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Our local school district has been distributing propaganda to support keeping schools open during an uncontrolled pandemic. There has been a common pattern among these statements, where a half-truth is written by transforming a straightforward fact into a more vague logical inverse of it.

In one case of this form of spin, the reality is that the health department did not determine where a child contracted COVID-19. The school district wrote, "The health department has found no evidence that the child contracted COVID at school." This half-truth allows for the erroneous interpretation that |the health department has determined that the child did not contract COVID-19 at school."

In another case, the truth is that the health department has not issued recommendations about whether any schools should be open or closed, but statements have been made repeatedly that "the health department hasn't recommended shutting down our schools." In context of the other instances where the district provided only partial information, the presentation seems to me to be intended to deceive readers into believing that the health department recommends that their school should remain open.

Is there a fallacy or other term for logically inverting statements in an apparent attempt to mislead besides the more general term, "half-truth?"

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    Great addition to the knowledge base! – J D Dec 9 '20 at 17:11
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    This sounds like passing absence of evidence for evidence of absence, a variety of ad ignorantiam fallacy. It is subtly done, however, by using what is called implicatures, claims that statements are intended to convey without stating them explicitly. False implicatures work by breaking Grice's conversational maxims: being as truthful, informative, relevant and unambiguous as possible. "Found no evidence" is neither maximally informative nor unambiguous in this context. – Conifold Dec 10 '20 at 5:57
  • @Conifold my question was edited to be more general and while the edited version is a good question and answer, it's not exactly what I was asking. Your comment answers my original question, so could you post it as an answer? – glenviewjeff Dec 10 '20 at 20:32
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    @glenviewjeff Thanks, but not necessary! Seems to me like you're walking away armed with a better ability to identify and describe a form of poor reasoning, so my mission is done. The teacher in me just wanted to make sure by getting it from the horse's mouth. ; ) Good luck! – J D Dec 13 '20 at 16:52
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    @JD yes, I am grateful for the all of the useful information including yours. – glenviewjeff Dec 17 '20 at 19:25
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The school board's negative phrasing like "found no evidence" or "hasn't recommended" suggests an intention to pass absence of evidence for evidence of absence. The relationship between the two is complex and sometimes subtle, see When is absence of evidence not evidence of absence? It can be plausible when the evidence should have been forthcoming were the claim true, so its absence, despite a good faith effort to find it, goes against the claim. This is the type of situation that the phrasing exploits by allusion, except in this case no such expectation of evidence is plausible. So, if fully spelled out, this rhetorical tactic appeals to an argument from ignorance, the ad ignorantiam fallacy.

The way it is done is subtle, and of interest in itself, this goes to answering the title question. Misleading truths exploit what Grice termed conversational implicatures, claims that statements are intended to convey without stating them explicitly. So the philosophical term is false implicature. In everyday interactions we expect people and authorities to act cooperatively and in good faith when speaking, unless we have a positive reason not to. Grice distilled this into four conversational maxims: be as truthful, informative, relevant and unambiguous as the best of your knowledge permits. We rely on such cooperation to pass information that may take too long to spell out, or the speaker simply may not think to spell out.

False implicatures often work by breaking Grice's maxims: omitting salient information, introducing diversions ("red herrings"), exploiting ambiguity of language to shift emphasis, insinuate, etc. They are a common tactic employed in both political and commercial spin. Knachel in Fallacies of Linguistic Emphasis describes a court case (Bronston v. US) where the defendant was first asked if he has Swiss bank accounts, to which he answered no, and then asked if he ever had them in the past. His answer was that his company had such accounts. Both answers were true, but although he did not directly deny having personal Swiss accounts (he did), that was the obvious implicature under the maximum information maxim. Why bring up the company otherwise? The case went up to the Supreme Court on account of perjury.

When used intentionally, such verbal maneuvers approach lying, although people do distinguish the two (e.g. the Supreme Court ruled that Bronston's testimony was not, technically, perjury), see Are false implicatures lies? by Weissman and Terkourafi. In Christian ethics there is even a traditional term for it, the sin of omission. Verbal omission in this case. The school board's "found no evidence" and "hasn't recommended" omit that no evidence to the contrary was found and that no contrary recommendation was issued either. Moreover, it exploits ambiguity to allude to contexts with different expectations concerning the absences it deliberately highlights. So these statements are neither maximally informative nor unambiguous, and convey false implicatures.

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  • OUTSTANDING reference to an empirical investigation on epistemological concerns! The question of the classification of false implications is fascinating. Thanks. – J D Dec 13 '20 at 16:58
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Short Answer

Technically speaking, the intentional use of misleading language is more in the domain of rhetoric than logic and is known as sophistry. A fallacy is generally considered any persuasive argument of bad form. See What is the philosophical term used to describe flawed logic? for more details on what constitutes a fallacy.

