Logic – Greece & Aristotle
Heraclitus & The Logic Of The Cosmos
Hegel claimed that Heraclitus (535 – 475 BCE) was the first true philosopher in human history for recognizing that opposites such as good and bad or true and false change with perspective over time, just like day and night. Heraclitus may not have been the first philosopher ever, but he is the first Greek philosopher to talk about talking, logos, the basis for our word logic, and one of the first people in history to argue that the Cosmos is logical, but he does not mean logical in the way that Aristotle and many others think.
Heraclitus lived in Ephesus, which was part of the Persian empire for most of Heraclitus’ life, on what is today the West coast of Turkey, around the same time that Pythagoras and Parmenides, two of the other famous first philosophers of ancient Greece, lived in what is today Southern Italy. Pythagoras and Parmenides argued that true Being is unchanging, with Pythagoras focused on the harmony of mathematics and Parmenides the impossibility of non-being and thus change. Heraclitus argued that the only constant is change, all things are in continuous flux, and so we can never step in the same river twice, his most famous statement. He also argued that the cosmos is ruled by conversation, and wisdom is seeing how all things converse together by taking both sides.
The Fragments of Heraclitus are the opening and popular quotes of the single work that Heraclitus wrote, On Nature, the title of far too many philosophical texts of the Greeks, effectively “How Stuff Works,” which he left as an offering to the Temple of Artemis, one of the wonders of the ancient world. Before we read the first fragment and others, however, it is important to understand what Heraclitus means when he says the word ‘word’. The word that Heraclitus used for ‘word’ is logos, the Greek origin of our word logic. While modern people sometimes understand logic as a mathematical or computer language, for ancient Greek thinkers such as Heraclitus, Plato and Aristotle, logic is arguing, explaining and understanding things, a human practice that seeks agreement with others about what is common in things through conversation. Heraclitus uses the word word to refer to his own talk, his own text, his own understanding, but also the superior conversation of the gods which steers the cosmos, the true understanding and discussion.
Experts, the sort of people Heraclitus warns us about who spout tricky, lying words, argue that Heraclitus identified consciousness with the element air, the breath of life. When Heraclitus uses the word ‘word’, he is referring to the stuff of air, breath, speech and life, such that talking cosmology and philosophy is kindling our minds and civilization. Our mind fires see things in visions and mean things with words, heating air with fire to talk to each other, so when Heraclitus opens his text saying “This Word” is eternal but hard to understand, with ‘Word’ often capitalized and sounding biblical, he means his word and explanation of how the Universe works, as well as the plan of the Universe which causes everything to continuously happen. Heraclitus argues that human words are baby talk to the gods, so the best that his words can do is point us beyond human words to the unending mind of the Universe, which is the more “logical” and larger conversation. The text Heraclitus wrote supposedly opened with the words:
This wisdom (word, logos) is forever true, but we are unable to understand it before we hear it and are still unable to understand it even after we have hear it, even though all of existence follows from it. Some foolishly try to explain what I put in front of you by dividing things and saying how each thing truly is by itself, while the rest of humanity makes no attempt at all to understand, and do not see what they do while awake anymore than they remember what they did when asleep.
