Let me begin with a model. Suppose that there are 1000 men in the country and that 200 of them have committed ‘minor crimes’, things like shoplifting or turnstile jumping. Next, suppose that 20 of the 1000 have committed ‘major crimes’: murder, kidnapping, assault. While not everyone who commits a major crime also commits a minor crime, it is very common: 19 of the 20 major criminals are also minor criminals. Accordingly:
 The probability that a man commits a minor crime is 200/1000 = 20%.
 The probability that a man has committed a major crime is 20/1000 = 2%
 Since, of 20 men who committed a major crime 19 have also committed a minor crime, the probability that a man has committed a minor crime given that he has committed a major crime is 19/20 = 95%.
 Since, of 200 men who committed a minor crime, 19 have also committed a major crime, the probability that a man has committed a major crime given that he has committed a minor crime is 19/200 = 9.5%.
From these we can see that the probability that a man commits a major crime given that he commits a minor crime is much higher than the probability of major crime in the general population: 9.5% to 2%, or 4.75 times higher. The inverse is also true. The probability that a man commits a minor crime given that he commits a major crime is much higher than the probability of minor crime in general: 95% to 20%, or 4.75 times higher, again.
Suppose an investigator, A, discovers that B has committed a major crime. It is reasonable for A to conclude that B has likely committed a minor crime: the probability of that is 95%. On the other hand, if A discovers that B has committed a minor crime, it is not reasonable for A to conclude that B has probably committed a major crime. In this case, there is just a 9.5% probability that B has committed such a crime.
Note that A’s second inference remains unjustified even if A points out that the percentage of minor criminals who are also major criminals is much higher than the percentage of major criminals in general. In fact, one would expect A to find that the percentage is 4.75 times higher. It would, nonetheless, remain highly unlikely, just 9.5%, that a minor criminal is also a major criminal.
I will go one step further, for reasons that will become apparent. Suppose that psychologists discover that the disposition that inclines someone to minor crime is the same one that inclines one toward major crime (the differences in rates are, say, attributed to circumstances). This is consistent with the story above because the probability of each kind of criminal activity is higher given the other than either is in the general population. This still doesn’t change the fact that it is improbable that a minor criminal is also a major criminal.
So, in sum, even if:
[I] P and Q raise each other’s probability (i.e. the probability of P given Q is greater than the probability of P, and the probability of Q given P is greater than the probability of Q);
[II] The probability of P given Q is high (perhaps very high);
it does not follow that:
[III] The probability of Q given P is high.
One simply cannot infer [III] from [I] and [II].
I bring all of this up in light of a recent essay by Kate Manne on Tara Reade’s accusation of sexual assault against Joe Biden. I will not comment on the specifics of the case as I am only concerned with the structure of Manne’s reasoning. She writes that people doubt Reade because of “an unwillingness to believe that Biden is ‘the type’” to commit sexual assault even though “[w]e know, alas, that Biden is the type”. How do we know this? Because, Manne states, he “sniffed and kissed” a politician’s hair, six other women have said that he touched and kissed them in ways that made them uncomfortable, and he made jokes about being permitted to hug and touch people onstage. Let us grant that these are bad behaviours and label them “creepy”. Now, one might think that someone could be creepy without committing sexual assault, but according to Manne:
Such sentiments betray a failure to understand that Biden’s demonstrably inappropriate behavior emanates from the same sense of privileged male entitlement that often underlies more serious sexual breaches, including sexual assault of the kind Reade alleges.
Accordingly, she concludes that we ought to believe Reade.
The problem with this line of reasoning is that it is logically identical to the hypothetical case above in which the investigator, upon noticing a minor crime, concludes that there is a high probability that the perpetrator has also committed a major crime, because each raises the probability of the other due to a common type of cause. If we equate creepiness with minor crime and sexual assault with major crime, then even if 95% of sexual assault perpetrators are also creeps, and the same “sense of privileged male entitlement” is causally implicated in both, we still do not know that a majority, or even a significant minority, of creeps are also perpetrators of sexual assault. Being a creep does not entail that the probability that one has committed more serious transgressions is high. This is what is shown by the invalidity of moving from [I] and [II] to [III].†
Of course, it is possible that the situation is different in real life: that most creeps assault even if most assaulters are non-creepy, or even that the two categories are co-extensive. While this is implausible, because serious crime is in fact much less common than minor crime‡, it could be true. However, to believe this we would need to see empirical evidence that it is true, and Manne provides none. My point is not that her conclusion is false just that her argument for it is invalid.