Long Answer

Once one introduces the notion of having the intention to use fallacies to deceive others, the term most often used to describe the intention to mislead by fallacy is sophistry. From MW:

sophistry noun
soph·​ist·​ry | \ˈsä-fə-strē\

plural sophistries
Definition of sophistry

1 : subtly deceptive reasoning or argumentation
2 : sophism sense 1

Deliberate sophistry is a hyponym or type of lying, which is often defined broadly as any communication with the intent to deceive. From a philosophical stand point in logic, the notion of interest is known as intentionality which is a technical term which does not mean 'to intend', but rather is construed more broadly and is often described as 'an agent's ability to have aboutness'. From SEP:

In philosophy, intentionality is the power of minds and mental states to be about, to represent, or to stand for, things, properties and states of affairs. To say of an individual’s mental states that they have intentionality is to say that they are mental representations or that they have contents. Furthermore, to the extent that a speaker utters words from some natural language or draws pictures or symbols from a formal language for the purpose of conveying to others the contents of her mental states, these artifacts used by a speaker too have contents or intentionality. ‘Intentionality’ is a philosopher’s word: ever since it was introduced into philosophy by Franz Brentano in the last quarter of the nineteenth century, it has been used to refer to the puzzles of representation, all of which lie at the interface between the philosophy of mind and the philosophy of language.

Whereas lying can occur through omission and commission, sophistry is more generally a more subtle use of omission that takes advantage of the omission bias inherent in people's defeasible reasoning. That makes it much more difficult to detect and counter. Plus, it often gives someone the protection of having plausible deniability.

Every day, human beings go about their business of trying to determine what other people are thinking in their transactions. In philosophy, one can wonder if others even have minds and this is known as the problem of other minds, but it is much more natural and common to presume others have minds as part of what might be constituted as a folk psychology.

Lastly, it's worth noting that between the inability to read minds and overcome plausible claims of denial, human beings are subject to having cognitive distoritions, whereby strong emotions influence human reasoning. As such, sometimes sophistry can be unintentional, and as such has given rise to a philsophical razor known as Hanlon's Razor:

Hanlon's razor is a principle or rule of thumb that states, "never attribute to malice that which is adequately explained by stupidity".1 Known in several other forms, it is a philosophical razor that suggests a way of eliminating unlikely explanations for human behavior. It is likely named after Robert J. Hanlon, who submitted the statement to a joke book. Similar statements have been recorded since at least the 18th century.

Thus your claim that the school district is willfully engaged in manipulating people is actually quite the complicated epistemological affair. Your claims that they are intentionally lying to achieve an end in a court of law would be subject to quite a rigorous process of discovery and trial.

The etymology from the MW entry shows some historical origins of the term:

Sophistry Has Roots in Greek Philosophy

The original Sophists were ancient Greek teachers of rhetoric and philosophy prominent in the 5th century B.C. In their heyday, these philosophers were considered adroit in their reasoning, but later philosophers (particularly Plato) described them as sham philosophers, out for money and willing to say anything to win an argument. Thus sophist (which comes from Greek sophistēs, meaning "wise man" or "expert") earned a negative connotation as "a captious or fallacious reasoner." Sophistry is reasoning that seems plausible on a superficial level but is actually unsound, or reasoning that is used to deceive.

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Special pleading.

Special pleading

  1. (Law) a pleading that alleges new facts that offset those put forward by the other side rather than directly admitting or denying those facts
  2. (Law) a pleading that emphasizes the favourable aspects of a case while omitting the unfavourable

Their formulation avoided the admission that one obvious possibility not excluded by the health department was that the child contracted COVID-19 at school.

It should be taken into account that the child presumably spent the regulation time at school, making the probability that he did contrat COVID-19 at school relatively high, possibly higher than outside school.

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  • Ah... the law!!!! – J D Dec 9 '20 at 19:34
  • @JD Well, not so much the law as the dictionary. – Speakpigeon Dec 10 '20 at 10:18
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Half truths, in general, are often equivocations

The fallacy of equivocation occurs when a key term or phrase in an argument is used in an ambiguous way, with one meaning in one portion of the argument and then another meaning in another portion of the argument.

But your examples seem - at least seem - to be cherry picking, as only one side of the argument is presented, without concern for opposing views (how many dead?) or the full implications of the interpretation (they didn't get covid-19 from anywhere?)

Any lack of concern with the soundness of an argument makes for a fallacy or sophistry. It often seems up for debate what fallacy name you use, because you have to reconstruct what is being suggested in propaganda.

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