‘Conspiracy Theory’ as a Tonkish Term: Some Runabout Inference-Tickets from Truth to Falsehood

ABSTRACT

I argue that ‘conspiracy theory’ and ‘conspiracy theorist’ as commonly employed are ‘tonkish’ terms (as defined by Arthur Prior and Michael Dummett), licensing inferences from truths to falsehoods; indeed, that they are mega-tonkish terms, since their use is governed by different and competing sets of introduction and elimination rules, delivering different and inconsistent results. Thus ‘conspiracy theory’ and ‘conspiracy theorist’ do not have determinate extensions, which means that generalizations about conspiracy theories or conspiracy theorists do not have determinate truth-values. Hence conspiracy theory theory – psychological or social scientific research into conspiracy theorists and what is wrong with them – is often about as intellectually respectable as an enquiry into bastards and what makes them so mean.

KEYWORDS:

• Tonk
• Prior
• Dummett
• conspiracy theories

Introduction: Logic, Tonk and Bastards

You know what I hate? Philosophical papers which relate some matter of great political pith and moment to an arcane issue that is neither understandable by, nor of any interest to, anyone but professional philosophers (their authors often operating under the grotesque delusion that they are thereby doing their duty as public intellectuals). This, I am sorry to say, is just such a paper.

In fact in some ways it is even worse. I am not just going to relate conspiracy theories and their believability to an arcane issue that only philosophers care about or can understand – I’m going to relate conspiracy theories to an ultra-arcane set of issues which only a minority of philosophers either care about or can understand. My excuse is that although I will be starting with an arcane issue in the Philosophy of Logic, I shall be arguing for a thesis with implications both for conspiracy theory ‘research’ and for policy proposals based on that research. I shall be arguing, in effect that research into what is wrong with ‘conspiracy theories’ or ‘conspiracy theorists’ is (often) about as intellectually respectable as research into what it is about ‘bastards’ that makes them so mean. And policies designed to combat ‘conspiracy theories’ or ‘conspiracy theorising’ are (by and large) not much better than policies designed to address the ‘too many bastards’ problem or to somehow transform ‘bastards’ into better people.

I draw on the New Zealand logician Arthur Prior’s famous paper ‘The Runabout Inference Ticket’ (1960), plus some of Sir Michael Dummett’s remarks in Frege: The Philosophy of Language (1981), to argue that ‘conspiracy theory’ and ‘conspiracy theorist’ are tonkish, indeed mega-tonkish terms; ‘tonkish’ being a term of art derived from Prior’s paper. The problem with tonkish terms (as I shall explain below) is that they license inferences from truths to falsehoods, often with harmful effects. And the problem with what I call mega-tonkish terms is not just that they can be used, and often are used, to derive false or debatable claims from bona fide truths, but that the rules governing their use are inconsistent which means that, as commonly employed, they do not have determinate extensions. Given the confused, inconsistent and tonkish rules governing ‘conspiracy theory’ and ‘conspiracy theorist’ there is no fact of the matter about whether something is a conspiracy theory or whether someone is a conspiracy theorist, just as there is no fact of the matter about whether somebody is or is not a bastard. At best, there is a fact of the matter about whether something is a conspiracy theory or somebody is a conspiracy theorist according to X (where ‘X’ is a stand-in for a person, a group or a standard). And if there is no fact of the matter about whether something is a conspiracy theory or somebody is a conspiracy theorist – if, given the meanings of ‘conspiracy theory’ and ‘conspiracy theorist’ as currently employed, claims like ‘The January 6^th Committee is pushing a conspiracy theory’ or ‘Ivan is a conspiracy theorist’ do not have stance-independent truth-values – then generalizations about conspiracy theories or conspiracy theorists don’t have stance-independent truth-values either, including generalizations about what, if anything, is wrong (or usually wrong) with conspiracy theorists or conspiracy theories. Thus, a purported piece of social science or philosophical research that deals in such generalizations is likely to be fundamentally flawed. You cannot for example ‘examine the individual-level correlates of belief in conspiracy theories and general conspiratorial predispositions’ (as in Miller, Saunders, and Farhart 2015) if one person’s (irrational) conspiracy theory is another person’s (rational) recognition of a real-world conspiracy. In the words of Brian Keeley,¹ there is no ‘there’ there for social scientists to investigate, no uncontested set of social phenomena to analyze or explain, any more than there is an uncontested class of bastards whose moral deficiencies can be investigated, explained or rectified.

But I am getting ahead of myself. My claim is that as commonly employed, ‘conspiracy theory’ and ‘conspiracy theorist’ are not only tonkish but mega-tonkish terms, and that this carries adverse implications for certain kinds of conspiracy theory research (specifically, generalist research which dilates on the intellectual and sometimes the moral shortcomings of ‘conspiracy theories’ and ‘conspiracy theorists’ as such without bothering to define these terms). But ‘tonk’ and ‘tonkish’ are terms of art in Philosophical Logic and are largely unknown even to the academic public. Obviously if I am to retain some shreds of respectability as a public intellectual, I will have to explain some of the arcane terminology involved, terminology that is not only unfamiliar to non-philosophers but is also unfamiliar to those philosophers with no particular yen for the Philosophy of Logic.

’And’, ‘Not’, ‘Or’ and ‘If-Then’

Prior’s paper, on which I shall be relying, is a critique of Inferentialism in the Philosophy of Logic. But Inferentialism is itself a rival to the truth-conditional conceptions of meaning and consequence to which Prior himself subscribed, and we need to understand these conceptions before we can get on to Inferentialism and Prior’s devastating critique. I apologize to logically literate grandmothers for teaching them to suck eggs, and advise them to skip this section. But I think that I have something important to say and I don’t want my arguments to be lost on non-logicians. Hence the need for elementary explanations.