Unfortunately, Heraclitus thinks that most people are fools and effectively asleep, saying when we dig we find far more earth than gold (22) and the best are worth ten thousand. (49) Even though thought is common to all (113) and everyone has the capacity to dive into themselves to better know and rule themselves, (116) gaining wisdom to see, speak and act more in concert with everything and everyone outside of themselves by doing so, (112) most people do not understand the people and things they see everyday, but think that they do. (17)
Heraclitus says that most people don’t know how to listen or how to speak, (19) how to give and how to take, balancing self and other. We have the disease of pride, (46) which is more important to extinguish than our house when it catches fire. (43) We have trouble listening to what our own eyes and ears are telling us (107) and are often “absent when present”, hearing others as well as the deaf (34) and acting as if we are asleep, (73) dreaming things about the world that are delusional because we cut ourselves off from other things with our desires, separating our small fire from the big one. Thus, most people are “fluttered with every word,” (87) shaken because they seek permanence in isolation rather than integration, bringing not safety but rather anxiety. Heraclitus says that all the power of emperors is merely time playing like a child building sandcastles. (52)
Some follow the mind beyond the mortal world, seeking knowledge and wisdom about the cosmos overall, which you would think would set you in the right direction, but Heraclitus ridiculed the famous poets and philosophers of his day, saying that after listening to the words of many, he had heard not one who realized wisdom is beyond all other things, with perspective beyond what can be expressed in mere human words. (108) It is wise to remember that rhetoric is the prince of liars, (81) we all seem like babies and apes to the gods who don’t see any of us as beautiful or hear anything we say as wise. (79, 82, 83) Heraclitus said, “In everything we have achieved the excellence of apes,” and, “Awake, we share one world in common, but asleep we each turn aside into a world of our own.” (89)
Like dogs, we bark at the unfamiliar, (97) but we can gain the wisdom to see that it is not good to get everything we desire (110) and what fights us also helps us, with many never understanding that the harmony of the cosmos is good against bad like a bow on a string. (8, 51) Heraclitus says that hunger makes satisfaction pleasant, as sickness does health and tired does rest, (111) and jokes that surely good and bad are the same thing to doctors, who demand payments for torturing the sick. (58) It is unclear whether or not Heraclitus thinks that horrible cures are useless, or proof that the cosmos works in contradictory, conversational ways, and is giving us heck to show us the light.
Pyrrho, Sextus & Skepticism
Pyrrho (360 – 270 BCE), the founder of Skepticism of ancient Greece, was from Elis, Northwest of Athens on the Dorian peninsula. Diogenes Laertius says that Pyrrho was a painter, an interesting profession for a thinker who argues that reality is appearances and human judgements are images that never fully capture the original. The word skeptikos meant inquirer, someone who investigates matters continuously, as if we always need to seek further beneath appearances. While skeptics are relativists, critical of claims to absolute universal knowledge, skeptics seek relative truth and insight as continuous engagement.
As a young painter, Pyrrho became fascinated with philosophy through the works of Democritus, the atomist who was quite skeptical of human judgements in spite of his atomic theory. Democritus said, “Reason is a powerful persuader”, and about the gods and the workings of the heavens, “Man is what we know”. Critical of knowledge, said we should have much thought rather than much learning, and said, “In reality, we know nothing, for truth is in the depths,” arguing that we must remind ourselves that we are always relatively removed from the reality that surrounds us.
Pyrrho traveled with his teacher Anaxarchus, also a follower of Democritus, and Alexander, student of Aristotle and emperor, to Persia and India, some sources say as a soldier and others as a scholar. Alexander failed to conquer India, unlike he had Egypt and Persia. It is said that Pyrrho learned from the Persian Magi as well as Indian ‘gymnosophists’, a strange term meaning those who trained and studied both gymnastics (likely yogic postures) and philosophy. These could have been Jains, who were known for logical debate as well as extreme practices of bodily discipline, sometimes fasting while standing in the jungle for days. Sources say that one Indian gymnosophist set himself on fire to go willingly to death, terrifying Alexander and his entourage.
Pyrrho’s skepticism is summed up under the term acatalepsia, withholding judgement. Like Zeno, Pyrrho taught that any belief can be countered by the opposite belief which contradicts it. Thus, like Jains, Pyrrho held that reality is not one-sided, like human judgements, and that all judgements are partial and should be treated as hypothetical, as a best guess. As evidence of this, Pyrrho pointed to the continuous fact of differences of opinion among both the foolish and the wise, constant argument among both the educated and uneducated, the common and the distinguished alike. Legend has it that Pyrrho could defeat anyone in argument, then take his opponent’s position and defeat his own. He could do this because he knew that human truth was fundamentally one-sided, and so could not eliminate opposition.
Sextus Empiricus (160 – 210 CE) is the Greek skeptic whose Pyrrhonian texts survive, including Outlines of Pyrrhonism, Against the Professors, Against the Mathematicians, Against the Astronomers, Against the Rhetoricians, Against the Musicians, Against the Ethicists, Against the Logicians, Against the Physicians, Against the Physicists, and, most centrally, Against the Dogmatists. Sextus was likely a doctor who lived in Alexandria, Egypt, but some sources place him in Athens and others in Rome. The famous Greek doctor Galen says skepticism was a popular philosophy among doctors, as it is always possible to be wrong about a diagnosis and change treatment depending on outcomes, such that practical judgement is an imperfect process of interpretation.
