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Beyond a reasonable doubt

November 17, 2013

Last night I had a long conversation about what role, if any, probabilistic evidence should have in our reasoning about “the things that matter” (meaning, I suppose, the fundamental structure of our relationships with each other, the world, God, ourselves.) What are we to make of language like this:

  • “Considering all the arguments for and against, I hold there to be a 90% chance that God exists, and so call myself a deist.”
  • “Considering all the arguments for and against, I’m 95% certain I should marry this woman, and so will do so (if she consents).”
  • “Considering all the arguments for and against, I’m 99% sure he committed the crime, and so vote to convict.”

Has it any place in philosophical discourse?


The class for which I’m TAing has recently been reading Plato’s Gorgias, in which Socrates has this to say about refutation (in Donald Zeyl’s translation):

[471e] My wonderful man, you’re trying to refute me in oratorical style, the way people in law courts do when they think they’re refuting some claim. There, too, one side thinks it’s refuting the other when it produces many reputable witnesses on behalf of the arguments it presents, while the person who asserts the opposite produces only one witness, or none at all. This ‘refutation’ is worthless, as far as truth is concerned, [472a] for it might happen sometimes that an individual is brought down by the false testimony of many reputable people. Now too, nearly every Athenian and alien will take your side on the things you’re saying, if it’s witnesses you want to produce against me. […472b…] Nevertheless, though I’m only one person, I don’t agree with you. You don’t compel me; instead you produce many false witnesses against me and try to banish me from my property, the truth.

In other words: truth does not depend on popular consensus. This is not an epistemological claim about how to tell, “objectively,” what is true; it’s an ethical attitude, a decision to live on the estate of truth. Socrates would abandon his rightful property were he to allow the beliefs of others to determine what he holds to be true. But it’s also grammatical: to assent to a statement X, not because one understands it to be true, but because others assent to it, simply doesn’t count as holding it to be true. Knowledge requires understanding, requires being able to stand behind an account (logos) of why what is true, is true. And once Socrates can do so, the number of witnesses on the opposing side doesn’t matter.


But this is not an arrogant Romantic self-reliance; conversation is supremely important to the Socrates of the Gorgias. “[485a] And what kind of man am I? One of those who would be pleased to be refuted if I said anything untrue, and who would be pleased to refute anyone who says anything untrue; one who, however, wouldn’t be any less pleased to be refuted than to refute.” The difference is that conversation means responding to the account the other gives, trying to see whether you too can stand behind it, trying to convince them to join you if you cannot join them. There’s no counting involved. Socrates would not put it in these terms, but would, I think, agree with the following statement: probabilistic attempts at certainty fail because they forget that arguments are made through language, by persons, and seek to enter into the truth; they treat logoi as empirical data points.


So Socrates would have no truck with “Considering all the arguments for and against, I hold there to be a 90% chance that God exists.” That’s fine for practical things (though not ideal), but intolerable (and unethical) when dealing with “the things that matter,” the things that structure how we make sense. But then: can we ever know anything about “the things that matter,” other than that we know nothing? These things, after all, aren’t going to just wait around for us; if we refuse to stand behind any account of justice, or the good, or love, or God, until we understand it fully, we are, in fact, accepting that we will die before we are ready to stand anywhere, to make any sense.


The practical urgency of this dilemma comes out most clearly, perhaps, in the criminal justice system, which (unlike most aspects of our democratic government) requires jury members to be in complete agreement about the guilt of the accused, and requires them to consider that guilt not just probable, but “beyond a reasonable doubt.” That phrase doesn’t, I think, have a formal definition, but I take it to mean “the prosecution must offer an interpretation of the available evidence that demonstrates that it is the only possible interpretation to which any reasonable person could assent.” 99% certainty that he committed the crime is neither sufficient, nor necessary, nor relevant. The jury isn’t being asked to give its best guess, it’s being asked to stand behind the decision it makes.