So, let us start with meaning before moving on to logical consequence (or the concept of following from). The words whose meaning we are initially interested in are what Medieval logicians called syncategorematic expressions, that is, the words that constitute the form rather than the matter of formally valid inferences. They are nowadays known as logical connectives, specifically: ‘all’, ‘some’, ‘and’, ‘or’, ‘not’ and ‘if – then’. (Some logicians would like to extend this list but these are enough to be going on with.) I should forewarn readers that some people find the truth conditional conception of meaning hard to understand, not because it is complex, but because it seems so mind-blowingly banal. So don’t be put off if the ideas I am developing seem too truistic to be worth saying. The truth conditional theory of meaning for the logical connectives really is pretty banal, though not so banal as to go uncontested.

What is the meaning of ‘and’? The meaning of ‘and’ is to be understood in terms of the conditions under which propositions like Trump is honest and Biden is old would be true. With Trump is honest and Biden is old the condition is (unsurprisingly) both that Trump is honest and that Biden is old. Now you may be happy with the idea that Biden is old but be inclined to dispute the proposition that Trump is honest. No matter. The point is that to understand ‘and’ is to understand what has to be the case for conjunctions – that is, propositions like Trump is honest and Biden is old – to be true. And the condition is that both of the conjuncts – both of the propositions connected by the ‘and’ – should themselves be true. (You see what I mean about mind-blowing banality?)

What about ‘or’. Here again the meaning of ‘or’ is to be understood in terms of the truth conditions of the propositions in which ‘or’ forms the main connective, such as Biden is old or Trump is honest. These are known in the trade as disjunctions and the propositions combined in a disjunction – in this case that Biden is old and that Trump is honest – as disjuncts. In Logic we prefer a non-exclusive conception of ‘or’, sometimes expressed in everyday discourse as ‘and/or’. Thus the truth-condition of Biden is old or Trump is honest is that at least one of the disjuncts should be true. Thus, Biden is old or Trump is honest is true because Biden is indeed ancient which means that at least one of the disjuncts is true even if the other is not. Moreover, if at least one of the disjuncts is true, then the disjunction is still true, even if both of the disjuncts are true, as in Biden is old or Trump is dishonest.

Now for ‘not’. Unsurprisingly, the truth condition for Trump is not honest or, as we pedantically put it, It is not the case that Trump is honest, is that it is false that Trump is honest. A negative proposition such as It is not the case that Trump is honest is true if it is false that Trump is honest and false if it is true that Trump is honest. A negative proposition, Not-p has the reverse truth-value of the proposition p that it negates. And that (so say the classical logicians) is all you need to know to understand the meaning of the ‘not’ operator.

Thus far there is nothing to frighten the horses, and maybe quite enough to send the horses to sleep. But the truth-conditional analysis of the logical connective ‘if-then’, is a little more contentious, at least as it appears in classical logic. It is not so much that the analysis is wrong but that many people think that there is more to be said. However, that is an enormous can of worms that I shall be leaving largely unopened. Sceptical readers are asked to bear with me, as nothing in my overall argument depends on the thesis that the classical analysis of ‘if-then’ is adequate. It is enough for my purposes if you are willing to concede that the classical analysis captures part of the meaning of if-then propositions. With these caveats in mind, here goes: the truth-condition for a proposition such as If Trump is honest, then the election was stolen is that it is not both the case that Trump is honest and that election was not stolen. Alternatively, we can characterize the truth-condition as the claim that either Trump is not honest or that the election was stolen.

So much for meaning; now for logical consequence. A conclusion X follows from or is the logical consequence of a set of premises K (where the premise set may have only one member) if and only if a) the premises cannot be true and the conclusion false and b) that this is guaranteed by the meanings of the logical connectives involved (the non-logical contents of the premises and conclusions being irrelevant to the validity of the inference).

We can see how this works if we consider some of the rules of inference that characterize the logical connectives. These can be divided into introduction and elimination rules. An introduction rule for a logical expression δ is a rule which licenses inferences from premises in which δ does not appear to conclusions in which it does. Per contra, an elimination rule licenses inferences from premises in (at least one of) which δ does appear to a conclusion from which it is absent. The truth-conditional account of the meanings of the logical connectives allows us to see why it is that these inferences are valid; that is, why the premises cannot be true and the conclusion false.

Let us start with And-Introduction. The rule is that if you have two premises, one being that Trump is honest the other being that Biden is old, you can infer (that is it is okay to infer) that Trump is honest and Biden is old. The reason that this inference is valid is that it is impossible for the two premises to be true without the conclusion being true, since what the conclusion says is that both premises are true. Next, And-Elimination. This says that if you have the premise that Trump is honest and Biden is old, then you can infer the conclusion a) that Trump is honest and you can also infer the conclusion b) that Biden is old. Again, the truth-conditional theory of meaning helps explain why these inferences are valid. It is impossible for the premise that Trump is honest and Biden is old to be true, and either of the conclusions a) that Trump is honest or b) that Biden is old to be false because what the premise says – what its truth-condition amounts to – is that both of these potential conclusions are true.

Now for Or-Introduction. This says that from a premise such as Biden is old you can infer the disjunction that either Biden is old or Trump is honest. Again, we can see why given the meaning of ‘or’ the premise cannot be true and the conclusion false. What the premise says is that Biden is old. What the disjunctive conclusion says is that at least one of the two disjuncts Biden is old and Trump is honest is true. And our premise was precisely one of these two disjuncts. Hence the premise can’t be true and the conclusion false.² Or-Elimination, otherwise known as Disjunctive Syllogism is rather more useful and rather more interesting. This says that if you have two premises, one a disjunction (Either Trump is honest or the election was kosher) and the other the denial of one of the disjuncts (Trump is not honest), then you can infer the other disjunct as a conclusion (The election was kosher). Again, the meaning of ‘or’ as explicated in terms of truth-conditions enables us to see why such inferences are valid. A disjunction is true if and only if at least one its disjuncts is true. So if it is true that either Trump is honest or the election was kosher, then at least one of the two disjuncts, a) that Trump is honest or b) that the election was kosher must be true. Our second premise is that Trump is not honest, that is that one of the two disjuncts is false. So if at least one of the two disjuncts is true and one of them is not, then the other disjunct (in this case that the election was kosher) must be true. The two premises cannot be true and the conclusion false.

