Special Presentation on The Limitations Of Formal Logic - The "Truth Table" Example

  • Martin has pointed out what appears to be an excellent opportunity to put together a special presentation on Epicurean views of "formal logic" and its relationship to reality. The opportunity comes from our mention in an earlier thread of the following statement by Torquatus in Cicero's On Ends:

    Again, the thread reference was here, and below is a copy of Martin's post: RE: Issues In The Meaning And Definition of Logic

    One way of stating the issue is that the laws of formal logic in fact do allow a syllogistic construction in which the conclusion is true while one or more premises or false. This is not the way non-experts think that logic works, so it is important that non-experts understand what the experts are asserting, so that they can see that the assertions of formal logic need not be connected with reality -- and for that reason normal people should not infer that formal logic can be used to "disprove reality."

    We're going to see if we can put together some reference material that will make this issue easier to understand, and hopefully trace it all the way back to Aristotle if not earlier.

    The issue of logic being a tool that can be consistent within itself, and yet not be connected with practical reality, is something that we see come up over and over. It seems to me that this is counterintuitive to the way most non-experts approach the issue of logic, so it will be great to see if we can develop a presentation that will make the issue easier for the average person to understand.

  • Cassius

    Changed the title of the thread from “Special Presentation on "Truth Tables" and Formal Logic” to “Special Presentation on The Limitations Of Formal Logic - The "Truth Table" Example”.
  • Post by Martin ().

    This post was deleted by the author themselves: The spacing in the tables got messed up. ().
  • Martin I have glanced at both the the lit.edu material and your additional notes.

    This looks to be a very interesting presentation!

    Thinking forward to how you begin the presentation, I do not see anything in the Lit.edu material as to the meaning of the variables that will be used in the tables, and I presume that is one of the central issues that you will be describing in terms of how these operations are not necessarily tied to reality.

    Is there a way to summarize or add to the handout picture the nature of this issue? I think you will be very thoroughly explaining how, given the premises of the exercise, the results of formal logic are reached.

    So is the issue in the "premises of the exercise" themselves? And how do we start off the presentation emphasizing that aspect, so that we do not get lost in the weeds?

    I am reminded of this from Hermotimus:


    Perhaps an illustration will make my meaning clearer: when one of those audacious poets affirms that there was once a three-headed and six-handed man, if you accept that quietly without questioning its possibility, he will proceed to fill in the picture consistently—six eyes and ears, three voices talking at once, three mouths eating, and thirty fingers instead of our poor ten all told; if he has to fight, three of his hands will have a buckler, wicker targe, or shield apiece, while of the other three one swings an axe, another hurls a spear, and the third wields a sword. It is too late to carp at these details, when they come; they are consistent with the beginning; it was about that that the question ought to have been raised whether it was to be accepted and passed as true. Once grant that, and the rest comes flooding in, irresistible, hardly now susceptible of doubt, because it is consistent and accordant with your initial admissions. That is just your case; your love-yearning would not allow you to look into the facts at each entrance, and so you are dragged on by consistency; it never occurs to you that a thing may be self- consistent and yet false; if a man says twice five is seven, and you take his word for it without checking the sum, he will naturally deduce that four times five is fourteen, and so on ad libitum. This is the way that weird geometry proceeds: it sets before beginners certain strange assumptions, and insists on their granting the existence of inconceivable things, such as points having no parts, lines without breadth, and so on, builds on these rotten foundations a superstructure equally rotten, and pretends to go on to a demonstration which is true, though it starts from premises which are false.

    Just so you, when you have granted the principles of any school, believe in the deductions from them, and take their consistency, false as it is, for a guarantee of truth. Then with some of you, hope travels through, and you die before you have seen the truth and detected your deceivers, while the rest, disillusioned too late, will not turn back for shame: what, confess at their years that they have been abused with toys all this time? so they hold on desperately, putting the best face upon it and making all the converts they can, to have the consolation of good company in their deception; they are well aware that to speak out is to sacrifice the respect and superiority and honor they are accustomed to; so they will not do it if it may be helped, knowing the height from which they will fall to the common level. Just a few are found with the courage to say they were deluded, and warn other aspirants. Meeting such a one, call him a good man, a true and an honest; nay, call him philosopher, if you will; to my mind, the name is his or no one's; the rest either have no knowledge of the truth, though they think they have, or else have knowledge and hide it, shamefaced cowards clinging to reputation.

    How do we make that point at the very introduction of the topic?

  • A variable in the tutorial (or proposition as I denote it more specific in my additions) is a place holder for a sentence, whereby that sentence needs to be meaningful to the extent that it can be true or false.

    Epicurus knew and even Aristotle was aware of that binary logic might be applicable in full only to timeless sentences and those which refer to past events but not to events in the future. If everybody gets a good enough understanding on Monday and there is time left, we can expand the discussion into the pitfalls of applying logic to future events and how quantum logic avoids those pitfalls. It will still take several months until I finish a book from which I hope to gain a deeper understanding and more confidence in applying quantum logic. I know enough to say something about it but a complete stand-alone presentation on quantum logic will have to wait until 2022.

  • Epicurus knew and even Aristotle was aware of that binary logic might be applicable in full only to timeless sentences and those which refer to past events but not to events in the future.

    YES - that is the issue, and I think it's absolutely critical that people understand that before, during, and after they try to absorb the presentation, because otherwise the problem diagnosed in the Hermotimus excerpt is undetectable.

    Do you have any specific references on those two categories (1) timeless sentences (2) future events?

    I believe part of what you are referring to must include the Epicurus reference to not being willing to state whether Hermarchus will be alive or dead tomorrow.

    And this comment is not directed just to Martin - everyone who is at all interested in this issue needs an understanding of this, so we need to develop means of explaining it that are as memorable as possible.

  • Examples:

    Reference in DeWitt as to the Hermarchus example (however DeWitt is probably wrong in this first one to say Epicurus "ignored" the issue - the reason we have the example is that he was giving the proper response to the problem):

    Seaching for "dialectic" in EAHP produces a huge number of hits. Here are some of the most on point:


    Another, as to education:

  • These excerpts from a nearby post are also relevant:

    Especially this part from Philip DeLacy as to Philodemus' "On Methods of Inference" -->

    The last reference I would throw into this pot is a comment by Richard Dawkins in which he seems to also place Aristotle in Plato's camp:

    Last excerpt illustrating someone who fell victim to this issue, from Heller's biography "Ayn Rand and the World She Made":

  • This exercise is helping me see the connection between this "formal logic" problem and the problem of "necessity."

    Since Epicurus was rejecting "necessity" in human life, in favor of "free will," then it's logical he would be suspicious of too-broad claims of "necessity" in anything involving human life.

    So when DeLacy says:

    combine Epicurus' rejection of dialectic with his rejection of "necessity" and it seems to me that you have a pretty sweeping rejection of the reliability of syllogistic logic in virtually every aspect of human affairs. That doesn't mean syllogistic logic isn't reliable in regard to "material" issues, because the letter to Herodotus points out that most things in the universe are as they have been set in motion from the "formation of the world."

    So it looks like you end up with both necessity (and formal logic) being useful in most purely non-living affairs, but "free will," and therefore freedom from formal logic, in the affairs of living things with freedom of action.