Would Plato eat at Chic-Fil-A?

A discussion with a friend of mine about the recent events with Chic-Fil-A supporting anti-gay rights groups got me thinking about a metaphor of Plato's from The Republic. As much as I hate to "jump on the bandwagon", this does give a great opportunity to discuss some important philosophical questions pertaining to morality and discrimination.

While I myself am not a Platonist (I'm a modern, reformed Aristotelian, if I had to put a label on my thought), Plato does have some interesting things to say about the subject of discrimination. The original context of the discussion concerns the role of women in The Republic, in Book V beginning around line 454. The discussion occurs between Glaucon and Socrates. Since this is pulled from the middle of a text, I will bold the lines Socrates says. For those unfamiliar with Plato, Plato did not simply write out his views, but used his mentor Socrates as a character to express his own views in dialogue form with other characters, often based on real life Greek political figures or philosophers.

Ah! Glaucon, great is the power of the craft of disputation.

Why is that?

Because many fall into it against their wills. They think they are having

not a quarrel but a conversation, because they are unable to examine what

has been said by dividing it up according to forms. Hence, they pursue

mere verbal contradictions of what has been said and have a quarrel rather

than a conversation.

That does happen to lots of people, but it isn’t happening to us at the

moment, is it?

It most certainly is, for it looks to me, at any rate, as though we are 

falling into disputation against our will.

How?

We’re bravely, but in a quarrelsome and merely verbal fashion, pursuing

the principle that natures that aren’t the same must follow different ways

of life. But when we assigned different ways of life to different natures

and the same ones to the same, we didn’t at all examine the form of natural

difference and sameness we had in mind or in what regard we were

distinguishing them.

No, we didn’t look into that.

Therefore, we might just as well, it seems, ask ourselves whether the

natures of bald and long-haired men are the same or opposite. And, when

we agree that they are opposite, then, if the bald ones are cobblers, we

ought to forbid the long-haired ones to be cobblers, and if the long-haired

ones are cobblers, we ought to forbid this to the bald ones.

That would indeed be ridiculous.

And aren’t we in this ridiculous position because at that time we did

not introduce every form of difference and sameness in nature, but focused

on the one form of sameness and difference that was relevant to the

particular ways of life themselves? We meant, for example, that a male

and female doctor have souls of the same nature. Or don’t you think so?

I do.

But a doctor and a carpenter have different ones?

Completely different, surely.

Therefore, if the male sex is seen to be different from the female with

regard to a particular craft or way of life, we’ll say that the relevant one

must be assigned to it. But if it’s apparent that they differ only in this

respect, that the females bear children while the males beget them, we’ll

say that there has been no kind of proof that women are different from

e men with respect to what we’re talking about, and we’ll continue to believe

that our guardians and their wives must have the same way of life.

And rightly so.

Next, we’ll tell anyone who holds the opposite view to instruct us in

this: With regard to what craft or way of life involved in the constitution

of the city are the natures of men and women not the same but different?

That’s a fair question, at any rate.

And perhaps he’d say, just as you did a moment ago, that it isn’t easy

to give an immediate answer, but with enough consideration it should not

be difficult.

Yes, he might say that.

Shall we ask the one who raises this objection to follow us and see

whether we can show him that no way of life concerned with the management of the city is peculiar to women?

Of course.

- Plato 454-455b, translation by G.M.A. Grube, revised by C.D.C. Reeve (Hackett, 1992)

Now that you have read the dialogue, what does this mean? The scene begins with Socrates commenting to Glaucon that the power of disputation (the ability to argue logically) is a great gift, because people often think they are merely having a conversation, they are in fact disagreeing and because they lack the skills to construct logical arguments, end up disagreeing over mere terminology and end up playing what are essentially word games; perhaps, a reference to what today we call the informal fallacies.Glaucon then worries that this is what is occurring between him and Socrates, and Socrates confirms the worry. Socrates says that they have not discussed how they are differentiating the ways in which people are alike or different from each other, and how this should play a role in deciding what role people ought to have in society. Socrates gives the example of two cobblers, one who is bald, and one who is not bald. Socrates says that if baldness is an essential part of being a cobbler, then the cobbler with hair should not be allowed to work as a cobbler. Glaucon agrees that this would be ridiculous. Socrates adds that this absurdity arose because they did not consider every way in which things can be alike and different. Socrates asks if Glaucon does not agree that a male and female doctor have the same type of soul. Think of it as, do a male and female doctor both not need the same kind of devotion to be able to be a good doctor? Glaucon responds that male and female doctors do have the same kind of soul. Socrates then asks if doctors and carpenters do not have the same soul. Glaucon responds that they are certainly a different kind of soul. In other words, the professions of being a doctor and being a carpenter take a different kind of person to do the job well. Socrates the points out that men and women different in respect to doing these things in terms of accidental physical properties. Men beget children, and women bear children. Socrates concludes that these differences are simply irrelevant to the discussion of whether or not women would be suitable guardians (to put this in context, a guardian is a philosopher-monarch of Plato's ideal Republic).

