Truth suffers from too much analysis

Socrates Begging

Posted by allzermalmer on March 13, 2011

There once was this man called Socrates.  Socrates was a philosopher, and known as the teacher of Plato, among other philosophers. He lived in the city-state of Athens from around 469 BC to 399 BC. He is known for the Socratic method, which is going around and asking people questions and having them attempt an answer to the question. Most people did not like him for this, because he eventually showed that their answers were not adequate and problematic. There is also a well known syllogism with Socrates.

All men are mortal.

Socrates is a man.

Therefore Socrates is mortal.

We will get back to this argument in a bit. Nevertheless, before I do that I need to lay some things out first. I will first talk about deductive logic (specifically syllogisms) and a little bit on inductive logic. Then I will deal with epistemology, which is based on how we know something is the case. Knowledge claims tend to rely on using logic to support its conclusions, so I will deal with both.

The argument presented is a syllogism. A syllogism is a deductive argument in which two premises are given, and the conclusion necessarily follows from those two premises. The argument presented is a valid argument. Valid arguments are where the conclusion necessarily follows from the premises. An invalid deductive argument is when the conclusion doesn’t follow from the premises.

Here is an example of an invalid argument: All cats eat mice; Whiskers eats dog-food; Therefore Whiskers is a cat. The conclusion does not follow from the premises, and so we can say it is invalid.

There are two types of premises that can be given in a syllogism. (1.) A general premise or (2.) a particular premise.

A general premise deals with “All”, “No”, “Some”, or “Some…not”. General premises deal with general terms, which are terms that describe, or put, something in a category, like that of ‘a philosopher’, ‘mortal’, or ‘drives a Buick’.  A particular premise uses singular terms, which pick out a specific thing, like that of ‘the world’s greatest philosopher”, ‘this child’, or ‘Socrates’. One way to understand it is that general terms can have a general form of a so-and-so‘. A singular term can have the general form of ‘the so-and-so’. General terms are indefinite and singular terms are definite.

Here is something that the philosopher J.S. Mill stated about general premises: “A general proposition is one in which the predicate is affirmed or denied of an unlimited number of individuals; namely, all, whether few or many, existing or capable of existing, which possess the properties connoted by the subject of the proposition. “All men are mortal” does not mean all now living, but all men past, present, and to come.”

Now logic, and therefore syllogisms, don’t deal with if a premise is true or not. Logic is only concerned with the form of an argument. Epistemology  (theory of how we know something) is concerned with the truth of the premises. So the question becomes, with the Socrates syllogism, how do we know that those premises are true? More specifically, how do we know that the general premise is true?

There are two ways we can handle this. (1.) We can say that the premises are true by definition, which means that they are necessarily true, or (2.) we can say that they are true by experience and this is based on inductive arguments, which means they are contingently (possibly) true.

Something is necessarily true when it is truth based on logic (laws of logic), meaning of concepts, or necessary connections between properties. Necessary truths mean it would be self-contradictory to deny. Here is a general premise that is a necessary truth: All bachelors are unmarried males.

Something is possibly true when it is logically possible, which is something that is not self-contradictory. This is an example of a possible truth: I run a mile in 1 minute. There is no logical contradiction in this statement. (It might not seem physically possible, but there is no contradiction in it)

How do we know that a particular premise is true, like ‘I can run a mile in 1 minute’? We could know this by experience. Thus, we could observe that I ran a mile in 1 minute. Now our experience only deals with particulars. We never experience general things.

Now back to the syllogism. So how did we arrive at the first premise of “All men are mortal”?

The general premise can be supported by a previous argument in which the conclusion was derived that “All men are mortal”. However, this pushes the question back one step. Long story short, we are lead to an infinite regress. We would have to keep going back further and further, and it would never end. So we can arrive at this conclusion based on it either being true by definition, but then it has no empirical content behind it, or we arrive at it by induction (which is based on experience).

So what is an inductive argument? J.S. Mill stated that an inductive argument is: “the process by which we conclude that what is true of certain individuals of a class is true of the whole class, or that what is true at certain times will be true in similar circumstances at all times…Induction, as above defined, is a process of inference; it proceeds from the known to the unknown…Induction properly so called…be summarily defined as Generalization from Experience”

So induction would follow this general form: a^1 is a swan and is white, a^2 is a swan and is white, a^3 is a swan and is white, a^4 is a swan and is white, and etc. Therefore, All swan are white. We go from our particular experience of finding certain individual swans are white, and we conclude that all the unknown swans that we will meet with future experience will be white.

Now we can use this same type of enumeration of experience with the syllogism I presented earlier on. So if “All men are mortal”, then the conclusion  that “Socrates is mortal”, would necessarily be involved in the general premise “All men are mortal”. Thus, if we don’t already know that ” Socrates is mortal” then we can’t know that “All men are mortal”. The conclusion is already contained within the premise “All men are mortal”. For Socrates is part of “All men”.