Sextus says that in any matter being investigated we can A) assert we have found the truth, B) deny that any truth can be known, or C) continue to investigate. The first is dogmatism, which he says includes Aristotle, Epicurus and the Stoics. Sextus says early in the work that the Stoics are his chief dogmatic opponents, the last we will cover. The second is the position of the Academics, of Plato’s Academy. The third position is that of skeptics like him, who continue to investigate and describe things as they appear. Pyrrho is the first, according to Sextus, to systematically and thoroughly commit himself to skepticism. The second position, a pessimistic nihilism Sextus identifies with members of Plato’s Academy long after Plato, is not for Sextus genuine skepticism, but a dogmatic position that knowledge and truth are impossible.
Sextus says that by suspending judgement, we can achieve tranquility. Clearly, this suspension of judgement is not a suspension of investigation, and neither is achieving tranquility. How are we to suspend judgement? Sextus says that it comes through opposing appearance against counter-appearance and opinion against counter-opinion, “crosswise” as Sextus puts it. As an example, he gives a tower which has flat sides appearing round from a distance. There was a similar example in a children’s show I watched as a kid where a witness on the street says two triangles and a square robbed a bank, but the witness on the roof says two circles and a square robbed the bank, and it turns out that a pyramid, a cone and a cylinder in little bank-robber masks robbed the bank.
While dogmatists argue about what is universal and common to all, arguing that Plato or Epicurus is exclusively right, Sextus says that poets and playwrights have a better understanding, knowing all too well the tragedy that follows from various feelings and convictions. The dogmatists, claiming to exclusively know the truth, are themselves part of a dispute, evidence that one must take a position on a matter to see things a certain way. The various dogmatic schools, opposed to each other as well as to skepticism, show that dogmatism is insufficient for investigating truth. We believe that the sun will rise because the sun has risen again and again, not because we or anyone has proven it certainly will tomorrow.
Sextus says that all the modes of skepticism before him have been boiled down to two by recent skeptics such as himself: Things must either be known in themselves, or known via something else. If things are known in themselves, it results in circular reasoning. If things are known in something other than themselves, it results in infinite regress. Consider that if we ask Steve if he is honest, Steve could tell us he is, which is circular and uncertain, or he could ask Tom, who says Steve is honest, but now we don’t know how honest Tom is. If we ask Steve about Tom, this is circular, but if we ask Mary about Steve and Tom, now we have to ask Steve or Tom or somebody else about Mary. It would be incredible if everyone was lying to us intentionally in a strange conspiracy, but not unusual that a large group sustains a belief we find quite wrong. This is known in some circles as the Problem of the Circle and the Line, and it still has a central place in debates about foundationalism, the position that there are basic logical beliefs.
Aristotle, Interpretations & Perfect Forms
Plato, Aristotle’s teacher, argued that the One, the mind of the Cosmos, unfolds via logos and logic, like Heraclitus says, which makes the Cosmos logical, but what is the form of the cosmic logic that underlies all things? In Plato’s Parmenides, the title character argues that the “greatest difficulty” is that if we know things by their forms, then we only know the forms by knowing the form of the forms, which either leads to an infinite regress, or ends in the One as the form itself, which is quite simple and circular, explaining nothing in particular. Parmenides proceeds to show Socrates many contradictory conclusions about the One and all, including that it is both one and many, does and doesn’t exist, changes and doesn’t change, and does and does not have contrary, contradictory properties.
Plato does not stop there like Heraclitus, Pyhrro or Sextus, however, and continues through his plays to have Socrates say that there is a fixed, unchanging form, and accuses Heraclitus, Homer and most philosophers other than Pythagoras with confusing forms with continuous flux. In Plato’s Theaetetus, Socrates says we can go through a wagon part by part, primary element by primary element, just as we write words letter by letter, such that we find “the way to the whole through the parts,” as if there is a set number of things to know, the forms, and an order through which to know them. Unfortunately the Theaetetus dialogue ends with Socrates saying he has to get to court about some sort of trial, and that he and Theodorus should meet again tomorrow. Hopefully all of that worked out. Plato probably wants students to join his school and learn the forms from him, personally.