As a matter of fact, however, Manne believes there is empirical evidence against Biden, writing: “Reade’s testimony is evidence that the sexual assault occurred”. This is, to put it mildly, unpersuasive. The mere existence of the assertion that P is not evidence that P. For evidence of this, I submit all the perfectly sincere declarations, some in book form, in favour of astrology, palm reading, healing crystals, guardian angels, past lives, UFO abductions, world Jewish conspiracies, homeopathy, Obama’s foreign birth, Elvis’s ongoing life, the government response to the COVID-19 pandemic, Hitler’s survival, and millions of other examples. People are people, so we sometimes lie, forget things, make mistakes, follow the party line, suffer from delusions, seek attention, carry out vendettas, get swept up in movements, engage in wishful thinking, etc. The mere existence of an uttered sequence of syllables is evidence for the existence of the utterance but, on its own, not much else.
Much of Manne’s essay attempts to convince the reader that Reade’s testimony should not be doubted even though: it has gaps; she waited years to reveal it; she has added to it over time; and there are no other accusations against Biden. Manne is right that all of these could be the case even if Reade is telling the truth, but this demonstrates only that certain considerations fail to be conclusive as counter evidence, not that the existence of an utterance is evidence of its content.
If testimony were evidence, then so much the worse for innocent until proven guilty. Manne tries to soften the blow:
After all, we’re not contemplating convicting this man or taking away his civil liberties. We’re contemplating not believing his story—knowing, moreover, that he has lied many times before—and potentially withholding from him the chance to run for our highest office on this basis. Although this would undoubtedly be a very serious matter, the accusations he is facing are yet more so.
This is neither comforting nor convincing. First, if testimony is evidence, then Biden’s denial of assault is evidence in his favor, so why not believe his story? It cannot be just that he has lied before, because we all have, including Reade. Is it because of the existence of Reade’s counter testimony? That just leaves a stalemate.
If we were, secondly, to break the stalemate by refusing to believe Biden because he is a powerful man, then this would be an instance of “what the philosopher Miranda Fricker calls ‘testimonial injustice,’ wherein someone is not believed because of her social position”, decried by Manne earlier in her essay.
Thirdly, denying someone the opportunity to contend for a job because of the existence of an assertion may not be as serious as imprisonment, but it is serious. Imagine a philosophy department refusing to interview a candidate just because someone she worked with accused her of something; do we really want it to be that easy to sabotage, or be sabotaged by, one’s competitors?
Finally, pace the final sentence in the quotation above, what is serious is what Biden is accused of, not the accusation itself. The latter is not evidence, so it is not even in the same league of seriousness as the former. If it were, then it would be appropriate to consider conviction or the removal of civil rights, which Manne rightly rejects.
While I do not – to overstate the obvious – know whether Biden is guilty, I do know that Manne has provided no reason to believe that he is. I can only hope that we do not lose sight of the wisdom of suspending judgement until the evidence is in; genuine evidence, that is, not just an accusation or invalid reasoning.
Joshua Mozersky is Professor of Philosophy at Queen’s University (Kingston). His primary interests are in the philosophy of science, philosophy of language, and metaphysics. Some of his essays have appeared in Philosophical Studies, Synthese, International Studies in the Philosophy of Science, The Oxford Handbook of Time, and The Blackwell Companion to Time. His book, Time, Language, and Ontology was published in 2015 (Oxford).
† See these statistics, for example, which show that rates of property crime are much higher than rates of violent crime in the U.S.; hardly a surprise.
‡ Another problem: whether creepiness and sexual assault stem from a “single sense of male privilege” is an empirical proposition that requires evidence. A philosopher who claims to know which sense is responsible for which actions in an individual is engaged in a priori psychology.