Here is an example of how we derive a general conclusion with “All men are mortal”. Heraclitus is mortal, Pythagoras is mortal, Aristotle is mortal, Plato is mortal, Socrates is mortal, Xenophanes is mortal, Thales is mortal, Parmenides is mortal, Zeno is mortal, and etc. Thus All men are mortal. Now we set up the Socrates argument. “All men are mortal; Socrates is a man; Therefore Socrates is mortal”. As we can see, Socrates is already contained in “All men are mortal”.

As Mill states, “generals are but collections of particulars, definite in kind but indefinite in number”.

Here is another example: All Etonians wear top hats; Smith is an Etonian; Therefore Smith wears top hats. If we don’t already know that “Smith wears top hats”, then we can’t know that “All Etonians wear top hats”. For since ” Smith is an Etonian”, it can only be true that All Etonians wear top hats if Smith wears a top hat. Thus “All Etonians wear top hats” assumes that “Smith wears a top hat”. The general premise assumes the truth of the conclusion. It begs the question. The truth of the general premise assumes the truth of the particular premise (which is the conclusion).

What does it mean to beg the question? The logician Irving M. Copi states “the fallacy of begging the question.. consists in assuming the very proposition one is attempting to establish by argument.” We are trying to establish that Socrates is mortal, and so we assume that “Socrates is mortal” with our general premise of “All men are mortal”. This is a problem that has been known to logicians for a long time, and this is a problem when we come to claim knowledge (epistemology) by attempt an to use deduction, unless the general premise is analytic.

How do we justify induction by knowledge? If we use the past success of induction to justify induction, then we are using induction to justify induction. This begs the question. If we use deduction, then we have to use a general premise. However, to use a general premise will either be analytic, and true by definition, or rely on induction. Thus it will either be devoid of empirical content or beg the question. Induction also assumes the Uniformity of Nature. As J.S. Mill states, “Whatever be the most proper mode of expressing it, the proposition that the course of nature is uniform, is the fundamental principle, or general axiom of Induction.”

We could use the principle of the Uniformity of Nature. This principle, as J.S. Mill states, is “that what happens once, will, under a sufficient degree of similarity of circumstances, happen again, and not only again, but as often as the same circumstances recur.” However, how do we know that what has happened in the past will happen in the future? Well, we know this from experience. So we have to rely on induction again to solve this, but then this begs the question as well. We also have no experience of the Uniformity of Nature, since it is a general  statement, and experience is based on particulars. The Uniformity of Nature is a general principle, and thus not particular.

We could use the Uniformity of Nature to form a deductive argument. However, since it is a general premise, it would either have to rely on being true by definition or based on induction. So we go through a vicious circle again, which is begging the question.

This problem is known as The Problem of Induction. It was covered by the philosopher David Hume in both his works called A Treatise of Human Nature & An Enquiry Concerning Human Understanding. There are many websites that deal with the problem of induction, if anyone is interested or already does not know about it.

Sextus Empiricus, the ancient skeptic, talks about this very issue of deduction: “Well then, the premise “Every man is an animal” is established by induction from the particular instances; for from the fact that Socrates, who is a man, is also an animal, and Plato likewise, and Dion and each one of the particular instances, they think it possible to assert that every man is an animal;so that if even a single one of the particulars should apparently conflict with the rest of the universal premise is not valid; thus for example, when most animals move the lower jaw, and only the crocodile the upper, the premise “Every animal moves the lower jaw” is not true. So whenever they argue “Every man is an animal, and Socrates is a man, therefore Socrates is an animal”, proposing to deduce from the universal proposition “Every man is an animal” the particular proposition “Socrates is an animal”, which in fact goes (as we have mentioned) to establish by way of induction the universal proposition, they fall into the error of circular reasoning, since they are establishing the universal proposition inductively by means of each of the particulars and deducing the particular proposition from the universal syllogistically.”

Here Sextus Empiricius talks about coming up with a general premise (which he calls universals) from induction: “It is also easy, I consider, to set aside the method of induction. For, when they propose to establish the universal from the particulars by means of induction, they will effect this by a review either of all or of some of the particular instances. But if they review some, the induction will be insecure, since some of the particulars omitted in the induction may contravene the universal; while if they are to review all, they will be toiling at the impossible, since the particulars are infinite and indefinite. Thus on both grounds, as I think, the consequences is that induction is invalidated”

Let’s recap.

1. We only experience particulars

2. General principles are not particulars

3. Thus we don’t experience general principles

4. General principles are either true by definition or derived from induction

5. What is true by definition is not based on experience

6. Induction uses past experiences to predict future experiences

7. Induction assumes the general principle of the Uniformity of Nature

8. Thus to use induction begs the question

9. Deductive arguments rely on general propositions

10. General propositions derive conclusions that are contained within the general proposition to begin with

What we come to is that it is very hard to justify our knowledge claims either deductively or inductively, if we base it upon experience. It also comes that Socrates was just begging to us the whole time.


A System of Logic, Ratiocinative and Inductive by J.S. Mill

Informal Logic by Irving M. Copi and Keith Burgess-Jackson

Introduction to Logic by Harry Gensler

Outlines of Pyrrhonism by Sextus Empiricus


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