The metaphor here is brilliant. Just as baldness and having hair are just physical traits that do not affect someone's ability to be a cobbler, neither does the role one plays in the creation of children affect the ability to be a wise person capable of ruling a state. What does this have to do with gay rights, though?


If it is not fair to judge someone's capacity to perform a task based on their physical appearance, then it is not fair to judge anyone based on contingent properties about them. That is, it is not fair to judge people about things that they cannot help. After all, physical traits are just a specific type of thing of a larger category of things that people cannot help. Since it is in fact unfair to judge someone's ability to do a job based on their physical appearance, then it is not fair to judge someone based on contingent properties about them. (This is deduced by the rule of inference known as modus ponens). 

A contingent property, as I said, is something about someone that is accidental, that they cannot help. This is a general ethical principle, that you shouldn't judge someone about something they cannot help. After all, it is only voluntary actions that should be criticized morally. This is hinted at here by Plato speaking through Socrates, and was later solidified as an ethical principle by Aristotle. Aristotle wrote that, "Virtue, then, is about feelings and actions. These receive praise or blame if they are voluntary, but pardon, and sometimes even pity, if they are involuntary." (Aristotle, 1109b30) Aristotle goes onto specify that the key difference between a voluntary action and an involuntary action is that an involuntary action is one done out of external physical forces or out of ignorance of how to act during a situation. For example, if you choose to murder someone to obtain their money, that is a voluntary choice. If you burn down a house while sleepwalking, that is involuntary. What of cases where you are compelled to do something wrong by someone else or some external cause, but choose to do it anyway, for example, if your family is kidnapped and you are forced to do something horrible to have them returned safely, and you choose to do the horrible thing to save your family? Aristotle calls these non-voluntary actions. (For more information, see the Nicomachean Ethics, Book III, chapter 1)

How then, does this relate to discrimination? Discrimination occurs when someone is excluded from positive treatment or given negative treatment over something that they cannot help. Essentially, it is punishment for something that they cannot control, or over something that is not a matter of moral concern, such as the religion they practice (unless their religious practices involve immoral behavior) This can occur over skin color, gender, sexuality, and so on.

Some maintain that homosexuality is a choice, and use that as a basis for discriminating against them. Such people often point out that homosexality does not occur in nature. In fact, it does, as discussed in Bruce Bagemihl's book Biological Excubrence: Animal Homosexuality and Natural Diversity.  A recent study even found that deleting a certain gene in a rat's DNA can cause them to be homosexual, showing that homosexuality can be caused by a genetic mutation. There even appear to be physical differences between a person of a gender who is straight, and one who is not. This can be seen here at wikipedia, with multiple citations for each fact for those who would like to investigate. (I'd like to avoid the "appeal to wikipedia", so please, do check out the citations).

It is evident, then, that homosexuality is not a choice. This can be found simply by asking anyone about their sexuality. Regardless of your own sexuality, ask yourself, "Did I choose to like the gender I like, or did it come naturally to me?"

Since homosexuality is not a choice, it is not something someone can help. From Plato's point of view, it is something that is an accident of someone's nature, and does not affect their ability to do anything, just as being bald or having hair does not affect someone's ability to be a cobbler. Plato would most likely be very opposed to laws such as "don't ask, don't tell" which, until President Obama had it disposed of, was a law that prevented homosexuals from openly serving in the military. Plato would fully support Obama's decision to get rid of the law, as it deemed them from being unfit to participate in the activities of the state for something irrelevant. From Aristotle's point of view, being homosexual isn't a voluntary choice, and since only voluntary choices are in the scope of ethical judgement, homosexuality falls outside the scope of ethical judgement. There is, however, a distinction from desiring to do something, and doing something. Homosexual acts do not violate any ethical duty. If in a mature, consenting relationship, a homosexual act is no different than a heterosexual act between two consenting people of proper age, since both acts are not treating someone as a mere means to an end, and no harm is being done. So, while homosexuality itself may be involuntary, the voluntary act of homosexual relations still does not seem to violate any ethical rules (unless, you wish to argue that any sex that does not result in procreation is a sin, in which case, the gender of the person with whom you are having sex is not relevant. Nevertheless, I do not believe that sex outside of attempts at procreation is wrong.)

