Propositional Logic, Truth Tables, and Epicurus' Objection to "Dialectic"

  • 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”.
  • Martin I have glanced at both the the 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 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.

  • Quote

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

    Currently, my references are only in German:

    Carl Friedrich von Weizsaecker's German original "Aufbau der Physik" of "The Structure of Physics", English edition by Thomas Görnitz, Holger Lyre, Springer Science & Business Media, 2007, ISBN 1402052359, 9781402052354:

    In that book, the book "Quantum logic" from P. Mittelstaedt is referenced. I still have the notes from attending his lectures at University of Cologne about 35 years ago.

    Some articles in "Physik Journal".

  • Also directly relevant to our topic tonight is Usener 376:


    Cicero Academica II.30.97 (Lucullus): They will not get Epicurus, who despises and laughs at the whole of dialectic, to admit the validity of a proposition of the form “Hermarchus will either be alive tomorrow or not alive,” while dialecticians demand that every disjunctive proposition of the form “either x or not-x” is not only valid but even necessary. See how on his guard the man is whom your friends think slow; for “If,” he says, “I admit either of the two to be necessary, it will follow that Hermarchus must either be alive tomorrow or not alive; but as a matter of fact in the nature of things no such necessity exists.” Therefore let the dialecticians, that is, Antiochus and the Stoics, do battle with this philosopher, for he overthrows the whole of dialectic.

    Cicero, On The Nature of The Gods, I.25.70 (Cotta speaking): Epicurus did the same sort of thing in his argument with the logicians. It is an axiom of the traditional logic that in every disjunctive proposition of the form “X either is … or is not …” one of the alternatives must be true. He was afraid that if he admitted anything of this sort, then in a proposition such as “Tomorrow Epicurus will either be alive or he will not be alive,” one or the other of the statements would be a necessary truth: so to avoid this he denied that there was any logical necessity at all in a disjunction proposition, which is too stupid for words!

    Cicero, On Fate, 10.21: Now here, first of all, if it were my desire to agree with Epicurus and deny that every proposition is either true or false, I would rather accept that blow than agree that all things come about through fate; for the former opinion gives some scope for discussion, but the latter is intolerable. So Chrysippus strains every sinew in order to convince us that every proposition is either true or false. Epicurus is afraid that, if he concedes this, he will have to concede that whatever comes about does so through fate; for if either the assertion or the denial is true from eternity, it will also be certain – and if certain, also necessary. [cf. Ibid., 9.19]

    Potentially Relevant in Addition:

    U380 (this may be a good clue to those categories in which dialectical formal logic is especially to be distrusted:

    Aetius, Doxography, I.29.6 [p. 326 Diels] (Plutarch, I.29.2; Stobaeus Anthology, Physics 7.9): Epicurus says that chance is a cause which is uncertain with respect to persons, times, and places.

  • One more from Lucian, similar to Hermotimus, this time from Incaromenippus, An Aerial Expedition. The main relevant part is in bold below but I left text before and after since it is so colorful:

    Menippus. Well, a very short survey of life had convinced me of the absurdity and meanness and insecurity that pervade all human objects, such as wealth, office, power. I was filled with contempt for them, realized that to care for them was to lose all chance of what deserved care, and determined to grovel no more, but fix my gaze upon the great All. Here I found my first problem in what wise men call the universal order. I could not tell how it came into being, who made it, what was its beginning, or what its end. But my next step, which was the examination of details, landed me in yet worse perplexity. I found the stars dotted quite casually about the sky, and I wanted to know what the sun was. Especially the phenomena of the moon struck me as extraordinary, and quite passed my comprehension; there must be some mystery to account for those many phases, I conjectured. Nor could I feel any greater certainty about such things as the passage of lightning, the roll of thunder, the descent of rain and snow and hail.

    In this state of mind, the best I could think of was to get at the truth of it all from the people called philosophers; they of course would be able to give it me. So I selected the best of them, if solemnity of visage, pallor of complexion and length of beard are any criterion—for there could not be a moment's doubt of their soaring words and heaven-high thoughts—and in their hands I placed myself. For a considerable sum down, and more to be paid when they should have perfected me in wisdom, I was to be made an airy metaphysician and instructed in the order of the universe. Unfortunately, so far from dispelling my previous ignorance, they perplexed me more and more, with their daily drenches of beginnings and ends, atoms and voids, matters and forms. My greatest difficulty was that, though they differed among themselves, and all they said was full of inconsistency and contradiction, they expected me to believe them, each pulling me in his own direction.

