Truth suffers from too much analysis

Archive for March, 2011

Ten Tropes of Skepticism

Posted by allzermalmer on March 24, 2011

Sextus Empiricus lays out the Ten Tropes of skepticism that are to lead to suspension of judgment.

They follow three different main categories, and each with at least two tropes.The three main categories of the tropes are as follows:

  1. The subject who judges
  2. The object judged
  3. The subject who judges & the object judged

Here is the first category: The subject who judges.

  1. The opposing perceptions and views of the world which characterize different species: “For how could one say, with regard to touch [for example], that animals are similarly affected whether their surfaces consist of shell, flesh, needles, feathers or scales? And, as regards hearing, how could one say that perceptions are alike in animals with a very narrow auditory canal and in those with a very wide one, or in those with hairy ears and those with ears that are hairless… [P]erfume seems very pleasant to human beings but intolerable to dung beetles and bees, and the application of olive oil is beneficial to human beings but kills wasps and bees.”
  2. The opposing perceptions and views of the world which characterize different individuals: thus “…the greatest indication of the vast and limitless difference in the intellect of human beings is the inconsistency of the various statements of the Dogmatists concerning what may be appropriately chosen, what avoided, and so on.”
  3. The opposing perceptions and views of the world which characterize different sense organs: thus “Pictures seem to the sense of sight to have concavities and convexities,” for example, “but not to the touch,” and “Let us imagine someone who from birth has …lacked hearing and sight. He will start out believing in the existence of nothing visible or audible, but only of the three kinds of quality he can register. It is therefore a possibility that we too, having only our five senses, only register from the qualities belonging to the apple those which we are capable of registering. But it may be that there objectively exist other qualities”
  4. The opposing perceptions and views of the world which characterize different circumstances: “Thus, things affect us in dissimilar ways depending on whether we are in a natural or unnatural condition, as when people who are delirious or possessed by a god seem to hear spirits but we do not…. And the same water that seems to us to be lukewarm seems boiling hot when poured on an inflamed place…. Further, if someone says that an intermingling of certain humors produces, in persons who are in an unnatural condition, odd phantasiai [impressions] of the external objects, it must be replied that since healthy people, too, have intermingled humors, it is possible that the external objects are in nature such as they appear to those persons who are said to be in an unnatural state, but that these humors are making the external objects appear to the healthy in a natural people other than they are.”

Here is the second category: The object judged

  1. the opposing perceptions and views of the world due to different quantities and structures: thus “[the] individual filings of a piece of silver appear black, but when united with the whole they affect us as white… And wine, when drunk in moderation, strengthens us, but when taken in excess, disables the body…”
  2. the opposing perceptions and views of what is right and wrong which characterize different ways of life, laws, myths and “dogmatic suppositions: for “among the Persians sodomy is customary but among the Romans it is prohibited by law; and with us adultery is prohibited, but among the Massagetae it is by custom treated as a matter of indifference, as Eudoxus of Cnidos reports… and with us it is forbidden to have intercourse with one’s mother, whereas with the Persians this sort of marriage is very much the custom. And among the Egyptians men marry their sisters, which for us is prohibited by law.

Here is the third category: The subject who judges & the object judged

  1. the opposing perceptions and views of the world that characterize different positions and distances and places: for example, “lamplight appears dim in sunlight but bright in the dark. The same oar appears bent in water but straight when out of it”
  2. the opposing perceptions and views of the world that characterize mixtures: thus “we deduce that since no object strikes us entirely by itself, but along with something, it may perhaps be possible to say what the mixture compounded out of the external object and the thing perceived with it is like, but we would not be able to say what the external object is like by itself… The same sound appears one way when accompanied by a rarefied atmosphere, another way when accompanied by a dense atmosphere”
  3. the opposing views possible because of the relativity of all things: “…since all things are relative, we will suspend judgment about what things exist absolutely and in nature… This has two senses. One is in relation to the judging subject [different subjects perceiving differently]… The other in relation to the conceptions perceived with it…”
  4. the opposing perceptions and views of the world due to constancy or rarity of occurrence: for “The sun is certainly a much more marvelous thing than a comet. But since we see the sun all the time but the comet only infrequently, we marvel at the comet so much as even to suppose it a divine portent, but we do nothing like that for the sun. If, however, we thought of the sun as appearing infrequently and setting infrequently, and as illuminating everything all at once and then suddenly being eclipsed, we should find much to marvel at in the matter.”

The main points are these (taken from Wikipedia):

  1. Different animals manifest different modes of perception
  2. Similar differences are seen among individual men
  3. For the same man, information perceived with the senses is self-contradictory
  4. Furthermore it varies from time to time with physical changes
  5. In addition, this data differs according to local relations
  6. Objects are known only indirectly through some medium like air, moisture, etc.
  7. These objects are in a condition of perpetual change in color, temperature, size and motion
  8. All perceptions are relative and interact one upon another
  9. Our impressions become less critical through repetition and custom
  10. All men are brought up with different beliefs, under different laws and social conditions

These modes should be sufficient for us to suspend judgment on anything that goes beyond our sensory experience. It prevents us from saying anything dogmatically. We would suspend judgment that goes beyond our direct perception. To see more about what goes beyond direct perception check out Direct v. Indirect Knowledge.

Most of our knowledge, or proclaimed knowledge, of things is indirect knowledge. However, these aren’t the only tropes of skepticism. There are five more, and of those five, three form the trilemma of justification of knowledge claims. I will share those later.