I hope then, it is clear that discrimination against homosexuals or any other group of people, is morally wrong. Ideally, this would be intuitively obvious to people, just as it is intuitively obvious to many people that racism is wrong. If it is not intuitively obvious that discrimination is wrong to someone, against homosexuals or otherwise, I doubt that my arguments here would do anything to change the way that person thinks, but I thought it a good opportunity to explore the issue. As to the title of the blog post, I doubt that Plato would eat at Chic-fil-a, if for no other reason, than he would probably find their food to be quite distant from approximating the form of the good meal.

My Favorite Philosophers

Today's blog will be a bit lighter of a read. I will return to the God Hypothesis series in due time, but have decided to take a break (I actually wrote all of that in the span of about two days). I will present 4 of my favorite philosophers and why I consider them particularly interesting. All information is pulled from either the writings of these men themselves, or from the articles at the Stanford Encyclopedia of Philosophy.

Aristotle (384 BCE - 322 BCE) was a student of Plato's who founded his own school, the Lyceum. Plato believed that something called forms or ideas existed in a perfect realm apart from this one. These forms represent the perfect version of everything. For example, all the different trees on Earth are actually imperfect representations of the perfect form of a tree. Aristotle thought this was absurd, and thought instead that forms exist in the objects. Aristotle also disagreed with Plato's political ideas, which were totalitarian, and thought that it is better when the people are ruled by a constitutional government (what today we might call a constitutional republic). He also found monarchy and aristocracy to be acceptable. He thought that when a constitutional government becomes corrupt, it becomes a democracy. When a monarchy becomes corrupt, it becomes a tyranny. When an aristocracy becomes corrupt, it becomes an oligarchy. 

He also developed the first theory of causation. They are the material cause, the formal cause, the efficient cause, and the final cause. The material cause is the substance out of which something is made. The formal cause is the shape or form of an object. The efficient cause is what made it happen or come into being, and the formal cause is the reason why it exists or happened. The efficient cause is the closest of these to the modern concept of causation. Aristotle also was interested in science, and wrote extensively on physics. Of course, his physics is long outdated, but he was the first person to try and formulate actual laws of nature.

His ethical theory is called virtue ethics. Virtue ethics takes the virtuous act to be that which is in between two extremes. This is called the golden mean. For instance, if one has too little bravery, one is a coward. If one has too much bravery, one is impulsive. But in between those two is courage, which is facing one's fears. The goal of attaining the virtues is eudamonia, or happiness.

I admire Aristotle because he essentially founded science, and took the initiative to formulate his systems of thought in reaction to the perceived flaws in Plato's theories. I largely agree with his approach to ethical theory as well, and virtue ethics plays a large role in my own work in ethical philosophy.

 

David Hume (May 7, 1711 - August 25, 1776) was one of the Scottish philosophers of the later Enlightenment era in the Empiricist tradition, which meant he believed knowledge came from sensory experience. He was largely influenced by John Locke in his thought. Hume is perhaps most well known for his book An Enquiry Concerning Human Understanding. In it he explained his version of John Locke's epistemological views [theory of knowledge]. Hume made several important observations. One was that if the theory of ideas is true (which is the idea that sensory experience leaves behind mental representations behind called ideas, and that it is through the combination of these ideas that knowledge originates), then we have no direct contact with the real world. If we have no direct contact with the real world, then our knowledge of external things is not certain. He also realized that the concept of causation is not one that can be derived from sense experience in a certain manner because it is built on the principle of induction - which yields less certain knowledge than deduction. Hume's conclusion was that we have little true knowledge, and that most of what we consider true is merely belief. He realized that extreme skepticism is impractical however, and merely advocated being a skeptic in the sense of being aware that what you believe may be false.