Finally, the two rules of If-Then Elimination, otherwise known as modus ponens and modus tollens. Modus ponens goes like this. From a conditional premise such as If Trump is honest then the election was stolen and another premise affirming the antecedent (or the if-clause) such as Trump is honest, you are entitled to infer the conclusion that the election was stolen. Again, the truth-conditional interpretation of if-then explains why such inferences are valid. The truth-condition of the first premise if Trump is honest then the election was stolen is that it is not the case both that Trump is honest and that the election was not stolen. The conjunction of an honest Trump and a non-stolen election is debarred. The second premise says that Trump is honest. So if it is true that it is not the case that both Trump is honest and the election was non-stolen, and if it is true that Trump is honest, then it is true that the election was stolen. Since the conditional premise debars the conjunction of an honest Trump and a non-stolen election, and since the second premise asserts Trump’s honesty, they can only be true if the election was stolen. Modus tollens goes like this: from a conditional premise and a second premise denying the then-clause (technically known as the consequent) you can infer, as a conclusion, the negation of the antecedent. For example, from 1) If Trump is honest then the election was stolen and 2) the election was not stolen you can infer as a conclusion that 3) Trump is not honest. Again, the truth-conditional conception of meaning enables us to see why such inferences are valid. What the truth condition of If Trump is honest then the election was stolen amounts to is that either the election was stolen or that Trump is not honest. In other words, at least one of the pair of propositions the election was stolen and Trump is not honest is true. Since at least one of this pair of propositions is true and since one of them is false, the one that is true has to be the other. Again, an analysis of the truth-conditions helps us to understand why such inferences are valid.

Thus the meaning of the logical connectives is explained in terms of their truth-conditions, and this in turn enables us to understand why the standard rules of inference, conceived as introduction and elimination rules, are truth-preserving. They only license inferences in which the premises can’t be true and the conclusions false. But all this depends on the twin concepts of truth and falsehood. If you have a problem with the concept of truth, then you will need a new account of the meanings of the logical connectives; likewise, a new account of what makes the standard rules of inference valid. Enter Inferentialism.

Inferentialism and Inference-Tickets

Paul Feyerabend (1978), the anarchist philosopher of science, used to mock his mainly Popperian opponents as ‘truth-freaks’, owing to their obsessive fixation on truth. But in my view, it is not so much truth-freakery as anti-truth-freakery that has been the besetting sin of twentieth and twenty-first century philosophy. A great many philosophers have been suspicious of the concept of truth, either preferring some substitute such as warranted assertibility or drastically restricting the range of propositions that can be straight-forwardly true or false. This appears to have been the view of the middle Wittgenstein (roughly from his return to Cambridge in 1929 until the early 1930s).³ He seems to have thought a) that only propositions that are the truth-functions of elementary propositions can be genuinely true or false and b) that only propositions that can be conclusively verified can be true or false. Neither generalizations nor scientific theories are the truth-functions of elementary propositions, and (as Popper was at pains to point out⁴) neither generalizations nor scientific theories can be conclusively verified. Accordingly, if either a) or b) is correct, neither generalizations nor scientific theories (which Wittgenstein calls ‘hypotheses’) can be false or true. The idea is that open-ended generalizations and scientific theories (both labeled hypotheses) are not genuine candidates for truth and falsehood, let alone descriptions of reality, but are inference-tickets (a phrase due to Ryle⁵). These license us to move from premises to conclusions, often premises concerning past observations to conclusions consisting of future predictions. It is a naive error to suppose that ‘All swans are white’ is true if and only if all swans possess the property of whiteness. In fact, ‘All swans are white’ is neither true nor false. Rather it is an inference-ticket that enables you to move from the premise that Ziggy is a swan to the conclusion that Ziggy is white or from Ziggy is not white to the conclusion that Ziggy is not a swan. (This is, of course, an inference-ticket that will sometimes take you from the true to the false if you happen to relocate to Australasia.) But at least Wittgenstein thought that complex propositions in which elementary propositions were connected to one another by the truth-functional connectives – ‘and’, ‘not’, ‘or’ and ‘if-then’ (as classically understood) – could be straight-forwardly true or false, problems only arising with the entry of ‘some’ and ‘all’ (though he would presumably have excluded unverifiable claims from the class of elementary propositions). But some philosophers have been suspicious even of a truth-functional analysis of ‘and’, ‘not’, ‘or’ and ‘if-then’. Hence Inferentialism.

Inferentialism has many variants and has evolved over time,⁶ but for present purposes we can sum up the 1950s version as follows. The idea is that the meanings of logical connectives such as ‘and’, ‘or’, ‘not’ and ‘if-then’ are not to be given by their truth conditions (as above) but are wholly to be understood in terms of the inferences that they license, and in particular by their introduction and elimination rules. Introduction rules tell you when it is okay, given a preceding set of sentences which function as premises, to introduce a new sentence containing the expression in question (a conclusion). Elimination rules tell you when it is okay, given a sentence (or a set of sentences) containing the relevant expression [a premise or set of premises] to move to a new sentence (or set of sentences) from which that expression has been eliminated [a conclusion]. And that’s all there is to it. There really is nothing more to understanding the logical connectives than understanding their roles as constituents of inference-tickets. Inferentialism reverses the order of explanation sketched above. Instead of explaining the rules of inference in terms of pre-established meanings, the inferentialist explains meanings in terms of pre-established rules of inference. Inference comes first: truth and falsity are derivative.

Thus the meaning of ‘and’ is wholly given by the following introduction and elimination rules:

And-Introduction Rule

From a premise A and a premise B, infer (that is, you are licensed to infer)

A and B (or as logicians would have it: A & B or A ⋀ B).