At the same time, of course, each jury member is told to step outside himself and inhabit the common-sense-driven mind of the “reasonable man.” If I were a philosopher in the midst of an existential crisis, no longer certain that the external world exists, it would be impossible for me to stand behind any judgment I make as to the accused’s guilt or innocence, but if I were to allow that to influence my decision I would fail to properly execute the office of juryman. I would fail, too, if I were a conspiracy theorist who thought that criminals were never guilty, but were always framed by the police. I would also fail in the office of juryman if I refused to vote in accordance with the “reasonable man” of a society that held that people named Jones were always criminals. I don’t think Socrates would much like the legal fiction of the “reasonable man.”


Socrates was known to be courageous in battle, and, of course, when he was on trial in the law-courts. My class is about to read the Apology, where after his conviction and death sentence Socrates has this to say about certainty in the face of death (Grube’s translation)–note, too, what Socrates says about what it means to be a juryman rightly so called:

[40a] To you, as being my friends, I want to show the meaning of what has occurred. A surprising thing has happened to me, jurymen–you I would rightly call jurymen. At all previous times my familiar prophetic power, my spiritual manifestation, frequently opposed me, even in small matters, when I was about to do something wrong, but now that, as you can see for yourselves, I was faced with what one might think, and what is generally thought to be, the worst of evils, my divine sign has not opposed me, [40b] either when I left home at dawn, or when I came into court, or at any time that I was about to say something during my speech. Yet in other talks it has often held me back in the middle of my speaking, but now it has opposed no word or deed of mine. What do I think is the reason for this? I will tell you. What has happened to me may well be a good thing, and those of us who believe death to be an evil are certainly mistaken. [40c] I have convincing proof of this, for it is impossible that my familiar sign did not oppose me if I was not about to do what was right.

His language sounds mystical, but I don’t think he means anything by “prophetic power”/”spiritual manifestation”/”divine sign” other than “the sense I have, because I attempt to live in the truth, of whether or not what I am about to say will exile me from the truth.” He dies a martyr to truth, and that whatever doubts he has about the exact nature of justice, temperance, prudence, courage, piety, etc, he has no doubts about the correctness of this decision.


If anything troubles me about the figure of Socrates in his hagiographic aspect, it is his marriage. His wife was said to be “shrewish,” but that’s likely because Socrates didn’t do anything to support his family, preferring to discuss philosophy all day with whomever would listen. Did Socrates take his decision to marry seriously–the way a philosophically reflective person of today would–or did it happen to him as a matter of course, as something imposed on him by custom, before he began to devote his life to philosophy? The Biblical prophet Hosea married Gomer, a prostitute, as an emblem of God’s love for the unfaithful Israel. If Socrates’ relationship with Xanthippe shows us anything, it shows us the dark side of his view of the body as fundamentally an encumbrance, a nagging annoyance.


The conversation I had last night recalled these passages from Plato to my mind, and today at mass I could not help but be struck by the resemblance between the words of Socrates I quoted from the Apology and the words of the Gospel reading today (Luke 21:10-19, in the Douay-Rheims translation):

[10] Then he said to them: Nation shall rise against nation, and kingdom against kingdom. [11] And there shall be great earthquakes in divers places, and pestilences, and famines, and terrors from heaven; and there shall be great signs. [12] But before all these things, they will lay their hands upon you, and persecute you, delivering you up to the synagogues and into prisons, dragging you before kings and governors, for my name’s sake. [13] And it shall happen unto you for a testimony. [14] Lay it up therefore into your hearts, not to meditate before how you shall answer: [15] For I will give you a mouth and wisdom, which all your adversaries shall not be able to resist and gainsay. [16] And you shall be betrayed by your parents and brethren, and kinsmen and friends; and some of you they will put to death. [17] And you shall be hated by all men for my name’s sake. [18] But a hair of your head shall not perish. [19] In your patience you shall possess your souls.

Socrates would have no difficulty embracing these words were he told that the logos itself had spoken them. Nor would he take them to be promising a miracle; for him, the immortality of the soul is no miracle, rather the most reliable of truths. But if he were told that it was Jesus of Nazareth, and that what is being promised here is a resurrection of the body? Socrates refuses to say “I hold there to be a 90% chance that it is Good to seek for Truth”; but what about “I hold there to be a 90% chance that the Resurrection took place”? How can knowledge of an historical event, especially an historical event that is by its very nature an exception to the rule, not be empirical, rather than rational? “But we preach Christ crucified, unto the Jews indeed a stumbling-block, and unto the Gentiles foolishness….”