Hume also wrote important things on theology. The most important of them is the Dialogues Concerning Natural Religion, in which three characters discuss the divine. Cleanthes is a theist and a philosophical empiricist, and believes that the universe displays clear signs of intelligent design and that the existence of God can be inferred from this. Demea is also a theist, but believes the existence of God can be demonstrated through arguments from reason alone [a priori arguments], and that the nature of God can only be known through revelation. The character of Philo best represents the views of David Hume himself, and advocates a position that is at best deist, and at least agnostic. Philo does not believe that human reason is capable of discovering truths about the nature of the divine, let alone know of the existence. 

Hume also wrote the Natural History of Religion, which speculates as to the origins and nature of religious belief, and the famous essay On Miracles, which itself is a chapter in the Enquiry Concerning Human Understanding. In it, he explains why it is best to be skeptical of stories of miracles. Hume also wrote on ethics, aesthetics, political theory, economics, and other topics, but is primarily his work in epistemology and theology that impresses me. While I do not accept his skeptical conclusions, his work demonstrates the absurd consequences of the theory of ideas and raises many other important questions about the accuracy of human knowledge. 

 

Thomas Reid (May 7, 1710 - October 7, 1796) was another Scottish philosopher in the empiricist tradition, and was both an admirer and critic of David Hume. Reid differed from the three famous British empiricists (Locke, Hume, and Berkeley) in that he rejected the theory of ideas common to the three. Reid believed the theory of ideas held by the three major empiricists as well as René Descartes led to absurdly skeptical conclusions. He became a founding member of a particular tradition within Empiricism called the Scottish School of Common Sense. 

Reid was originally trained as a Presbyterian minister, beginning his ministry at a church in New Machar in 1737. He attained a professorship at King's College Aberdeen in 1752, where he wrote An Inquiry Into the Human Mind on the Principles of Common Sense. After its publication in 1764, he was offered a job at the University of Glasgow for the Professorship of Moral Philosophy, a position held previously by Adam Smith. He worked there until he retired in 1781. After his retirement, he wrote Essays on the Intellectual Powers of Man in 1785 and Essays on the Active Powers of Man in 1788.

As interesting as the questions that David Hume raised were, the implications were unsettling, if not downright disturbing. After all, if induction is invalid, then science is built on a major flaw. If we have no direct contact with the real world, one can never be sure that he or she is not being deceived, as in Descartes's thought experiment with the evil demon. Reid in particular was perturbed by these implications for science, as in his free time he was quite interested in chemistry and physics. Just as well, as a man of faith he was naturally unsettled by the implications Hume's writings had on theology. Reid thought Hume was a great thinker, and found now flaw in his arguments. However, Reid realized that though the arguments of Hume are right they are predicated on the truth of the theory of ideas. Reid did not think there was any real basis to this epistemological theory, and posited his own alternative theory often referred to as "common sense realism." 

 Reid was a philosopher of great prestige in his time, but sadly is somewhat obscure today. Due to Hume inspiring Immanuel Kant's theories, and Kant's attempts to synthesize the empiricism of Locke, Hume, and Berkely with the rationalism of the continental philosophers, it seems as if Reid and the Scottish School of Common Sense has been largely ignored in histories of philosophy. Reid's answers to Hume are worth considering, and are well thought out. They are not without flaws, however, and those flaws might be examined in a future post.

Charles Sanders Peirce (September 10, 1839 – April 19, 1914) was one of the United States of America's most brilliant philosophers. He worked in the fields of logic, mathematics, statistics, economics, philosophy, chemistry and other fields. In The Wisdom of The West, Bertrand Russell said of him ""Beyond doubt [...] he was one of the most original minds of the later nineteenth century, and certainly the greatest American thinker ever." Paul Weiss called him "the most original and versatile of American philosophers and America's greatest logician". 

His contributions to philosophy primarily came out of his epistemology and writings on the scientific method, and logic. He became the father of the philosophical tradition called pragmatism, characterized by the pragmatic maxim; "Consider what effects that might conceivably have practical bearings you conceive the objects of your conception to have. Then, your conception of those effects is the whole of your conception of the object." In other words, only limit your speculations to those things which are observable. This was designed to clean up metaphysics from too much unnecessary speculation. His pupil William James would later take this maxim to heart, but in a different way to mean that truth is what works. Peirce disagreed with this version of pragmatism, and began to call himself a pragmaticist in order to differentiate himself from that worldview. 