Aristotle (384 – 322 BCE) did just that, and studied with Plato at the academy for twenty years, from when he was 17 to Plato’s death (386 – 347 BCE). Aristotle’s father was the personal physician of Amyntas, King of Macedon. Sources say the Academy was taken over by Plato’s nephew Speusippus even though Aristotle was more qualified, possibly because Aristotle had come to disagree with Plato’s theory of ideal forms, so Aristotle left, traveled and studied in Ionia and Asia before King Philip of Macedon invited him to tutor his young son Alexander, thirteen at the time, who would go on to conquer and unify ancient Greece, Egypt and Persia within his brief empire. Aristotle also tutored Ptolemy and Cassander, who took over large parts of the empire after Alexander’s death.
Aristotle founded his school in Athens in 335 BCE, holding meetings of his students at a public gymnasium named the Lyceum after a form of Apollo as a wolf god. The Lyceum had seen earlier philosophers give public talks, including Socrates and Plato, and it continued to be the meeting place for followers of Aristotle until Athens was sacked by the Romans 250 years later. The followers of Aristotle were known as the Peripatetics, the “Walk-about-ers”, as Aristotle enjoyed walking as he lectured, taught and answered questions. In the mornings, he would walk with a select number of advanced students in detailed, advanced seminars, and then in the evening give general talks open to any who would gather. A study at Stanford has shown that if one wants to retain knowledge through study, one should sit, but if one wants to stimulate critical and creative thinking, walking outside is best.
After Alexander died, Aristotle feared being killed by the Athenians as he was not only a barbarian foreigner but the tutor of Alexander, who was not loved much by many Athenians. After he was accused publicly of impiety towards the gods, showing little in Athens had changed since the death of Socrates, Aristotle left Athens saying he would not allow the Athenians “to sin against philosophy twice”, recalling the death of Socrates due to similar charges. Aristotle died within a year of leaving Athens from a stomach illness. Some sources said that he was poisoned, like Socrates though not self-administered, but this is doubtful.
Aristotle is one of the most famous logicians in history, whom many would call the father of logic itself, but Aristotle, like Kanada of India, was not primarily interested in logic or debate, but rather what we can say about the cosmos and human mind, which includes what can or can’t be argued successfully about it. Followers of Aristotle, possibly including Andronicus of Rhodes, collected the six works Aristotle wrote about definition and debate, which may have been public texts or private sets of notes for his students, into a work known as the Organon around 40 BCE, 300 years after Aristotle started his talks and walks around the Lyceum. We will cover some of the central ideas of his Organon, including the four perfect forms of the syllogism, and what Christian theologians such as Boethius called the Square of Opposition.
In the Categories Aristotle assumes that things have purposes according to their natures, and these purposes correspond to concepts that can be put into words. Aristotle believes that we must observe nature and say what can be said of things, based on their similarities and differences. For example, Aristotle says that ‘animal’ can be said or predicated of both a man and an ox, just as ‘man’ and ‘animal’ can be predicated of any human male individual. A Genera or Genus is the family to which a thing belongs. This is paired with Species, the subgroup of the family. He says that if you are giving an account of a particular tree, you would say more with the species of tree than you would of the genus ‘plant’.
Aristotle writes, “The distinctive mark of substance is that it can admit contrary qualities. Thus, a color cannot be both white and black, nor can the same act be good and bad: this is true for any non substance, but substances can at different times be white and black…The same individual person is at one time white, at another black, at one time warm, at another cold, at one time good, at another bad.” Note that by “white” Aristotle means a sick, pale or elderly person, not a judgement about ethnicity. Aristotle says the proposition “He is sitting,” can be true, then false, then true as a person sits, stands, and then sits again. Aristotle denies that things can possess contrary qualities (be both white and black) or be in contrary states (good and evil) at the same time. The old joke about a newspaper being black and white and red all over says otherwise. Aristotle considers time, but does not consider that part of a person can be white, or pale, or sick, and another part not, like having great eyesight and a sore throat.