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Direct v. Indirect Knowledge

Posted by allzermalmer on March 23, 2011

I’m going to talk about the Direct v. Indirect dichotomy when it comes to knowledge claims.

Direct knowledge is something that we gain from observing something happening. An example is observing customers in a store and count how many bags of candy they purchase.

Indirect knowledge is seeing the effect of something. An example is looking through trash cans on garbage day to see how many empty candy bags are in each trash bin.

Another example might help. Direct observation is seeing both the cause and the effect. Indirect observing is just seeing the effect. We don’t see the cause of the effect that we are directly aware of.  Direct observation allows us to see something, and we tend to think that what we observe has a cause. When we see no cause, we only see the effect. Thus we infer that there was a cause that we didn’t directly observe.

When it comes to cause and effect, we can give it the abstract formula of a logical formula known as contingent statements. If X then Y. X–>Y. If I place litmus paper in a vile of acid, then it will change colors.

Now there is a logical fallacy known as affirming the consequent. The logical form is this: If X then Y; Y; Therefore X. If a cat then an animal; an animal; Therefore a cat. The real problem is that we can only, logically, affirm the antecedent, which has this logical form. If X then Y; X; Therefore Y. If a cat then an animal; a cat; therefore an animal.

The reason why affirming the consequent is a fallacy is because a different antecedent can have the same consequent. Here is the logical form of what I am talking about: If ~X then Y. If not a cat then an animal; not a cat; Therefore an animal.

When we have a statement, X, then it denies something as well. This is known as the logical inference as double negation. Double negation has this form: ~~X, which is equivalent to saying, X. So if I say, “This is a cat”, which has the logical form of X, then I am saying “It is not the case that this is not a cat”, ~~X.

Let us go back to my original statement of, If a cat then an animal. X–>Y. Now there could be an animal that is not a cat. For example, when we affirm ‘an animal’, it could be a dog, a bird, a bear, an elephant, a bird, a zebra, and etc.These are all ‘not a cat’, and thus all ~X.

Back to indirect knowledge. So we observe an effect through direct observation  and think there is a cause of it. So we observe Y of If X then Y. Now it could also be ~X that produced Y, and ~X could be a multitude of things. Thus, a multitude of antecedents could have produced Y.

So when we observe the effect of something, there are nearly infinite amount of things that could have caused them that we didn’t observe. There’s no logical reason to pick one antecedent over another when all of them have the same consequent. Thus, an effect gives us indirect evidence for an infinity of different causes.

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Story of Toy Story

Posted by allzermalmer on March 22, 2011

This is a continuation from Stuck In the Elevator.

In the movie Toy Story, and throughout all the other sequels to it, the toys come alive when no one is around to see them. In other words, the toys went from inanimate when the people were around to animate when they were gone. We find some of these ideas with children, and it is one thing that they imagine about. Thus they find it very interesting when they see it in movies.

Following the empirical stance, we find that this is certainly a realm of possibility. We have no reason to say that this doesn’t happen, and so the children can keep imagining it. The empirical stance only says that we don’t know if it happens or not. There is nothing that prevents this from happening and it is only through dogmatic assumptions that we dismiss this idea.

When I leave the room where the toys are, I no longer know what is going on there. I don’t even know, empirically, that it is still there. Thus, many things can happen while I am gone. My experience tells me nothing about it. All I would know is that the toys are in such-and-such position when I leave, and that they are in such-and-such position when I come back. My imagination could fill in all sorts of things that happened there, so long as they are not logical contradictions like A & ~A.

Of course someone could say that I didn’t see it happen when you were gone and I was there, but this doesn’t show anything. For they are inanimate when someone is there. Having knowledge through experience opens up many possibilities and keeps us from being dogmatic.


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Stuck in the Elevator

Posted by allzermalmer on March 21, 2011

Let us assume that all knowledge of what exists is to come from experience.

By experience I mean those things that come from our senses, which is  sight, touch, sound, smell, and taste. These are the things from which we come to know of ‘reality’. These are what impinges on our consciousness to let us know of what exists. We say that something exists when we have an experience of it. When we don’t have an experience of it, we say that we don’t know if it exists or even say that it doesn’t exist.

Experience shows us what is actual. Being actual means that it exists, and to know something exists is to be presented to our consciousness by the senses. Now our memory allows us to remember what was actual. For example, yesterday I had the experience of reading a specific book, ‘The Grand Design‘ by Stephen Hawking and Leonard Mlodinow. It is not actual now. For I do not have the experience of reading it now. I can remember that I read it, right now. However, it is not an actual experience right now. The only experience is that of recollection and not of existence, and the recollection happens now.

Now say that we step into an elevator. The dimensions of the elevator is 4 feet in length, and 3 feet in width, and 7 feet in height. Now say that the elevator closes. Our experience only shows that what is actual is what we are experiencing. What we are experiencing is just the contents of the elevator. This would be what we see, feel, smell, and hear while we are in the elevator. This is all that is actual, and this is all that we can say to exist. The elevator is the confines of our knowledge of existence, of what is actual.

Our experience doesn’t go outside of the elevator, or even make sense to talk about the outside of the elevator. As far as experience goes, it doesn’t exist or we don’t know it to exist. However, we can imagine that there are things that are existing while we are not experiencing them. The problem is that we can’t know that they are actual, or that they are existing then. We can imagine it, but that is just confined to within our own heads and not known to exist, like our memory of recollecting what was actual.

That is the limit of experience. That is the limit of knowledge by experience.

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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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