truth carrier that is the least plausible to him. But even that is a tough job. Which one is the least plausible? I think it is (1) given other arguments against monist sentence theory given by Swartz and Bradley. I am not very sure about this and it may be (6) instead which I find the second least plausible. On the other hand, I find (2) the most plausible and (8) the second most plausible. (4) is somewhat plausible I think, even though I have doubts about possible world semantics.

One may construct an ordered set after which truth carrier one has the most reason to reject. To me that would be {1, 6, 4, 8, 2}.1 Though one should bear in mind that these may not be independent. For instance, a web of belief with a belief in (1) would probably result in a more justified web of belief if one also rejected (2), (4) and (6).

1If two truth carriers are tried for plausibility, one may instead have them in an unordered set together inside the other. {1, 2, {3, 4}, 5, 6}

Norman Swartz on realism about abstract objects

“Although I generally prefer negative theories – those which posit as few unempirical concepts* as possible – my own leanings in this particular case are toward Realism. My attraction to the theory is bolstered by one further consideration: I can see no way to account for the existence of certain items, e.g. pieces of music, plays, and novels, other than by conceiving of them as abstract entities. Here I am considerably influenced by the arguments of C.E.M. Joad (1891-1953).
Joad argued ([105], 267-70) that the play Hamlet, for example, could not reasonably be identified with any particular in the world: neither with an idea in Shakespeare’s mind, nor with any manuscript he wrote, nor with any printed edition of the text, nor with any particular production, nor with any audio or video recording of any particular production. For Hamlet could exist even if any one or several of these were not to exist. While Joad, himself, rightly expressed some diffidence about his own arguments, I think that they add considerable impetus to a theory which would posit abstract entities.

Although I am a Realist, I am a reluctant Realist. For, to be frank, there is something exceedingly peculiar about positing entities which exist (subsist) outside of space and time. I, personally, would prefer a theory which could dispense with such mysterious entities. But I find the problems inherent in the various anti-Realist theories even more troubling. Realism is simply the better, in my estimation, of the available theories. But, like many other Realists, I do not much care for Realism. Recently one of my colleagues professed his repudiation of Realism by saying that he found the positing of abstract entities “ unintelligible ”. I share his displeasure. But I find myself unable to adopt his own anti-Realist position because I cannot in turn believe that the anti-Realist theories provide any better answer or that they can be developed without themselves having to posit at least some abstract entities.”

Norman Swartz, Beyond Experience, pp. 270-272, available online for free.

Identity and personal identity

Some people think that the identity notion is captured by the second proposal above. I think we need two notions of identity. I will not discuss that now.

Strict identity

For all things, for all things, for all predicates, that x and y are strictly identical logically implies that that x has predicate F is logically equivalent with that that y has predicate F.

(∀x)(∀y)(∀F)(x=Sy⇔(Fx⇔Fy)) [with obvious interpretation and =S meaning strict identity]

This is called Liebniz’s law.

Personal identity

Kennethamy:

“I think Liebniz’s law accommodates personal identity quite comfortably with the addition of a time quantifier: x and y are identical if any property possessed by x at time t is also possessed by y at time t. If you add a world quantifier it can also handle transworld identity rather well.“

For all things, for all things, for all predicates, for all times, that x and y are personally identical logically implies that that x has predicate F at time t is logically equivalent with that that y has predicate F at time t.

(∀x)(∀y)(∀F)(∀t)(x=Py⇔(Fxt⇔Fyt)) [with obvious interpretation and =P meaning personal identity]

This seems to work.

But I don’t understand the part about transworld identity. It seems to me that the above can handle transworld identity fine.

Primary truth bearers, none of them?

Primary truth bearers are the kind of entities that are always true or false. This is in contrast to secondary truth bearers that are only sometimes true or false. It seems possible that there are no primary truth bearers but that there are two or more secondary (= non-primary) truth bearers. All the theories that I am acquainted with are theories that include a primary truth bearers be it sentences, propositions, beliefs or whatever.