  And-Elimination Rule

1. From a premise A and B, infer (that is, you are licensed to infer) A.

2. From a premise A and B, infer (that is, you are licensed to infer) B.

And the meaning of ‘or‘ is wholly given by the following introduction and elimination rules:

Or-Introduction Rule

1. From a premise A infer (that is, you are licensed to infer) A or B (or as logicians would have it: A ⋁ B).

2. From a premise B infer (that is, you are licensed to infer) A or B (or as logicians would have it: A ⋁ B).

Or-Elimination Rule

1. From a premise A or B, and a premise not-A infer (that is, you are licensed to infer) B.

2. From a premise A or B, and a premise not-B infer (that is, you are licensed to infer) A.

Prior’s Response: The Runabout Inference Ticket

In ‘The Runabout Inference Ticket’ (1960) and its sequel ‘Conjunction and Contonktion Revisited’ (1964) the New Zealand philosopher and logician Arthur Prior developed a reductio of the view the meaning of a logical connective, such as ‘and’, ‘if-then’ or ‘or’, is solely determined by a set of inference-licenses rather than the truth-conditions of the propositions in which it appears. First he sets up his target:

If we are asked what is the meaning of the word ‘and’, at least in the purely conjunctive sense (as opposed to, e.g. its colloquial use to mean ‘and then’), the answer is said to be completely given by saying that

  (i) from any pair of statements P and Q we can infer the statement formed by joining P to Q by ‘and’ (which statement we hereafter describe as ‘the statement P-and-Q’), that

  (ii) from any conjunctive statement P-and-Q we can infer P, and

  (iii) from P-and-Q we can always infer Q.

Anyone who has learnt to perform these inferences knows the meaning of ‘and’, for there is simply nothing more to knowing the meaning of ‘and’ than being able to perform these inferences.⁷

In that case, said Prior, I can define the following connective ‘tonk’. The introduction rule is like that for ‘or’:

Tonk-Introduction: From A infer (that is, you are licensed to infer) A tonk B for arbitrary B.

The elimination rule is like that for ‘and’.

Tonk-Elimination: From A tonk B infer (that is, you are licensed to infer) B.

(We may say that ‘tonk’ comes in like an ‘or’ and goes out like an ‘and’). Put these two inference-tickets together and ‘tonk’ licenses you to infer anything you like. For example:

Tonk-Introduction: From Biden is old infer (that is, you are licensed to infer) Biden is old tonk Putin has no designs on Ukraine.

Tonk-Elimination: From Biden is old tonk Putin has no designs on Ukraine infer (that is, you are licensed to infer) that Putin has no designs on Ukraine.

Indeed, the rules for tonk license inferences from truths (obvious or otherwise) to propositions that are not only false but utterly bananas. For example, the rules for ‘tonk’ license inferences from Biden is old to The Moon is made of green cheese.

The moral of Prior’s paper (left unstated in ‘The Runabout Inference Ticket’ but spelt out in ‘Conjunction and Contonktion Revisited’) is that logical connectives should be defined in terms of their truth-conditions not their inferential roles, since otherwise there is no ban on the introduction of connectives that allow you to infer falsehoods from truths.

Now inferentialists have responded by accepting that there is indeed something radically wrong with ‘tonk’, but by insisting that this does not refute inferentialism. Rather, there is a constraint on the introduction of logical connectives, namely, that the rules governing such connectives should only license conservative extensions of the language, that is, that they should not license inferences to propositions not involving the new connective that were not licensed before. ‘Tonk’ obviously fails this test. (The locus classicus here is Belnap’s 1962 paper ‘Tonk, Plunk and Plink’.) But inferentialists face a problem: if they are not going to help themselves to the notions of truth and falsehood, it is hard to see why conservativeness is so important. What is wrong with inferences to propositions not involving the new connective that were not licensed before? The inferentialists might respond that non-conservative inference rules license us to move from the true to the false. But Prior could reply that if we need the threat of falsehood to motivate our concern for conservativeness, why not cut out the middleman and admit that what is really wrong with ‘tonk’ is that it licenses us to derive the false from the true? Either the concepts of truth and falsity are conceptually kosher, in which case there is no need to resort to conservativeness to explain what is wrong with ‘tonk’ as a connective, or they are not, in which case it is hard to motivate our concern for conservativeness.

However, it is not necessary for present purposes to adjudicate the issue between the inferentialists and the truth-conditionalists, though it is pretty obvious where my preferences lie. The point is that it is agreed on all hands that there is something radically wrong with tonkish terms, and that one way of characterising what is wrong with ‘tonk’ is that it confers a license to infer the false from the true. And there is another point on which inferentialists and truth-condition theorists are agreed: ‘tonk’ does not express a genuine concept or does not have a genuine sense. Either it has no meaning at all or it does not have a respectable meaning. Tonkish terms are, so to speak, intellectual trouble-makers. I shall be arguing below that they are political and ideological trouble-makers too.

Enter Michael Dummett

There are not many books about the Philosophy of Logic and Language with prefaces about the struggle against racism, but Dummett’s Frege: The Philosophy of Language (1981) is the big exception. (He explains that the reason that the book is a bit of a mess – which it is – is that he put it aside to fight against racism in England, only returning to the project when he had been decisively defeated. Some parts were lost, and he had problems putting the disjecta membra back together again.) But once we have done with the prefaces, the struggle against racism is largely left behind until we get to page 454, when Dummett discusses the semantics of racial, ethnic and other slurs. His claim is that they are tonkish, that is, that they can be characterized by introduction and elimination rules, licensing inferences from the true to the false, and indeed from the innocuous to the dangerous. Rather than discussing the real racial slurs that were current in the sixties and seventies and that were being used to pernicious effect, he discusses a somewhat passé expression that had fallen out of favour since WWI, and which was therefore less likely to cause offence: ‘Boche’. Like ‘tonk’, this can be understood in terms of its introduction and elimination rules.