In epistemology, he advocated a view called fallibilism. Falliblism is a recognition that our scientific knowledge is imperfect, and is essentially a moderate skepticism. He also phrased this world view in terms of critical common-sensism, and was heavily inspired by Thomas Reid's writings on common sense. Peirce thought that our natural faculties of common sense were reliable, but that the things taken for granted in common sense may turn out to be wrong. 

Peirce identified a particular type of reasoning called abductive logic, which is a type of inductive reasoning used in the early stages of the scientific method. It is essentially a method of hypothesis generation. After the abductive phase of the scientific method comes the deductive phase, where the consequences of the hypothesis are deduced, and the inductive phase, where data is collected and experiments conducted. Peirce wrote that, "Facts cannot be explained by a hypothesis more extraordinary than these facts themselves; and of various hypotheses the least extraordinary must be adopted." This is essentially the pragmatic maxim applied to science, and is more or less the principle of Ockham's razor, that the simplest explanation is often the best. 

I admire Peirce because of his rather common sense and practical views in epistemology. His fallibilism and critical common sensism are a good compromise between the skepticism of Hume and the Common Sense Realism of Reid. His analysis of the scientific method is an accurate and useful one. As a psychologist, it is important to be aware of the scientific method, as the history of psychology is filled with unscientific ideas (read: Freud, Jung) and even today there are many competing ideas in the fields of personality psychology, cognitive science, and evolutionary psychology. Applying the pragmatic maxim to such situations is an excellent way to look for the best explanation.

Can You Prove A Negative?

In the public sphere, it is often said that you cannot prove a negative. This often arises in debates about the existence of god and other claims relating to the supernatural. For example, you might hear in a debate between a theist and an atheist the phrase, “you can’t prove that god doesn’t exist, because you can’t prove a negative.”  It is not always the theist making this statement, either. Consider this dialogue between Ayn Rand and Phil Donahue in an interview:

Ayn Rand: No.
Donahue: Now the reason you don’t is because you can’t prove that such an entity or being or energy exists.
Ayn Rand: I can’t nor can anyone else. There is no proof.
Donahue: There is no proof so therefore you’ve concluded that there isn’t one?
Ayn Rand: That’s right.
Donahue: You can’t prove there isn’t.
Ayn Rand: You are never called upon to prove a negative. That’s a law of logic.

            Nor is Ayn Rand the only atheist espousing this sort of statement. James Randi is well known to say the phrase, “you can’t prove a negative.” You can see an example of this here. These sorts of statements require an examination of the concepts of proof, the burden of proof, what a law of logic is, and looking at the differences between deductive and inductive logic. Meaningful debate about something like the existence of god cannot take place when even the skeptics have a misconception about the nature of logic.

            What does it mean for something to be proven? Proof as it pertains to deductive argument is when you have a true premise that follows from true premises in a valid argument. If an argument has an invalid form, it does not matter if the premises and conclusions are all true, because an invalid deductive argument lacks the ability to give a guarantee. Validity is a guarantee that if the premises of an argument are true, and the conclusion is true, then the conclusion is guaranteed to be true. Deductive logic does not deal with probability but with certainty. If there is a result that has a false conclusion despite having true premises, then the argument is invalid. However, it is possible to have a true conclusion despite having a false premise and still be valid. If an argument has a true conclusion despite one of the premises being false, it is unsound. If the premises of an argument are true, the conclusion is true, and the form of the argument is valid, then you have a sound argument. You can challenge an argument by testing the validity, or challenging one of the premises if the argument is valid. For instance, if an argument is valid and is believed to be sound by one person, you can challenge the truth of one of the premises. If you can succeed in challenging the truth of one of the premises of the argument, it now is not clear if it is sound or not. If you can show a premise to be wrong beyond the shadow of a doubt, or that the form of the argument is invalid, then you have performed a refutation. These concepts are easily demonstrated by using something called a truth table. A little knowledge of logic is required to understand how a truth table works, so if one has not read an introductory book to deductive logic, or has not taken a logic course, it is recommended to read the following paragraph. Otherwise, if one is familiar with how a truth table works, you can skip the following paragraph. 