    Friend. How absurd that wise men should quarrel about facts, and hold different opinions on the same things!

    Menippus. Ah, but keep your laughter till you have heard something of their pretentious mystifications. To begin with, their feet are on the ground; they are no taller than the rest of us 'men that walk the earth'; they are no sharper-sighted than their neighbors, some of them purblind, indeed, with age or indolence. And yet they say they can distinguish the limits of the sky, they measure the sun's circumference, take their walks in the supra-lunar regions, and specify the sizes and shapes of the stars as though they had fallen from them. Often one of them could not tell you correctly the number of miles from Megara to Athens, but has no hesitation about the distance in feet from the sun to the moon. How high the atmosphere is, how deep the sea, how far it is round the earth— they have the figures for all that. Moreover, they have only to draw some circles, arrange a few triangles and squares, add certain complicated spheres, and lo, they have the cubic contents of Heaven.

    Then, how reasonable and modest of them, dealing with subjects so debatable, to issue their views without a hint of uncertainty; thus it must be and it shall be; contra gentes they will have it so. They will tell you on oath the sun is a molten mass, the moon inhabited, and the stars water-drinkers, moisture being drawn up by the sun's rope and bucket and equitably distributed among them.

    How their theories conflict is soon apparent; next-door neighbors? No, they are miles apart. In the first place, their views of the world differ. Some say it had no beginning, and cannot end; others boldly talk of its creator and his procedure. What particularly entertained me was that these latter set up a contriver of the universe, but fail to mention where he came from, or what he stood on while about his elaborate task, though it is by no means obvious how there could be place or time before the universe came into being.

    Friend. You really do make them out very audacious conjurers.

    Menippus. My dear fellow, I wish I could give you their lucubrations on ideas and incorporeals, on finite and infinite. Over that point, now, there is fierce battle; some circumscribe the All, others will have it unlimited. At the same time they declare for a plurality of worlds, and speak scornfully of others who make only one. And there is a bellicose person who maintains that war is the father of the universe.

    As to Gods, I need hardly deal with that question. For some of them God is a number; some swear by dogs and geese and plane-trees. [note: Socrates made a practice of substituting these for the names of Gods in his oaths.] Some again banish all other Gods, and attribute the control of the universe to a single one; I got rather depressed on learning how small the supply of divinity was. But I was comforted by the lavish souls who not only make many, but classify; there was a First God, and second and third classes of divinity. Yet again, some regard the divine nature as unsubstantial and without form, while others conceive it as a substance. Then they were not all disposed to recognize a Providence; some relieve the Gods of all care, as we relieve the superannuated of their civic duties; in fact, they treat them exactly like supernumeraries on the stage. The last step is also taken, of saying that Gods do not exist at all, and leaving the world to drift along without a master or a guiding hand.

    Well, when I heard all this, I dared not disbelieve people whose voices and beards were equally suggestive of Zeus. But I knew not where to turn for a theory that was not open to exception, nor combated by one as soon as propounded by another. I found myself in the state Homer has described; many a time I would vigorously start believing one of these gentlemen; “But then came second thoughts.”

    So in my distress I began to despair of ever getting any knowledge about these things on earth. The only possible escape from perplexity would be to take to myself wings and go up to Heaven.

  • Accurate history or not, here is something also relevant, given that it is so widely accepted as true about Plato:

    Plato FAQ: "Let no one ignorant of geometry enter"

    "Let no one ignorant of geometry enter"

    Tradition has it that this phrase was engraved at the door of Plato's Academy, the school he had founded in Athens.

    More detail:

    Biography: What was Plato Known for


    Plato (c.428-348 BCE)

    Although usually remembered today as a philosopher, Plato was also one of ancient Greece’s most important patrons of mathematics.

    Inspired by Pythagoras, he founded his Academy in Athens in 387 BCE, where he stressed mathematics as a way of understanding more about reality. In particular, he was convinced that geometry was the key to unlocking the secrets of the universe. The sign above the Academy entrance read: “Let no-one ignorant of geometry enter here”.