Heraclitus, an opponent that Plato and Aristotle argue against, thought that things were good and bad by perspective and positioning and so things can have contrary qualities and be in contrary states at the same time, and even in the same place. Aristotle completely denies the possibility of this, saying “If, then, someone says that statements and opinions are capable of admitting contrary qualities, his contention is unsound”. In his On Interpretation, Aristotle says that we must limit our discussion to propositions that are true or false exclusively. He argues that prayers, promises and requests are neither true nor false because they do not guarantee whether they will be fulfilled or not. An affirmation is a positive statement of something, a denial a negative statement. Thus, “I exist” is a positive affirmation, as is “This apple is red”, whereas ‘I do not exist’ or ‘I doubt that I exist’ are negative denials, as is “This apple is not red”.
Aristotle says there are also universal and particular statements, which corresponds to fixed, unchanging properties in things, particularly the forces above the lunar sphere and imperfect, changing properties and forms below. All people are good and No people are good are universal propositions, and Some people are good and Some people are not good are particular propositions. Notice that All people are not good and No people are good are equivalent and exchangeable, as are Not all people are good and Some people are not good. The Square of Opposition traditionally puts universal on top, particular on the bottom, down with us mortals, positive affirmation on the left and negative denial on the right, such that the top left positive universal corner is All people are good (All A is B), the top right negative universal corner is No people are good, the bottom left positive particular corner is Some people are good, and the bottom right negative particular corner is Some people are not good.
Sometimes Aristotle’s absolute statements are called generals, and sometimes universals, which is a problem, as we use the word general in a relative way, and the term universal in an absolute way, much like how the conjunction AND can be more inclusive and loose or exclusive and strict, requiring every last part to be included together. We can say that generally oxen have four legs, but if there is one or more oxen that don’t we can’t say that oxen universally have four legs. Aristotle would probably say that an oxen that doesn’t have four legs is not a full, healthy oxen, and using the term universal is more what he meant, arguing against Heraclitus that we can’t have some and some when it comes to fundamental categories such as four legged animals or oxen.
Aristotle says that the statements on what we can see as opposite corners of the Square of Opposition cannot both be true at the same time, such that All A is B and Some A is not B cannot both be true, contradicting each other, and No A is B and Some A is B cannot either. He also says that either the particular positive or particular negative must be true, such that either Some A is B or Some A is not B, but this is only true, as later logicians noted in commentaries on Aristotle, if there are some As to begin with. If there are no unicorns, then neither Some unicorns are good nor Some unicorns are not good need be true. Also, if unicorns exist, but are relatively good and not good, both and neither as Heraclitus or Nagarjuna would say, then not only both particulars, but all four corners are true, as all and some unicorns are good and not good.
Aristotle notices a problem with the categories of good and not-good, because not-good and bad are two different things if neutral, neither good nor bad, counts as not-good. We hear “not good” both ways, likely depending on time and place. Does A is good contradict A is bad or A is not good more? Confusingly, Aristotle says that neutrality is opposed to both good and bad, as it is neither, and tries to solve the problem by saying that if A is good, it seems more contrary, relatively speaking, to say A is not good than it is to say A is bad, which seems off. If I politely say A is not good, rather than say A is bad, and I am wrong either way, because A is actually good, I don’t know why the softer, safer statement is more wrong, especially if this threatens to make our reasoning unsound according to Aristotle’s earlier claims about categoricals.
Much like the two ways we use OR inclusively and exclusively, such that we can have more than one or only one choice, both or either the bottom particular corners of the Square can be true, such that if Some A is B, it is possible that Some A is not B, but not necessary, like inclusive OR, but only one or the other, but necessarily one, of the top universal corners of the Square While all and none are absolute and exclusive, like polar black and white, some and some not are relative and inclusive shades of grey. According to Hegel and others centuries later, when we are dogmatic we are like Aristotle and seek black and white absolute, objective answers, and when we are skeptical we are like Heraclitus and seek shades of grey and open, subjective questions.