Boche-Introduction: From ‘x is of German nationality’ infer ‘x is Boche’.

Boche-Elimination: From ‘x is Boche’ infer ‘x is barbarous and more prone to cruelty than other Europeans’.

‘Boche’, of course is an antiquated term, no longer in general use (and was so way back in the seventies when Dummett was putting his book together), but Dummett clearly wants to generalize his analysis to the racial and ethnic slurs that were bothering him at the time and which continue to do social and ideological damage in the here and now. Tonkish slurs are terms which are widely used as inference-licenses (of a kind that inferentialists would disapprove of since they are non-conservative) such that the inferences are derogatory to some group or groups. They can obviously lead from truths to falsehoods. Like everyone else, the vast majority of Germans are neither barbarous nor prone to cruelty.

‘Conspiracy Theory’ and ‘Conspiracy Theorist’ are Tonkish Terms

My thesis is that as commonly used ‘conspiracy theory’ and ‘conspiracy theorist’ not only tonkish but mega-tonkish terms. Their use is characterized not by one but by a number of different and conflicting sets of tonkish rules, all of which can be (and frequently are) used to take people from the true to the false. Hence:

1. They do not have respectable senses (as defined by either truth-conditions theorists or inferentialists);

• (2) They do not have determinate (uncontested) extensions. Hence ‘conspiracy theory’ and ‘conspiracy theorist’ do not constitute a set of phenomena suitable for psychological or social scientific investigation.

The most obvious and most widely used pair of tonkish rules, governing the use of ‘conspiracy theory’ are these – Tonkish Rules 1:

‘Conspiracy theory’ Introduction

From ‘This is a theory which posits a conspiracy’ infer (that is, it is okay to infer) ‘This is a conspiracy theory’.

‘Conspiracy theory’ Elimination

From ‘This is a conspiracy theory’ infer (that is, it is okay to infer) ‘This theory is false, crazy, or unbelievable’.

Though I have not put the point in precisely these terms, I have, in effect, argued repeatedly that these rules lead from truths to falsehoods, since many theories which posit a conspiracy are true, plausible or such that it is rational to believe or investigate them (see Pigden 1995, 2006, 2007, 2016, 2019, 2022). And for the die-hard inferentialist, it is also worth pointing out that these rules are non-conservative. We start from a premise in which the phrase ‘conspiracy theory’ does not appear via a sub-conclusion in which it does, to a final conclusion from which it is again absent.

Now it might be objected that when we argue from ‘This is a theory which posits a conspiracy’ to ‘This theory is false, crazy, or unbelievable’ we are not relying on a set of Tonkish inference rules. Rather, the argument is an enthymeme with a true missing premise:

1. This is a theory which posits a conspiracy.

2. Theories which posit conspiracies are almost always false, crazy, or unbelievable.

Therefore

3) This theory is false, crazy, or unbelievable.

However, as I and my co-conspirators have repeatedly argued, people often conspire, which means that the second premise is simply false.⁸ It just is not true that theories which posit conspiracies are almost always false, crazy, or unbelievable. So if the argument is construed as an enthymeme, it is obviously unsound.

A natural companion to the above set of rules for ‘conspiracy theory’ is the corresponding set of rules for ‘conspiracy theorist’, Tonkish Rules 2:

‘Conspiracy theorist’ Introduction

From ‘This person subscribes to a theory which posits a conspiracy’ infer (that is, it is okay to infer) ‘This person is a conspiracy theorist’.

‘Conspiracy theorist’ Elimination

From ‘This person is a conspiracy theorist’ infer (that is, it is okay to infer) ‘This person is crazy, silly or irrational’.

Fairly obviously these rules lead from truths to numerous falsehoods. As I have argued in Pigden (2022) every politically literate person subscribes to some theories that posit a conspiracy, and not all of them are crazy, silly or irrational.

The next set of rules are a variation on the first. Call them Tonkish Rules 3:

‘Conspiracy theory’ Introduction*

From ‘This is a theory that posits a conspiracy to which I (or the epistemic authorities I respect) do not subscribe’ infer (that is, it is okay to infer) ‘This is a conspiracy theory’.

‘Conspiracy theory’ Elimination

From ‘This is a conspiracy theory’ infer (that is, it is okay to infer) ‘This theory is false, crazy, or unbelievable’.

Quite a lot of people don’t always infer that a theory that posits a conspiracy is a conspiracy theory and is hence unbelievable, but only make this inference it if it is a theory that they, or those they respect, disbelieve. But even though these rules only license a restricted range of inferences (as compared to Tonkish Rules 1) they still license moves from truths to falsehoods since many theories that posit a conspiracy and are disbelieved by some speaker (or the epistemic authorities that she respects) are nonetheless true, plausible or rationally believable. These rules are also non-conservative. More importantly however, the introduction rule is implicitly indexical (since its application depends on the ideological or epistemic stances of the speaker and whoever she happens to admire) whilst the elimination rule purports not to be. Thus, it licenses people to move from indexical truths – truths about what I, the speaker disbelieve, or about what those that I admire disbelieve – to general claims about what is objectively false, crazy, or unbelievable. And these are claims that stand a decent chance of being false, since there are many people who disbelieve conspiracy-positing theories that are in fact true. Witness the Trumpians who (on the say-so of Trump himself and his acolytes on Fox News) disbelieve the claim that Trump and members of his entourage conspired to overturn the results of the 2020 election. For them this counts as a conspiracy theory since (unlike the conspiracy-positing theories to which they do subscribe) it is rejected by those that they respect and admire. And since, for them, it counts as a conspiracy theory, they can dismiss it as false, silly and unbelievable. Furthermore, the application of these rules tends to generate different and competing extensions of the term ‘conspiracy theory’. For some people, ‘The 2020 election was stolen’ is definitely a conspiracy theory, but for Trumpians it is not.