    Plato played an important role in encouraging and inspiring Greek intellectuals to study mathematics as well as philosophy. His Academy taught mathematics as a branch of philosophy, as Pythagoras had done, and the first 10 years of the 15 year course at the Academy involved the study of science and mathematics, including plane and solid geometry, astronomy and harmonics. Plato became known as the “maker of mathematicians”, and his Academy boasted some of the most prominent mathematicians of the ancient world, including Eudoxus, Theaetetus and Archytas.

    He demanded of his students accurate definitions, clearly stated assumptions, and logical deductive proof, and he insisted that geometric proofs be demonstrated with no aids other than a straight edge and a compass. Among the many mathematical problems Plato posed for his students’ investigation were the so-called Three Classical Problems (“squaring the circle”, “doubling the cube” and “trisecting the angle”) and to some extent these problems have become identified with Plato, although he was not the first to pose them.

    Platonic Solids

    Plato the mathematician is perhaps best known for his identification of 5 regular symmetrical 3-dimensional shapes, which he maintained were the basis for the whole universe, and which have become known as the Platonic Solids: the tetrahedron (constructed of 4 regular triangles, and which for Plato represented fire), the octahedron (composed of 8 triangles, representing air), the icosahedron (composed of 20 triangles, and representing water), the cube (composed of 6 squares, and representing earth), and the dodecahedron (made up of 12 pentagons, which Plato obscurely described as “the god used for arranging the constellations on the whole heaven”).

    The tetrahedron, cube and dodecahedron were probably familiar to Pythagoras, and the octahedron and icosahedron were probably discovered by Theaetetus, a contemporary of Plato. Furthermore, it fell to Euclid, half a century later, to prove that these were the only possible convex regular polyhedra. But they nevertheless became popularly known as the Platonic Solids, and inspired mathematicians and geometers for many centuries to come. For example, around 1600, the German astronomer Johannes Kepler devised an ingenious system of nested Platonic solids and spheres to approximate quite well the distances of the known planets from the Sun (although he was enough of a scientist to abandon his elegant model when it proved to be not accurate enough).

  • Shall we continue for the sake of completeness? ;)



    Pythagoras of Samos (c.570-495 BCE)

    Biography – Who was Pythagoras

    It is sometimes claimed that we owe pure mathematics to Pythagoras, and he is often called the first “true” mathematician. But, although his contribution was clearly important, he nevertheless remains a controversial figure.

    He left no mathematical writings himself, and much of what we know about Pythagorean thought comes to us from the writings of Philolaus and other later Pythagorean scholars. Indeed, it is by no means clear whether many (or indeed any) of the theorems ascribed to him were in fact solved by Pythagoras personally or by his followers.

    The school he established at Croton in southern Italy around 530 BCE was the nucleus of a rather bizarre Pythagorean sect. Although Pythagorean thought was largely dominated by mathematics, it was also profoundly mystical, and Pythagoras imposed his quasi-religious philosophies, strict vegetarianism, communal living, secret rites and odd rules on all the members of his school (including bizarre and apparently random edicts about never urinating towards the sun, never marrying a woman who wears gold jewellery, never passing an ass lying in the street, never eating or even touching black fava beans, etc) .

    The members were divided into the “mathematikoi” (or “learners“), who extended and developed the more mathematical and scientific work that Pythagoras himself began, and the “akousmatikoi” (or “listeners“), who focused on the more religious and ritualistic aspects of his teachings. There was always a certain amount of friction between the two groups and eventually the sect became caught up in some fierce local fighting and ultimately dispersed. Resentment built up against the secrecy and exclusiveness of the Pythagoreans and, in 460 BCE, all their meeting places were burned and destroyed, with at least 50 members killed in Croton alone.

    The over-riding dictum of Pythagoras’s school was “All is number” or “God is number”, and the Pythagoreans effectively practised a kind of numerology or number-worship, and considered each number to have its own character and meaning. For example, the number one was the generator of all numbers; two represented opinion; three, harmony; four, justice; five, marriage; six, creation; seven, the seven planets or “wandering stars”; etc. Odd numbers were thought of as female and even numbers as male.

    The Pythagorean Tetractys

    The Pythagorean Tetractys

    The holiest number of all was “Tetractys” or ten, a triangular number composed of the sum of one, two, three and four. It is a great tribute to the Pythagoreans’ intellectual achievements that they deduced the special place of the number 10 from an abstract mathematical argument rather than from something as mundane as counting the fingers on two hands.