Aristotle presents us with dozens of forms of argument called syllogisms that can be used in debate, but only the first four “perfect” forms, as others after Aristotle call them, require no additional information to be valid, as Aristotle himself tells us, so it is these four forms that the followers of Aristotle recreated for centuries. There is a syllogism with two premises and a conclusion for each corner of the Square of Opposition, and the conclusion of each is the statement of each corner. We take the medieval names for the four, which are Barbara, Celarent, Darii and Ferio, one for each of the first four consonants of the Latin alphabet.
If All A are B, and All B are C, then All A are C.
If all humans are animals, and all animals are alive, then all humans are alive.
In the Venn diagram form, if a circle A is entirely within a circle B, and this circle B is entirely in a third circle C, then circle A must be entirely inside circle C.
If All A are B, and No B are C, then No A are C.
If all humans are animals, and no animals are made of stone, then no humans are stone.
As a Venn diagram, if A is entirely within B, and no B is inside C, then no A can be inside C.
If Some A are B, and All B are C, then Some A are C.
If some animals are humans, and all humans are funny, then some animals are funny.
As a Venn diagram, if some A is inside B and all B is inside C then some A must be inside C.
If Some A are B, and No B are C, then Some A are not C.
If some animals are humans, and no humans are reptiles, then some animals are not reptiles.
As a Venn diagram, if some A is in B and no B is in C then some of A is outside C.
Aristotle argued we can derive true knowledge from chaining these forms together. He argues in the text that since the Scythians have no vines, they thus no grapes, no intoxication, and thus no flute players. Aristotle, like Plato in the Symposium, associates intoxication with flutes, like associating saxophones and scotch on the rocks. He gives another example. If something is metal, then it will cut, and since hatchets are made of metal, therefore hatchets will cut. In the 1600s, Sir Francis Bacon rejected the syllogism as fallible, just as Islamic scholars and scientists had before, arguing that they were too limited for doing varied and fine distinctions in science. Consider that all metal things do not cut, nor do all knives, the butter knife being an example of something metal and a knife that does not cut, created by a French nobleman to prevent his dinner guests from picking their teeth.
Aristotle states that, as we can see with the Ferio Venn diagram, if we only have some, some and some statements, we can’t draw conclusions at all. Aristotle sometimes goes back on his earlier statements and gives us examples when things that are normally universal and certain can be conditional, can be different in certain situations and circumstances. He says that it is never right to kill your father, but among the Triballi tribe, the gods sometimes demand it. Since the gods are one’s super-parents and one’s obligations to them supersedes one’s obligations to one’s parents, he says that the Triballi rightly sacrifice their fathers. Notice that Aristotle believes that the polytheistic gods are real and that human sacrifice is sometimes quite logical and rational. He also states in his other work that all crows are black and all swans are white, but unfortunately for Aristotle both white crows and black swans thrive in Australia.
Aristotle also provides us with defenses against syllogisms, to defend against presumably good arguments, but on the side that doesn’t seem to be certainly true. He says that in order to avoid having a syllogism drawn against one’s own argument, one should not let the opponent give the same term twice over. If one’s opponent argues that A is B, and B is C, therefore A is C, one should attack the twice used middle term (the B that links A and C in the syllogisms) to prevent an argument from reaching a conclusion. For example, if one’s opponent argues war is American, what is American is good, therefore war is good, one should argue that the war is only somewhat American, that only some of America is involved in war, or that only some of America is good because America is being used to link war to the good. It seems that we naturally know to do this in arguing, just like using the forms, long before we take a logic class or read Aristotle. If we want to destroy a position, we show that it is relative, not absolute.
In Aristotle’s Sophistical Refutations, he lists fallacies that are common errors in argument beyond mistakes made in chaining syllogisms and forms together, much as Gautama does in the Nyaya Sutra. The Fallacy of Equivocation is confusing a word that means one thing with meaning another. Many today use the classic Who’s on first routine to illustrate, with Who as the name of the player on first, so the question, Who’s on first? could be answered Who is, or Yes. The Fallacy of Amphibology is confusing a sentence that means one thing with meaning another, like equivocation, but for whole statements. If I say you can have one car or another, and you wrongly interpret my or to be inclusive, such that you can have more than one, I could accuse you of amphibology, as the sentence can be understood in more than one way. Notice that equivocation and amphibology is a mistake we can make in interpreting others, but also in interpreting ourselves, such that we are changing the thesis, as the Nyaya would say.