13 Comments leave one →
  1. November 17, 2013 5:09 pm

    Reblogged this on Mysteries and Manners and commented:
    Joseph at Ironical Coincidings has an excellent post on reasonable doubt, Socrates, and jury-men. I had to reblog it.

  2. Theresa permalink
    November 17, 2013 6:21 pm

    Hey Joseph, I really liked this post. It left me wondering, have you ever read Newman’s “Grammar of Assent”? In it, Newman gives a phenomenology of the mental act of assent to a proposition, and then in Chapter 10 he applies concepts as he has defined them to illustrate the process of coming to assent to revealed truths. Reacting against modern scientific rationalism, he “prefer[s] to rely on an accumulation of various probabilities…from probabilities we may construct legitimate proof, sufficient for certitude.” I don’t know, I guess I was just thinking you might want to check out that whole chapter – it’s quite a propos to the questions you raise about certainty in light of the historical facticity and concreteness of revelation.

    I was also thinking that it might be interesting to think about how Aristotle’s phronimos compares to the legal positivists’ fiction of the “reasonable man.” Aristotle is a little more optimistic than Plato about the possibility that common opinion bears truth, and he starts his investigation of virtue measuring it against the standard of the practically wise man – not an infallible, disembodied, rationalistic practical wisdom, but that guy down the street that everyone recognizes to be basically good and reasonable. Newman has something akin to Arisotle’s phronesis when he talks about the “illative sense”…some people just have it, and you know who they are; other people don’t.

  3. November 17, 2013 9:38 pm

    “Grammar of Assent” is something I really ought to read. I’ve never gotten around to it.

    I avoided bringing Aristotle into this post because it was already too sprawling, but you’re right that he offers a fascinating counter-point to Plato’s absolutism. He endorses the man-on-the-street (and calls skepticism insane) and yet, if I remember correctly, he still agrees with Plato that philosophy is a search for understanding of causes, not a search for certainty. I must think more about these issues. I (presumptuously) considered myself an Aristotelian in undergraduate but I’ve read so much Plato recently I’ve been slowly drifting into his orbit…

  4. Nick Olson permalink
    November 17, 2013 11:04 pm

    Socrates frequently employed language like “likelihood” or “probable.” So if Socrates was comfortable holding something to be true “more likely than not,” I suppose he would also be comfortable saying “the likelihood that X is true is greater than 50%.”

    Interestingly, that is the standard of proof in most civil cases–the judge or jury must side with the party that has the “preponderance of the evidence.”

    There are two problems with using that probabilistic approach: First, Most evidence is not easily translated into quantifiable probabilities. If an accused murderer’s alibi contradicts the testimony of one credible witness, you cannot ascertain a probability to the likelihood of the accused’s alibi being false, but you might say it’s more likely than not to be false. And if the accused’ alibi contradicts the testimony of two credible witnesses, you might say that the likelihood that the accused’s alibi is false is even less likely than before. In other words, folks can approach evidence comparatively (“more likely than not” or “more likely than before” or “even more likely) but cannot assign a numeric probability.

    Second, as you point out, certain beliefs structure how we make sense, and so using probabilistic analysis on foundational beliefs puts Descartes before the horse. For purely axiomatic issues, like whether subjectively-experienced stimuli bear relation to reality, you can’t assign probabilities–though perhaps you can still state “it’s more likely than not” or “I’m 99% sure” (meaning I’m almost certain)?

    For an issue like “Do you believe in God?” you could use a probabilistic approach by saying, as many have, that “it’s more likely than not” that God does/doesn’t exist. But I suppose if belief in God is a matter of faith/axiomatic acceptance or rejection rather than something that can be reasoned toward, then such a probabilistic approach doesn’t make sense.

    Two side notes about the law:

    1) Many laws in many states do not require unanimous juries. Some laws might only require 9 out of 12 jurors to be in agreement.

    2) Criminal juries are not necessarily asked to analyze what an objective, “reasonable person” would think. In fact, part of the point of a jury is that the decision is rendered by a cross-section of society, which some might say should encompass people’s different biases. (Of course, the clearly biased (e.g. racist) or those incapable of rendering a rational judgment (e.g. conspiracy theorists) are often removed from the jury during voir dire).