There is a corresponding pair of rules for ‘conspiracy theorist’. Consider Tonkish Rules 4:

‘Conspiracy theorist’ Introduction*

From ‘This person subscribes to a theory that posits a conspiracy to which I (or the epistemic authorities I respect) do not subscribe’ infer (that is, it is okay to infer) ‘This person is a conspiracy theorist’.

‘Conspiracy theorist’ Elimination

From ‘This person is a conspiracy theorist’ infer (that is, it is okay to infer) ‘This person is crazy, silly or irrational’.

The rules license moves from truths to falsehoods since many people subscribe to theories that posit a conspiracy that are disbelieved by some speaker or their epistemic authorities, without themselves being either silly, crazy, or irrational. Again, the introduction rule is implicitly indexical whilst the elimination rule purports not to be. Thus it licenses people to move from indexical truths to general claims that stand a good chance of being false. Furthermore, the application of these rules by different groups of people generates competing lists of supposedly crazy conspiracy theorists. For some people, Rachel Maddow is a conspiracy theorist, and therefore deluded or silly, since she thinks that the alleged Trump-Russia collusion continued beyond the 2016 presidential election. Her partisans repay the compliment with respect to those who think that Trump’s first impeachment was due to a deep-state conspiracy.

What complicates the issue is that many people employ two pairs of introduction and elimination rules that are indexical in a slightly different sense. The first implies that the theories to which they themselves subscribe, no matter how conspiratorial they may be, are not conspiracy theories and hence (prima facie) not unbelievable. The second implies that neither they themselves, nor the people they admire, are conspiracy theorists, even if they subscribe to theories featuring over-the-top conspiracies. Thus the following pair of rules is widely employed in everyday discourse – Tonkish Rules 5:

‘Conspiracy theory Negation’ Introduction

From ‘This is a theory (that may posit a conspiracy) to which I (or the epistemic authorities I respect) DO subscribe’ infer (that is, it is okay to infer) ‘This is NOT a conspiracy theory’.

‘Conspiracy theory Negation’ Elimination

From ‘This is NOT a conspiracy theory’ infer (that is, it is okay to infer) ‘This theory is not, or need not be, false, crazy, or unbelievable’.

Again, the introduction rule is implicitly indexical whilst the elimination rule purports not to be. Thus it licenses people to move from indexical truths about what they, or those they admire, believe to general claims about what is rationally believable; claims that stand a good chance of being false. For of course, some of the conspiracy-positing theories subscribed to by some people (and their epistemic authorities) are in fact false, crazy, or unbelievable. Again, there is a corresponding set of rules for ‘conspiracy theorist’ or rather its negation. Tonkish Rules 6:

‘Conspiracy theorist Negation’ Introduction

From ‘This is a person who subscribes to a theory that posits a conspiracy to which I (or the epistemic authorities I respect) ALSO subscribe’ infer (that is, it is okay to infer) ‘This person is NOT a conspiracy theorist [at least with respect to the relevant subject matter]’.

‘Conspiracy theorist Negation’ Elimination

From ‘This person is NOT a conspiracy theorist’ infer (that is, it is okay to infer) ‘This person is, prima facie, NOT intellectually or epistemically deficient’.

Here too, the introduction rule is implicitly indexical whilst the elimination rule purports not to be. Thus, it licenses people to move from indexical truths to general claims that stand a good chance of being false. For of course, some people who subscribe to some conspiracy-positing theories (endorsed, perhaps, by the epistemic authorities to which they give their allegiance) are in fact intellectually or epistemically deficient in some way.

The deployment of Rules 5 and 6, by different sets of people reinforces the tendency of Rules 3 and 4 to generate different and competing lists of ‘conspiracy theories’ and ‘conspiracy theorists’ and different and competing lists of crazies and intellectual delinquents. They can also be used to forestall and deter criticism and debate. As I have argued previously (Pigden 2006) the run-up to the Second Gulf War provides a case in point. Tonkish Rules 5, (the Introduction and Elimination Rules for ‘Conspiracy Theory Negation’) were deployed to protect two conspiracy-positing theories from critical examination with catastrophic effects. The disastrous Iraq War was justified by three conspiracy-positing theories, one (in my view) true but two false:

1. That the events of 9/11 were due to a conspiracy on the part of al-Qaeda.

• (2) That the regime of Saddam Hussein was in cahoots with al-Qaeda, making him in some sense an accessory to the events of 9/11.

• (3) That the regime of Saddam Hussein had successfully conspired to evade the UN inspectors and had acquired (or retained) weapons of mass destruction and perhaps was on the way (via the acquisition of yellowcake from Niger) to gaining a nuclear capability, thus making the regime a clear and present danger both to the UK and the US.

Theories 2) and 3) were both conspiracy-positing theories and indeed paradigms of false and irrational conspiracy theorizing, but the effective deployment of the Introduction and Elimination Rules for ‘Conspiracy Theory Negation’ protected them from critical examination until it was too late and the dead bodies had begun to pile up.

The Upshot

In so far as the terms ‘conspiracy theory’ and ‘conspiracy theorist’ have an extension, it is the result of the successive applications of a set of mutually inconsistent tonkish rules. Thus from a social scientific point of view there is no ‘there’ there. The categories ‘conspiracy theory’ and ‘conspiracy theorist’ (as commonly employed in the social sciences) are not sufficiently determinate or cohesive to be the proper objects of social scientific investigation.⁹ ‘My research shows that conspiracy theorists (or most conspiracy theorists) think/feel/believe Y or have characteristic X’ is in general not a sensible thing to say, absent a clear and non-tonkish definition of the term ‘conspiracy theorist’. How do you determine who is or is not a conspiracy theorist? If a ‘conspiracy theorist’ is simply defined (non-tonkishly) as somebody who subscribes to a conspiracy-positing theory, then (as I have argued in Pigden 2006, 2022) every historically literate person is a conspiracy theorist. Thus, your generalization (if true, which it probably isn’t) amounts to the following claim: ‘My research shows that historically and politically literate people think/feel/believe Y or have characteristic X’. If your sample is selected on the basis of ‘common-sense’ (that is, successive applications of mutually inconsistent tonkish rules) then your generalization runs a double risk of overstatement and understatement.