There are several fallacies Aristotle lists that seem sorts of amphibology. The Fallacy of Accent seems to be a sort of amphibology, understanding a sentence wrongly based on what word is accented, but Aristotle lists it separately. Many have noted that we hear sentences quite differently based on which word is accented, which we can see if we say the sentence I think that she should have got the job with the accent on each word, one at a time (Consider: I think that she SHOULD have got the job, versus I think that SHE should have got the job). There is also the Fallacy of Figure of Speech, which the Nyaya list also, misunderstanding a metaphor, which also seems a sort of amphibology, or at least equivocation, depending on how many words are used.
The Fallacy of Composition is wrongly attributing the property of a part to a greater whole. For example, “If water is wet, and humans are three fifths water, then humans are wet”, or “If San Francisco is progressive, then all of California is progressive”. The converse Fallacy of Division is wrongly attributing the property of the greater whole to a particular part, the fallacy of composition in reverse. For example, “If water is wet, and water has two hydrogen molecules, then hydrogen is wet”, or “If San Francisco is progressive, then my conservative uncle who lives there must be progressive”. Bigotry and prejudice are types of fallacious composition and division. If I say, “He is a Hindu, and he is a jerk, so all Hindus are jerks”, I have committed the fallacy of composition, judging the group by what is thought of the individual. Likewise, if I say, “All atheists are immoral, and she is an atheist, so she is immoral”, I have committed the fallacy of division, judging the individual by what is thought of the group.
There are several fallacies that mistake the structure of the argument as a whole, beyond mistaking the word or the statement. There is the Fallacy of Irrelevant Conclusion, missing the point, also known as a red herring. There is the Fallacy of Begging the Question, which similarly is stating something questionable, but saying something that requires further evidence rather than stating something that isn’t important. The Fallacy of False Cause is misunderstanding something prior as cause when it isn’t, such as thinking the moon causes people to go to sleep. Conversely, there is the Fallacy of Affirming the Consequent, assuming something prior is a cause when it isn’t, but it often is, such as thinking that if drugs can make people crazy, then all crazy people must be on drugs.
Finally, there is the Fallacy of the Multiple Question, asking a question that suggests things that either haven’t been stated or aren’t true, also known as a leading question. The famous unsavory example is ye olde Have you stopped beating your spouse and/or kids? My favorite joke from the long dead cartoon show The Critic is a fantastic leading question, along with qualifying for several of the fallacies covered. There is a fire in the skyscraper where Jay Sherman, television critic, shoots his show, and he passes out from the smoke in his dressing room. His chain-smoking coworker finds him, and she carries him down the stairs, drops him on the curb, and lights up another smoke. A TV reporter appears, and says, “Jay Sherman, isn’t this just like the time that the mother lifted the Volkswagen off of her child, except in this case, YOU are the Volkswagen, and the child… is the child in all of us.”
The Stoics, Chrysippus & Connectives
Stoicism was founded by Zeno of Citium (334 – 262 BCE), a Phoenician living in the capital of ancient Cyprus. Zeno practiced being a Cynic under Crates, living simply in public without luxury. Once, Crates had Zeno carry a pot of lentil soup around Athens all day, until Crates suddenly smashed the pot, covering a surprised Zeno in soup in the midst of a crowd. When Zeno began to run away embarrassed, Crates called out, “Why are you running, little Phoenician? Nothing terrible has happened to you!”, attempting to teach the young Zeno that the things and responsibilities we bear can suddenly be destroyed, and the judgements of others are not to be feared.
After studying Cynicism as well as Platonism, Pythagoreanism and other schools of thought, Zeno began teaching in the Athenian marketplace atop the Stoa Poikile, the raised “painted porch” a public stage painted with murals depicting the great battles involving the Athenians. It is from this porch that ‘Stoicism’ gets its name. Zeno’s lectures drew many followers, including rich patrons and kings. He was offered Athenian citizenship, but he declined, fearing it would betray and anger his fellow Phoenicians.