If one is not familiar with how a truth table works, then here is a crash course in logical annotation. It is best to become familiar with the symbols used in logic. The symbol for material implication (⊃) is read as “if…then.” For example, p ⊃ q is to be read as if p, then q. If a negation symbol known as the tilde (~) appears, it is to be read as “not”. So, ~p would be read as not p.  The conjunction symbol (•) is to be read as and. The disjunction symbol (∨) is to be read as “or”.  The therefore symbol (∴) represents a conclusion. It is important to be familiar with the forms of the premises as well.  The basic ones that will be reviewed here are called compound statements or binary operations. A conjunction (p•q) is true only when both components are true. A disjunction (p V q) is true as long as at least one component is true. The material implication (p ⊃ q) is true in every situation except for when the first component is true, and the second one is false. In other words, p ⊃ q is only false if p is true, and q is false. In every other situation, it is a true statement. The truth table works by establishing the possible truth conditions of each variable in an argument form in a systematic manner (starting with the variable furthest to the right alternating true and then false, and then doubling the trues and falses each variable to the left, so that the first one to the left is true, true, false, false, and so on). If one wishes to learn more, a guide to further logic symbols can be found here and a page on truth tables with examples can be read here. 

The first syllogism that will be examined is known as the modus tollens. This argument form states that if p is the case, then q is the case, q is not the case, therefore, p is not the case. This is represented symbolically as: 

p ⊃ q
 ~q,
∴~p

            Notice that the conclusion of the modus tollens is a negative. The purpose of this argument is to prove a negative. Is it valid? Let’s plug the variables into the truth table and find out. 

		First Premise	Second Premise	Conclusion	Valid?
p	q	p ⊃ q	~ q	~p
T	T	T	F	F	No
T	F	F	T	F	No
F	T	T	F	T	No
F	F	T	T	T	Yes

The truth table reveals that in no instance is there a case of all true premises and a false conclusion. This shows that yes, in this case, a negative can be proven. Let’s look at an example in action. If Loch Ness contained a monster, then the monster would have been found by someone. No one has found a monster in Loch Ness. Therefore, there is not monster in Loch Ness. This is quite true. If every single inch of the lake was searched for a monster, and no monster was found, the only conclusion to be drawn is that there is not a monster there. This is also a case where absence of evidence is evidence of absence.

          Let’s also look at another type of argument called a categorical syllogism. Categorical syllogisms were formulated by Aristotle, who discovered logic. While this sort of argument is very limited in what it can do, this is because it is the oldest type of logic there is. Modern logic has made many advances since then, but these remain useful to know. A categorical syllogism is comprised of three parts known as the major premise, the minor premise, and the conclusion. Each premise is called a proposition. The proposition in the major premise will contain a predicate and a middle term. The minor premise will contain a subject and a middle term. The conclusion will contain both a subject and a predicate. The major premise always comes first, and the minor premise second. These are abbreviated by S, M, and P. If one understands how to plot a vend diagram for these sorts of proposition, then skip the following paragraph.

 

It must be tested for validity. The problem, as you may have noticed, is that it does not use the same type of terms or structure as the symbolic logic of the modus tollens. The claims of a categorical syllogism are tested by plotting venn diagrams. Since these arguments concern classes of things, it is possible to represent those classes in a venn diagram. When making a venn diagram to test a categorical syllogism, draw a venn diagram consisting of two circles on top, and one on the bottom. The top left one represents S, the top right one represents P, and the bottom circle represents M. If something is a universal claim, meaning that a claim is made about all objects in the class, then it is illustrated by coloring in the region that something is not, so that only the appropriate regions overlap. For instance, if you color in the statement All S are P, then color in any regions of P that do not overlap with S. If the proposition is No S are P, color in the sections where S overlaps with P. If the proposition is Some S are P, then put an x in the region where they overlap. If the proposition is Some S are not P, then put an x in the region of S that does not overlap with P.  If something is a particular claim, meaning it deals with only specific objects within a subset, then it is illustrated by an x placed in the circle. In the event that the x could go in either spot, the x is placed on the line between two classes, but in that event, you automatically know that the argument is invalid. Only plot the two premises, and not the conclusion. If after diagramming the two premises the conclusion is represented, then you have a valid argument. If in the process of diagraming the premises the conclusion fails to be represented, then the argument is invalid. 

Let us look at a particular form of the categorical syllogism called the modus celarent. This argument goes, “No M are P. All S are M. Therefore, No S are P.” Is this valid? Let’s look at the venn diagram. 