Overstatement: it will probably be false with respect to some people who can reasonably be regarded as conspiracy theorists, namely the many people who subscribe to the enormous number of conspiracy-positing theories that are either well-proven or the kinds of things that it is sensible to believe or investigate.

Understatement: your generalization may well apply to people you have excluded from the class of conspiracy theorists, even though they can reasonably be regarded as such. Despite their professed disdain for conspiracy theories, both Bush and Blair were big-time conspiracy theorists, and probably had some of the characteristics for which ‘conspiracy theorists’ are widely condemned. Yet these generalizations are not supposed to apply to such exalted personages.

Bastard Studies: A Neglected Area of Enquiry?

The term ‘bastard’ in common parlance is governed by two sets of introduction and elimination rules that go something like this:

‘Bastard’ Introduction

From ‘This is a man of whom I (or the people I respect) deeply disapprove’ infer (that is, it is okay to infer) ‘This man is a bastard’.

‘Bastard’ Elimination

From ‘This man is a bastard’ infer (that is, it is okay to infer) ‘This man is arrogant, vindictive and deep down mean’.

This pair of rules obviously licenses moves from truths to falsehoods since many men of whom some people disapprove are neither arrogant, vindictive nor deep down mean. Again, the introduction rule is implicitly indexical whilst the elimination rule purports not to be. Thus it licenses people to move from indexical truths to non-indexical claims that stand a good chance of being false. Furthermore, there is no fact of the matter about whether someone is a bastard. One person’s bastard is another person’s strong, no-nonsense leader. The bastard-negation inference-tickets reinforce the point. Not many people are bastards in their own eyes¹⁰ or the eyes of the people who think well of them.

‘Bastard Negation’ Introduction

From ‘This is a man that I (or the people I respect) admire’ infer (that is, it is okay to infer) ‘This man is not a bastard’.

‘Bastard Negation’ Elimination

From ‘This man is not a bastard’ infer (that is, it is okay to infer) ‘This man is, prima facie, neither arrogant, vindictive nor deep down mean’.

Yet again, the introduction rule is implicitly indexical though the elimination rule purports not to be. Thus it licenses people to move from indexical truths to non-indexical claims which stand a good chance of being false. For of course some men admired by some people are indeed arrogant, vindictive and deep down mean.

Given that the extension of ‘bastard’ (in so far as there is such a thing) is determined by successive and inconsistent applications of the ‘bastard’ rules and the ‘Bastard Negation’ rules, the following is not a scientifically respectable research question:

‘Why are so many men such utter bastards?’

A great deal of conspiracy theory theory – that is, social scientific research on ‘conspiracy theories’, ‘conspiracy theorists’ and ‘conspiracist ideation’ – is just about as intellectually respectable as that.¹¹

Acknowledgments

Thanks to the audiences at a range of (mostly virtual) conferences and colloquia who have helped me to polish up this paper. These include the Otago Staff Seminar, the Pitzer College International Conference on the Philosophy of Conspiracy Theories, the University College Dublin Online Conference on Conspiracy Theories, and the Midwest Philosophy Colloquium. Thanks too to the members of the CTTSC online conspiracy seminar (headed by M Dentith) for keeping me up to the mark with current research.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Notes on contributors

Charles Pigden

Charles Pigden is Professor of Philosophy at the University of Otago, Dunedin, New Zealand, where he as taught since 1988. Though he thinks of himself primarily as meta-ethicist, he has publications on many subjects including logic Lakatos, the philosophy of religion, conspiracy theories, metaphysics, Hume, Jane Austen, Dostoevsky and Bertrand Russell.

Notes

1. Personal communication.

2. A problem that beginners have with Or-Introduction is that it looks like a rule that you would never want to employ in real life. What on earth is the point of inferring some random disjunction from one of its disjuncts? We can grant that if Biden is old, it is true that either Biden is old or Trump is honest, but why bother to make such an uninformative inference? But the fact that Or-Introduction is usually rather pointless – and even, as Grice (1989) pointed out, that it sins against our conversational conventions – does not mean that the inferences it licenses are not logically valid or (to put another way) that every disjunction is not a logical consequence of each of its disjuncts.

3. ‘What is essential to an hypothesis is that it arouses an expectation, i.e. its confirmation is never completed. It has a different formal relation to reality from that of verification. Belief in the uniformity of events. An hypothesis is a law for forming propositions’; ‘The point of talking of sense-data and immediate experience is that we’re after a description that has nothing hypothetical in it. If an hypothesis can’t be definitively verified, it can’t be verified at all, and there’s no truth or falsity for it’ (Wittgenstein 1975, 44 and 283). See also Stern, Rogers, and Citron (2016): ‘A proposition can be verified or falsified, & is equivalent to a method of verifying or falsifying. Hypotheses are not verifiable or falsifiable in the same sense [hence not propositions]’.

4. See for instance Popper (1972a, 1972b).

5. Ryle (1950).

6. The most distinguished contemporary representative being Brandom (1994).

7. Prior attributes this thesis to Hare, Strawson and Kneale, and accurately but surprisingly to Popper: accurately, because as Binder, Thomas, and Peter (2022) make plain, Popper definitely believed that the meanings of the logical connectives are wholly determined by their introduction and elimination rules; surprisingly, because Popper’s critical realism affords what seems to me a decisive argument against the logical inferentialism that he also apparently espoused.

1) If ‘and’, ‘or’, ‘if-then’ etc. are to be understood in terms of the inferences that they license (and not in terms of the truth-conditions of the sentences in which they appear), then disjunctions, conjunctions and conditional claims are to be understood as inference-tickets (and not in terms of their truth-conditions).