    3) The standards of proof are often defined by statute, though your guess was remarkably accurate. If you’re interested, here is a list of instructions to be given to Florida juries in murder trials:

  5. November 18, 2013 10:00 pm

    Thanks for the comment Nick. Some counter-thoughts:

    Socrates definitely uses words like “probably” in conversation but I’m not convinced he’s talking percentages; I suspect he means something like “according to common sense.” It’s fascinating how he relies on common sense even as he demonstrates its insufficiency. Note that the distinction between the expert and the non-expert for Socrates isn’t that the non-expert never alights on the proper approach (to carpentry, to generalship, to logic, etc), but that if he does so, it does so by guesswork.

    On the question of faith in God, I was actually avoiding using words like “axiomatic” because I don’t think Socrates takes faith in the Good and True to be “axiomatic” in the way we usually understand that word, i.e. “can’t be proven, and is in a sense optional, but is thought to produce good results.” Socrates, at least, believes that we really do have REASONS for believing in the ideals, and that our belief in them counts as KNOWLEDGE, not just as something we posit so that our system will work.

    I’m not sure I can go along with this claim, but it’s not completely crazy, and seems to me a good alternative to “axiom” talk (which I’ve been suspicious of ever since I realized mathematicians talk that way for very different reasons than do philosophers). Some people think we know the external world exists, not that we just posit our access to it axiomatically. Socrates would argue that we know the ideal world exists even more securely than we know the external world does.

    Thanks for the info on how law stuff actually works. I hadn’t realized some juries only required 9/12–is that only for lesser offenses? I do still think that even if the law doesn’t explicitly tell jurymen to “pretend you’re a normal reasonable person” it’s to a certain extent implicit in the idea of a jury; for example, jury members shouldn’t (though I suppose they can’t be stopped?) decide the case based on whether they want to get home in time for dinner. The implicit reason for that, I think, is that no reasonable person could honestly say “He is guilty because I want to go home”…

  6. Chris Wolfe permalink
    November 20, 2013 5:31 pm

    “Has [probabilistic evidence] any place in philosophical discourse?”
    I can’t read that question and not think of Blaise Pascal. Pascal would say: Yes!

    Also, Plato’s definition of knowledge as “justified true belief” (Theatetus) is susceptible to the exceptions or “defeaters” of justifications that Gettier pointed out. I imagine there are some probability and “trust in authority” issues involved coming at Plato from that angle, too

  7. November 20, 2013 7:53 pm

    Gettier is, of course, a problem for our contemporary ideas of what “knowledge” means, but I’m not sure it really causes any problems for the kind of knowledge Plato has in mind. Plato (for the most part) doesn’t care about things like “Whether Jones will get the job.” That’s a yes/no question with an empirically verifiable answer (and because it’s empirical it’s impossible to be 100% certain anyway). Boring. Knowledge for Plato more often means “What is the correct way to build a house,” “What is the good life,” “What is the good.” Knowledge in these cases just IS the account that justifies the knowledge. If the account I give of “how to build a house” is true, there’s no way for a Gettier case to intervene, because what justifies that I know how to build a house JUST IS my knowledge of how to build a house.

    Pascal is of course an interesting case. I’ll be reading him in more depth in a few months and will have more to say about the Wager then probably.

  8. Chris Wolfe permalink
    November 21, 2013 12:16 pm

    That’s a good answer about Gettier, I think you nailed it. But one of the examples you site at the beginning does seem to me to be a yes/no question with an empirically verifiable answer, very different than the question of “how to build a house”:
    “Considering all the arguments for and against, I’m 99% sure he committed the crime, and so vote to convict.”
    The other examples “does God exist” and “should I marry this woman” aren’t that kind of question, even though the crime example justification does involve probability. Statistics-based laws of science also involve probability, but are more like the crime example.

  9. November 23, 2013 2:46 pm

    I pretty much agree. Though I’d say the law question isn’t entirely empirical; there’s still questions of motive. Granted, as I understand it, they mostly ignore the philosophically problematic aspects of treating that as a matter of fact.


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