Zeno was also known for speaking briefly, and chastising others who spoke at length without getting to the point. After his follower Ariston had been talking at length, Zeno said, “It would be impossible for you to speak this way if your father had not been drunk when he made you”. When another young follower was speaking too long, Zeno said, “Your ears have run down into your throat”. When yet another young follower was making unfounded arguments, Zeno said, “This is why we have two ears and only one mouth”. He is also said, “It is better to trip with the feet than with the tongue”.
For Zeno and the Stoics, studying Logic was important for investigating, arguing and avoiding deception, to prevent being persuaded by the faulty arguments of others. Zeno believed that some matters are incomprehensible but others are comprehensible, and it is the goal of philosophy to refrain from pursuing the incomprehensible and pursue and grasp the comprehensible. Zeno taught his stages of argument via logic by using his hand as a metaphor. Stretching out his hand, palm open as if to receive, he would say, “Perception is like this”. Closing his fingers slightly, he would say, “Assent is like this”. Zeno considered assent, or agreement, to be a free act, such that we can choose whether or not to agree with our perceptions. Closing his hand into a fist, Zeno would say, “Comprehension is like this”, and then clasping his fist in his other hand, he would say, “Knowledge is like this”.
Chrysippus (279 – 206 BCE) was the second patriarch of Stoicism who systematized Zeno’s teachings, saying, “Give me the principles, and I will find the proofs myself”. Originally from Ionia, he moved to Athens as a young man where he wrote hundreds of works, all of which are lost, only fragments surviving in the works of others. While Aristotle’s syllogisms make use of ‘If’ and ‘then’, they do not deal with common conjunctions such as ‘and’, ‘or’, and ‘because’. Chrysippus also used conjunctions to make probabilistic statements, such as ‘more likely than’ and ‘less likely than’. He also studied paradoxes, like those of the Eleatic Zeno, and logical fallacies. In ancient Greece and Rome, Chrysippus was as famous a logician as Aristotle for his work, but because the Neo-Platonists took up the logic of Aristotle, Plato’s student, and not Stoic logic, it was Aristotle’s logic that became famous in the Islamic Golden Age and Medieval Europe. It was only with the development of modern logic that Chrysippus’ genius was again recognized.
Epictetus (55 – 135 CE) was a Stoic slave who lived in Rome. His master was secretary to the infamous emperor Nero, who supposedly fiddled while Rome burned. After acquiring his freedom, he taught Stoicism in Rome until philosophers were banned from Rome by Emperor Domitian in 89 CE, a ploy to get rid of rivals who happened to be adherents of Stoicism. Moving to Nicopolis, a Greek city between Athens and Rome, Epictetus set up a Stoic school where he taught until his death decades later.
Origen, the early Christian historian and philosopher, tells a story about Epictetus when he was still a slave that may be mere legend but became a famous illustration of the aims of Stoicism. The story goes that once, when Epictetus’ master became angry (presumably at Epictetus for maintaining a stoic attitude in a heated moment), his master broke his leg to punish him. Epictetus, undisturbed by the pain or condition of his leg, responded by criticizing his master for irrationally destroying his own property. Epictetus asked his master how he could hope to be an effective slave with a broken leg.
It was not the pain or the imposition that bothered Epictetus, but the illogical nature of the act which did not serve a rational and objective purpose. Note that Epictetus does not say that slavery is irrational, but using slavery inefficiently is irrational, is not in accord with the cosmic Logos. Epictetus was said to have a lame leg by various sources, but, according to the Stoic philosopher Seneca, Epictetus was born with the deformity. This is likely the inspiration for the super-logical space alien Spock from Star Trek, who continuously reminds the amorous, over-acting Captain Kirk, “That is not logical, Captain.”
A) Create four statements that form a set, one for each of the four corners of the Square of Opposition, such as, for the first corner, All cows have horns, but use your own example. Which two pairs contradict one another?
B) Create an example of a Barbara, Celarent, Darii and Ferio syllogism of your own.