The conclusion that no S are P is represented after diagramming both premises. This means that the argument form is valid. Note that the conclusion is a negative statement. A practical, although silly, example of this argument would be, “No mammals are reptiles. All humans are mammals. Therefore, No humans are reptiles.” Each of the premises in this argument are true statements. The form of the argument was shown to be valid. Therefore, the conclusion must be true. The negative proposition that no humans are reptiles was just proven.  

                Those are just two instances of a negative being proven in different types of logical syllogism. A point needs to be made that in inductive logic, there is no discussion of proof. Nor is there talk of validity and invalidity. Instead, there is talk of strong and weak induction. Why is this? Induction does not deal with proof or disproof, but with substantiating and denying claims. It is also used to find things out about the world. It is one of the key types of logic used in the scientific method. However, a claim can be inductively falsified. Suppose that all through your life, you see tables as rectangular shaped. Then, one day you are invited to a friend’s house for dinner. They have a round table, instead of a rectangular one, and you have never seen a round table before and did not know that round tables existed. You likely would have the idea “all tables are rectangular” in your head, but now that would be falsified. This is induction by simple enumeration, and is perhaps the easiest type of induction to perform, as well as easiest to falsify. The conclusion that all tables are rectangular is an inductive generalization. Note how this differs from anything in deduction. Take into account the mathematical field of statistics. Statistics collects data and tries to find correlations between several variables. If possible, statistics tries to look for causal relationships, but there is a classic mantra in statistics: correlation does not equal causation. For instance, aggressive crimes increase with the increased sale of ice cream. Is there a direct link there? No, it wouldn’t make sense for ice cream sales to affect murder rates. However, a third cause could be responsible for the two: summer heat. The purpose of this is to demonstrate the uncertainty of induction. It wouldn’t make sense to speak of proof or disproof. 

It is likely that when people repeat the mantra “you can’t prove a negative”, they are thinking along the lines of inductive logic. For instance, take the claim that there are aliens out there, and you are discussing this with someone. You say that there is no evidence of intelligent life on other planets, and your friend responds, “You can’t prove that there isn’t life on another planet.” You respond that “you are never called upon to prove a negative. You can’t prove a negative.” Your friend’s mistake would be shifting the burden of proof onto you. Your mistake would be saying that you are never called upon to prove a negative and can’t do that. The proper response would be, “no, you can’t just shift the burden of proof onto me. We are debating the proposition that there is intelligent life elsewhere in the universe. You are making that claim, and it is your job to substantiate that claim with evidence.” If you are skeptical of the proposition that intelligent life exists elsewhere in the universe, that doesn’t mean you believe there isn’t intelligent life on other planets, only that you lack any reason to be certain about it. The same goes for debating the proposition that a god exists. For the existence of a deity, things get trickier. If the definition of a deity offered by the believer is a specific one and contains contradictions, then the skeptic has to point out the contradictions in the definition of that deity to show that the deity does not exist. If the debate is just over the proposition that there is “someone up there”, then burden of proof is on the theist, and the skeptic wins if the theist fails to establish any reasonable evidence. 

The same applies for a sketchy premise in a deductive argument. If a premise in an argument fails to be demonstrated as true, and you challenge it, it would be wrong for the argument's giver to shift the burden of proof to you. Take the previous example of the Loch Ness monster, but in a different valid argument form called modus ponens, which takes the form, "If P, then Q. P, therefore, Q."

   This time, let the argument be, "If there were a monster in Loch Ness, then someone would have found it. A photograph was taken of it, therefore, there is a monster in Loch Ness." Granting the premises to be true, the conclusion must also be true. And there have been claims that the Loch Ness monster has been photographed. However, as a good skeptic, you would challenge the second premise’s truth. As it turns out, these photographs are faked, which undermines the soundness of the argument.

Hopefully this clears up the confusion amongst people about the concept of proof and the burden of proof. Again, it is possible to prove a negative as shown by the two examples from deductive logic. Those are not the only two ways to prove a negative, as there are many more. This was not meant to be an exhaustive list of every way to prove a negative. It has also been shown that inductive claims can be falsified (this is a driving force behind scientific progress, by the way!). Hopefully, those who read this will walk away with a better understanding of how to conduct a debate an analyze an argument.

Recommended reading: Introduction to Logic by Irving M. Copi & Carl Cohen -- any edition should suffice. There's also an online logic textbook here, and the youtube channel of Dr. Jason Campbell has a few lecture series on logic. If you are unable to take a logic course at a college, these resources are recommended to learn more about logic.