    However, Pythagoras and his school – as well as a handful of other mathematicians of ancient Greece – was largely responsible for introducing a more rigorous mathematics than what had gone before, building from first principles using axioms and logic. Before Pythagoras, for example, geometry had been merely a collection of rules derived by empirical measurement.

    Pythagoras discovered that a complete system of mathematics could be constructed, where geometric elements corresponded with numbers, and where integers and their ratios were all that was necessary to establish an entire system of logic and truth.

    The Pythagorean Theorem

    He is mainly remembered for what has become known as Pythagoras’ Theorem (or the Pythagorean Theorem): that, for any right-angled triangle, the square of the length of the hypotenuse (the longest side, opposite the right angle) is equal to the sum of the square of the other two sides (or “legs”).

    Written as an equation: a2 + b2 = c2.

    What Pythagoras and his followers did not realize is that this also works for any shape: thus, the area of a pentagon on the hypotenuse is equal to the sum of the pentagons on the other two sides, as it does for a semi-circle or any other regular (or even irregular( shape.

    Pythagoras' (Pythagorean) Theorem

    Pythagoras’ (Pythagorean) Theorem

    The simplest and most commonly quoted example of a Pythagorean triangle is one with sides of 3, 4 and 5 units (32 + 42 = 52, as can be seen by drawing a grid of unit squares on each side as in the diagram at right), but there are a potentially infinite number of other integer “Pythagorean triples”, starting with (5, 12 13), (6, 8, 10), (7, 24, 25), (8, 15, 17), (9, 40, 41), etc. It should be noted, however that (6, 8, 10) is not what is known as a “primitive” Pythagorean triple, because it is just a multiple of (3, 4, 5).

    Pythagoras’ Theorem and the properties of right-angled triangles seems to be the most ancient and widespread mathematical development after basic arithmetic and geometry, and it was touched on in some of the most ancient mathematical texts from Babylon and Egypt, dating from over a thousand years earlier. One of the simplest proofs comes from ancient China, and probably dates from well before Pythagoras’ birth. It was Pythagoras, though, who gave the theorem its definitive form, although it is not clear whether Pythagoras himself definitively proved it or merely described it. Either way, it has become one of the best-known of all mathematical theorems, and as many as 400 different proofs now exist, some geometrical, some algebraic, some involving advanced differential equations, etc.

    It soon became apparent, though, that non-integer solutions were also possible, so that an isosceles triangle with sides 1, 1 and √2, for example, also has a right angle, as the Babylonians had discovered centuries earlier. However, when Pythagoras’s student Hippasus tried to calculate the value of √2, he found that it was not possible to express it as a fraction, thereby indicating the potential existence of a whole new world of numbers, the irrational numbers (numbers that can not be expressed as simple fractions of integers). This discovery rather shattered the elegant mathematical world built up by Pythagoras and his followers, and the existence of a number that could not be expressed as the ratio of two of God’s creations (which is how they thought of the integers) jeopardized the cult’s entire belief system.

    Poor Hippasus was apparently drowned by the secretive Pythagoreans for broadcasting this important discovery to the outside world. But the replacement of the idea of the divinity of the integers by the richer concept of the continuum, was an essential development in mathematics. It marked the real birth of Greek geometry, which deals with lines and planes and angles, all of which are continuous and not discrete.

    Among his other achievements in geometry, Pythagoras (or at least his followers, the Pythagoreans) also realized that the sum of the angles of a triangle is equal to two right angles (180°), and probably also the generalization which states that the sum of the interior angles of a polygon with n sides is equal to (2n – 4) right angles, and that the sum of its exterior angles equals 4 right angles. They were able to construct figures of a given area, and to use simple geometrical algebra, for example to solve equations such as a(ax) = x2 by geometrical means.

    The Pythagoreans also established the foundations of number theory, with their investigations of triangular, square and also perfect numbers (numbers that are the sum of their divisors). They discovered several new properties of square numbers, such as that the square of a number n is equal to the sum of the first n odd numbers (e.g. 42 = 16 = 1 + 3 + 5 + 7). They also discovered at least the first pair of amicable numbers, 220 and 284 (amicable numbers are pairs of numbers for which the sum of the divisors of one number equals the other number, e.g. the proper divisors of 220 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55 and 110, of which the sum is 284; and the proper divisors of 284 are 1, 2, 4, 71, and 142, of which the sum is 220).