Exploring the notion of primary truth bearer

This notion of primary truth bearer seems to me to warrant further investigation and clarification. I would like to find a more rigorous description than the one I gave above. What is meant by “always” in that context?

It seems to me that it is best to think of it in relations to facts. There is something in relation to the fact that the Earth is spherical that is true/false. What is it? To say that there is a primary truth bearer is to say that:

For all facts, there exists a truth bearer of a certain kind in relation to that fact.

Though I am still not satisfied. This “of a certain kind” is not formalizable. I want a formalizable version. The below seems to capture the same idea and it is formalizable:

For all facts, there exists a truth bearer such that that truth bearer has the property true/false in relation to that fact and that truth bearer is of a certain kind.

(∀x)(∃y)(Rxy∧Cy)

The fact and truth bearer distinction

Note the distinction between facts and whatever it is that it true/false. “fact” here means things such as the spherical planet referred to by “Earth”. It is not the Earth that is true/false. Since we’re assuming that there is something that is true/false, it has to be something else.

A joint sentence and proposition theory of truth bearers

It seems possible that there is not a single kind of entity that has the property true/false in relation to all facts. Perhaps a theory could be that in all relations to facts where a sentence of the right kind has been uttered, it is that sentence that is true/false and in cases where such a sentence has not been uttered it is a proposition that is true/false.

What are the merits of such a theory? One thing is that it posits less objects than does a pluralistic theory which posits more than one entity being true/false in relation to a single fact. On grounds of simplicity of ontology, we should prefer the above theory. (Maybe. See the next passage.)

The above theory posits exactly the name number of truth bearers as does a monist proposition theory, that is, one for each fact.

Infinities and comparisons

I’m not well versed in infinite math, but I think there is a sense in which a theory that posits more than exactly one truth bearer for each fact posits more truth bearers than a theory that posits exactly one? There is an infinite number of facts in each case. I don’t know the technical answer.

Simplicity and truth bearers kinds

Is there some reason for preferring a theory that posits only a single kind of truth bearers over a theory that posits multiple kinds if the number of truth bearers is the same? Maybe. We seem to favor theories on the same grounds in other fields.

The sentence theory of truth bearers – problems with cognitively meaninglessness and logical implication

In a sentence theory of truth bearers, what it means to say that a sentence is cognitively meaningful is that it is true or false. To say that it is not cognitively meaningful (i.e. cognitively meaningless) means that it is not true or false.

In contrast, in a proposition theory of truth bearers, what it means to say that a sentence is cognitively meaningful is that it expresses a proposition. To say that a sentence is cognitively meaningless means that it does not express a proposition.1

I wonder if there is some problem with cognitively meaningfulness, logical implication and a sentence theory of truth bearers. Consider:

P. Colorless green ideas sleep furiously.

Q. The Earth is spherical.

Now consider a sentence that is about a logical implication from (P) to (Q):

S. That colorless green ideas sleep furiously logically implies that the Earth is spherical.

Now, it seems to me that if (P) is cognitively meaningless, then any sentence of which (P) is an antecedent or consequent, is cognitively meaningless too.

But now recall how a logical implication is defined. P implies Q iff there is no possible world in which Q is false and P true. But this is the case above. (P) is not true in any possible world at all2 and so any logical implication in which it is the antecedent is true. (Also where it is a consequent.) Thus, (S) is true. Contradiction. Something is terribly amiss.

Maybe some other definition of logical implication is needed. Suppose we stop defining it in terms of truth and falsity, and use the “is the case” phrase instead. Logical implication can then be defined as this: P logically implies Q iff there is no possible world in which P is the case and Q is not the case. Presumably all cognitive meaningless sentences are not the case. They are not false either because the semantic truth relations only hold for cognitively meaningful sentences. Now given the definition of logical implication all logical implications with a cognitively meaningless sentence as the antecedent are true. Again contradiction.

Notes

1By “means” I literally mean “means”. Not to be confused with an implication interpretation. I do not want to imply that some pluralistic proposition theory of truth bearers is false.

2Ignore potential problems with sentences meaning something else in a possible world.