2) If disjunctions, conjunctions and conditional claims are to be understood as inference-tickets, then large scale-theories (including scientific theories) composed (at least in part) of disjunctions, conjunctions and conditional claims are to be understood as inference-tickets (and not as representations of reality).

3) But (so Popper and his disciples such as Alan Musgrave insist) large scale theories and in particular scientific theories are not to be understood as inference-tickets, but as representations of reality.

4) So it is not the case that ‘and’, ‘or’, ‘if-then’ etc. are to be understood in terms of the inferences that they license (rather than the truth-conditions of the sentences in which they appear).

See Popper (1972a), Chapters 1 & 10 and (Popper 1972b), Chapters 2, 8 & 9 for Popper’s robustly realistic understanding of scientific theories, and Musgrave (1980) for a brilliant refutation of Wittgensteinian instrumentalism.

8. See for example, Keeley (1999), Coady (2003), Basham (2003), Hagen (2020), and Dentith (2014).

9. Tsapos (2023) and Duetz (2023) in this issue also argue that there are problems with conceptualizations of the terms ‘conspiracy theory’ and ‘conspiracy theorist’ in the social science literature. Shields (2023) argues that attempts to develop such a conceptualization risk becoming a form of problematic conceptual domination.

10. There are exceptions of course. My Father remembered a WWII drill sergeant who endeavoured to intimidate his charges by proclaiming in stentorian tones ‘THEY CALL ME THE BASTARD – BECAUSE I AM!’. It didn’t work. The young recruits concluded that if he was going to come on like a pantomime villain, they would treat him as such, and responded with a chorus of ‘boos’. Also, some people use ‘bastard’ in a minimally pejorative way such that all men are potentially bastards without any implication that they are vindictive, arrogant or mean. Witness General Patton’s famous maxim: ‘No bastard ever won a war by dying for his country. He won it by making the other poor dumb bastard die for his country’. A more interesting case involving subtle shifts of pejorative meaning occurred during the Bodyline Bowling Tour in 1932. The captain of the English cricketing team, Douglas Jardine, developed the tactic of bowling at the bodies of the Australian batsmen rather than the wicket and was denounced as a bastard in consequence. He went to the Australian changing rooms to complain, only to be met at the door by the Australian vice-captain, Vic Richardson, who turned to his teammates and said: ‘OK, which of you bastards called this bastard a bastard?’.

11. Should I name and shame? Well, why not? Here are some papers that I came across after five minutes’ googling.

‘Meta-analytical evidence indicates the robust association between collective narcissism and conspiracy theories is moderated by the content of conspiracy theories’ (de Zavala, Bierwiaczonek, and Ciesielski 2022). But how can any evidence, whether meta-analytical or otherwise, indicate a robust association between collective narcissism and conspiracy theories, if it is indeterminate whether something is or is not a conspiracy theory? And if a conspiracy theory is simply a theory which posits a conspiracy, I very much doubt whether such a robust association holds.

‘Conspiracy beliefs are often viewed as a form of psychopathology, closely linked to anxiety, paranoia, and maladaptive traits. … This article presents a framework for understanding conspiracy beliefs as a paradoxical adaptation to historical trauma’ (Bilewicz 2022). But if we are defining ‘conspiracy beliefs’ as beliefs positing a conspiracy then there are many conspiratorial beliefs that are neither due to anxiety and paranoia nor adaptive responses to historical trauma, but are simply the products of historical and political literacy. If not, then the term ‘conspiracy belief’ does not have a determinate extension. Of course, it is no doubt true that some conspiracy beliefs (as non-tonkishly defined) are adaptive, but false, responses to historical trauma but it is equally true that many are not.

‘Conspiracy thinking can be viewed as a form of narrative comprehension … Comprehenders routinely favor information that is consistent with their perspective, but conspiracy thinkers likely do this to a greater extent, due to the low levels of cognitive reflection they exhibit. Conspiracy thinkers do this as well, but their knowledge base deviates from that of the mainstream, as a result of exposure to large amounts of misinformation’ (Zwaan 2022). Zwaan appears to be employing ‘conspiracy thinkers’ (aka ‘conspiracy theorists’) in accordance with something like Tonkish rules 2, since he assuming that theories which posit a conspiracy are ipso facto irrational, exhibiting ‘low levels of cognitive reflection’ because of an exposure ‘to large amounts of misinformation’. If conspiracy theorists are people who believe in theories that posit conspiracies, then this claim is false, since many conspiracy thinkers are perfectly rational, exhibiting high levels of cognitive reflection as a result of exposure (including self-exposure) to large amounts of accurate information, in the form of reputable histories and biographies. Of course, if he is deriving his conception of ‘conspiracy thinkers’ from common usage then his claims are untestable (and hence prima facie unscientific) since there is no fact of the matter about whether someone is or is not a ‘conspiracy thinker’. And if there is no fact of the matter about whether somebody is a ‘conspiracy thinker’ then his generalizations about all or most conspiracy thinkers, won’t have determinate truth-values.

Zwaan is assuming that conspiracy thinkers are (mostly?) irrational and is then developing a theory about what makes them irrational (‘low levels of cognitive reflection’ because of an exposure ‘to large amounts of misinformation’). The trouble is that the claim that conspiracy thinkers are mostly irrational, is either false (if conspiracy thinkers are simply people who subscribe to conspiracy-positing theories) or too indeterminate to be testable. Worse, it may be tautologous if he implicitly defining a ‘conspiracy thinker’ as somebody who subscribes to a theory that it is irrational to believe. In that case the claim that conspiracy thinkers are mostly irrational will be tautologically true, but his explanation of what it is about conspiracy thinkers that makes them irrational will be untestable without independent criteria for determining whether somebody who subscribes to a conspiracy theory does so irrationally and therefore qualifies as a ‘conspiracy thinker’.