    Music Theory

    Pythagoras is credited with the discovery of the ratios between harmonious musical tones

    Pythagoras is credited with the discovery of the ratios between harmonious musical tones

    Pythagoras is also credited with the discovery that the intervals between harmonious musical notes always have whole number ratios. For instance, playing half a length of a guitar string gives the same note as the open string, but an octave higher; a third of a length gives a different but harmonious note; etc.

    Non-whole number ratios, on the other hand, tend to give dissonant sounds. In this way, Pythagoras described the first four overtones which create the common intervals which have become the primary building blocks of musical harmony: the octave (1:1), the perfect fifth (3:2), the perfect fourth (4:3) and the major third (5:4). The oldest way of tuning the 12-note chromatic scale is known as Pythagorean tuning, and it is based on a stack of perfect fifths, each tuned in the ratio 3:2.

    The mystical Pythagoras was so excited by this discovery that he became convinced that the whole universe was based on numbers, and that the planets and stars moved according to mathematical equations, which corresponded to musical notes, and thus produced a kind of symphony, the “Musical Universalis” or “Music of the Spheres”.

  • Here's an article from the Internet Encyclopedia of Philosophy on "Propositional Logic" which appears to be becoming the term of choice to refer to what Epicurus questioned. Since many of the texts use "dialectic" however we probably still need to correlate those terms

    Propositional Logic | Internet Encyclopedia of Philosophy

    Propositional Logic

    Propositional logic, also known as sentential logic and statement logic, is the branch of logic that studies ways of joining and/or modifying entire propositions, statements or sentences to form more complicated propositions, statements or sentences, as well as the logical relationships and properties that are derived from these methods of combining or altering statements. In propositional logic, the simplest statements are considered as indivisible units, and hence, propositional logic does not study those logical properties and relations that depend upon parts of statements that are not themselves statements on their own, such as the subject and predicate of a statement. The most thoroughly researched branch of propositional logic is classical truth-functional propositional logic, which studies logical operators and connectives that are used to produce complex statements whose truth-value depends entirely on the truth-values of the simpler statements making them up, and in which it is assumed that every statement is either true or false and not both. However, there are other forms of propositional logic in which other truth-values are considered, or in which there is consideration of connectives that are used to produce statements whose truth-values depend not simply on the truth-values of the parts, but additional things such as their necessity, possibility or relatedness to one another.

    Or is it possible that we need to consider "Dialogical Logic"

    Dialogical Logic | Internet Encyclopedia of Philosophy

    Dialogical Logic

    Dialogical logic is an approach to logic in which the meaning of the logical constants (connectives and quantifiers) and the notion of validity are explained in game-theoretic terms. The meaning of each logical constant (such as “and”, “or”, “implies”, “not”, “every”, and so forth) is given in terms of how assertions containing these logical constants can be attacked and defended in an adversarial dialogue. Dialogues are described as two-player games between a proponent and an opponent. A dialogue starts with an assertion made by the proponent. This assertion can then be attacked according to its logical form by the opponent. Depending upon the kind of attack, the proponent can now either defend against, or attack, the opponent’s move. The two players alternate until one player is unable to make another move. In this case, the dialogue is won by the other player who made the last move. An assertion made in the initial move by the proponent is said to be valid, if the proponent has a winning strategy for it, that is, if the proponent can win every dialogue for each possible move made by the opponent. The dialogical approach was initially worked out for intuitionistic logic and for classical logic; it has been extended to other logics, among them modal logic and linear logic.

    I see there does not appear to be an entry on "Dialectic"

    Dialectic - Wikipedia


    From Wikipedia, the free encyclopedia

    Jump to navigationJump to searchFor varieties of language, see Dialect. For electrical insulators, see Dielectric.

    Dialectic or dialectics (Greek: διαλεκτική, dialektikḗ; related to dialogue; German: Dialektik), also known as the dialectical method, is a discourse between two or more people holding different points of view about a subject but wishing to establish the truth through reasoned argumentation. Dialectic resembles debate, but the concept excludes subjective elements such as emotional appeal and the modern pejorative sense of rhetoric.[1][2] Dialectic may thus be contrasted with both the eristic, which refers to argument that aims to successfully dispute another's argument (rather than searching for truth), and the didactic method, wherein one side of the conversation teaches the other. Dialectic is alternatively known as minor logic, as opposed to major logic or critique.

    Within Hegelianism, the word dialectic has the specialised meaning of a contradiction between ideas that serves as the determining factor in their relationship. Dialectical materialism, a theory or set of theories produced mainly by Karl Marx and Friedrich Engels, adapted the Hegelian dialectic into arguments regarding traditional materialism. The dialectics of Hegel and Marx were criticized in the twentieth century by the philosophers Karl Popper and Mario Bunge.

    Dialectic tends to imply a process of evolution and so does not naturally fit within classical logics, but was given some formalism in the twentieth century. The emphasis on process is particularly marked in Hegelian dialectic, and even more so in Marxist dialectical logic, which tried to account for the evolution of ideas over longer time periods in the real world.

    of course THIS, referencing Popper, who is an author Martin has discussed reading:


    Karl Popper has attacked the dialectic repeatedly. In 1937, he wrote and delivered a paper entitled "What Is Dialectic?" in which he attacked the dialectical method for its willingness "to put up with contradictions".[62] Popper concluded the essay with these words: "The whole development of dialectic should be a warning against the dangers inherent in philosophical system-building. It should remind us that philosophy should not be made a basis for any sort of scientific system and that philosophers should be much more modest in their claims. One task which they can fulfill quite usefully is the study of the critical methods of science" (Ibid., p. 335).

    In chapter 12 of volume 2 of The Open Society and Its Enemies (1944; 5th rev. ed., 1966), Popper unleashed a famous attack on Hegelian dialectics in which he held that Hegel's thought (unjustly in the view of some philosophers, such as Walter Kaufmann)[63] was to some degree responsible for facilitating the rise of fascism in Europe by encouraging and justifying irrationalism. In section 17 of his 1961 "addenda" to The Open Society, entitled "Facts, Standards and Truth: A Further Criticism of Relativism", Popper refused to moderate his criticism of the Hegelian dialectic, arguing that it "played a major role in the downfall of the liberal movement in Germany [...] by contributing to historicism and to an identification of might and right, encouraged totalitarian modes of thought. [...] [And] undermined and eventually lowered the traditional standards of intellectual responsibility and honesty".[64]

    The philosopher of science and physicist Mario Bunge repeatedly criticized Hegelian and Marxian dialectics, calling them "fuzzy and remote from science"[65] and a "disastrous legacy".[66] He concluded: "The so-called laws of dialectics, such as formulated by Engels (1940, 1954) and Lenin (1947, 1981), are false insofar as they are intelligible."[66]


    That last line is a good one: "False insofar as they are intelligible!" :)

  • A good time to restate the question:

    What we are trying to do ultimately is get a firm fix on what it was that Epicurus was rejecting, while still embracing "reason" in PD16!

    All this discussion of details is irrelevant and worthless unless we keep that goal in mind.

  • OMG that is very interesting! Thank you Joshua! What what a great Latin phrase for the pseudo-Romans like Don and me -- EX FALSO SEQUITUR QUODLIBET! How many occasions that fits!

    And I bet you're right that if we researched Soissons we could find more that is relevant to the essential insight of the "It isn't necessary that Hermarchus be either alive or dead tomorrow so I'm not engaging in your game" observation!

    (until such time as OMZ is established to mean Oh My Zeus I've stuck with OMG)

    Now we have to know what a PARVIPTONIAN is!

  • Also need to note for Don't benefit here that while I still today think that the issue of absence of necessity, arising from human free will, is an important part of the refusal to say that hermarchus must be either alive or dead tomorrow, I continue last night's caveat that I could be wrong on that and that there may still be a purely logical point beyond necessity that Epicurus was concerned about.

    So I would say that until that issue is resolved we're still on the hunt for the most exact way to express Epicurus' concern.

    Maybe it's two steps that are independent of each other in the Hermarchus example ----

    1 - there's no direct linkage (necessity) between the proposition and the conclusion. (a general objection to all propositional logic)

    2 - the reason there's no direct linkage in this particular case is the presence of human free will. (the specific absence of linkage that applies in this case)