Systematic Philosophy

to know what can be known

Organizing Theoretical Material: Basic Tips

If you try to build a philosophical system, you will eventually generate a lot of material. At first, you will just have a few arguments. Then you will have 20. Then 50. Then 150. Then more. And when you have more than 150 arguments, you only have two options: organize your material or be buried beneath it.

Tip #1: Name your documents clearly

Most people who build philosophical systems use multiple documents. If you use multiple documents, you should be sure to name all of your documents clearly. Do not use bland, uninformative filenames like these:

  • philosophy.doc
  • other thoughts.txt
  • stuff.docx

Use filenames that clearly indicate what each document contains. Pick filenames you will understand at a glance a year from now. Don’t be afraid of length. Use long filenames. Use spaces and hyphens. Did you just complete your first draft of your thoughts on metaphysics? Did you just finish your second systematic exposition of your views on ethics? If so, you could use filenames like these:

  • Thoughts On Metaphysics – First Draft.docx
  • Ethics – Second Systematic Exposition.txt

You may want to include your name or initials in the filename. You may also want to include the date. It takes a few extra seconds to type a longer, clearer filename. But long filenames can save you hours of time in the future when you want to look back at what you have written.

Tip #2: Use version numbers

As you work to build your philosophical system, you will inevitably go through multiple drafts. It is important to keep track of these drafts. This will make it easy for you to trace the development of your views on different matters.

One great way to keep track of drafts is using version numbers. Take your current draft of a document. Add “- working” to the filename. This will be the working version of your document. Now whenever you want to alter the document, alter the working version. Whenever you substantially alter the working document, save the working document and save an alternate version of the document. Name each alternative version by replacing the “- working” with some version number. The documents named with version numbers should then be left unaltered and will always be available for examination.

For instance, suppose that I am working on metaphysics and I have entitled the document I am writing “Metaphysics – GA.docx”. To use version numbers in the way just described, I first create a working version of the document, which I entitle “Metaphysics – GA – working.docx”. Henceforth, this will be the only version of this document I edit. Next, I save a copy, which I entitle “Metaphysics – GA – 1.0.docx”. Then I work on developing my metaphysical views. As I go, I edit the working document. Whenever I make substantial changes, I save the working version and additional versions of the document, which I entitle “Metaphysics – GA – 1.1.docx”, “Metaphysics – GA – 1.2.docx”, “Metaphysics – GA – 2.0.docx” and so on.

When using two-digit version numbers (e.g., 2.3), it is customary to increment the first number and reset the second number to zero after making a large revision to the content and to increment the second number and leave the first number unchanged after making a small but noteworthy revision to the content.

Tip #3: Break up walls of text

Imagine you are presented with a document. The document has no sections, no paragraphs, no lists of bullet points. No words are italicized. Nothing is bolded or underlined. It is simply an enormous, single-spaced wall of text.

It is hard to work with a wall of text. You cannot determine at a glance what it contains. Does it contain five claims? Or ten? Does it contain three arguments for the second claim or two arguments for the third claim? With a big block of text, the only way to know is to read it.

Luckily, it is possible to present material more clearly. Do not simply use long, unstructured sequences of sentences. Break the document into sections. Give each section an informative title. Use paragraphs. Put different ideas into different paragraphs. Underline or italicize important claims. Use numbered lists to present arguments. Make it obvious what the text contains merely by modifying its appearance. This will make it much easier for you to find things and understand them when you look at the document later.

Don’t let this be your text.

Tip #4: Use color coding and highlighting

In addition to indentation, underlining and so on, it is also extremely useful to use color coding and highlighting. Do you have old material you need to revise? Highlight it all yellow. Do you want to see the weak points of your arguments at a glance? Color all of the dubious statements red.

Tip #5: Use shortcut keys and macros

If you are building a philosophical system, you will end up using your word processor for hours and hours. As a result, it is worth taking some time to figure out how to use your word processor more efficiently. Learn the relevant keyboard shortcuts: keyboard shortcuts are much faster than using the mouse to navigate through menus. If possible, program in new keyboard shortcuts or macros for actions you perform frequently.

For instance, in Microsoft Word it is possible to use macros to program keyboard shortcuts for color coding text. If you color code text frequently, this is extremely useful.

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Written by Geoff Anders

August 3, 2011 at 3:09 am

Posted in Uncategorized

How Should We Assess Premises?

If an argument is transparently valid, then its quality is determined by the quality of its premises. This raises the question: “How should we assess the premises of an argument?”

A central question

The question “How should we assess the premises of an argument?” is a central question. In fact, it is the central question of philosophical methodology. It is possible to distinguish philosophical methods on the basis of how they say we should assess premises.

Various proposals

Philosophers have proposed various answers to the question of how we should assess premises. Some philosophers advocate the method of certainty, which says that we should assess premises on the basis of whether they are known to be true with absolute certainty. Others advocate the method of elegance, which says that the quality of a premise depends on how simple or elegant that premise is. Some advocate the method of common sense, which says that we should assess premises on the basis of how commonsensical they are. Philosophers advocate other methods as well.

A scale of plausibility

When we assess a premise, we assign it some degree of plausibility. Degrees of plausibility stretch from perfect plausibility to perfect implausibility. A perfectly plausible premise is one we know to be true with absolute certainty. A perfectly implausible premise is one we know to be false with absolute certainty. Between these extremes there are many degrees. We might assess a premise as being very plausible, mildly plausible, neutral, mildly implausible or very implausible. Other degrees between these are possible as well.

Degrees of plausibility are degrees of goodness. The more plausible a premise is, the better that premise is. Or at least, the better that premise is in terms of how it contributes to helping an argument accomplish its purpose.

If a premise is perfectly plausible, we will say that it is a “perfect” premise. Otherwise, we will call it an “imperfect” premise.

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Written by Geoff Anders

May 31, 2011 at 11:03 pm

Posted in Uncategorized

What Is A Final Conclusion?

In order to understand what an argument is, you need to know what a final conclusion is. Luckily, the definition of “final conclusion” is extremely simple.

What a final conclusion is

The “final conclusion” of an argument is simply a proposition in that argument that has been selected to be called “the final conclusion”. That’s it.

Of course, in order for something to be an argument, it must represent its final conclusion as being entailed by one or more of the propositions in the argument. This means that you cannot simply select any step in an argument to be the final conclusion. You have to select one of the conclusions of that argument.

What about the last proposition?

We have defined the term “final conclusion” one way. Some people prefer to define it another way. In particular, some people prefer to arrange the steps of an argument in a sequence on the basis of which are supposed to entail which, and then define “final conclusion” as “the last proposition in the sequence”.

Obviously, people can define terms however they would like. So anyone is free to use the term “final conclusion” as just described. In fact, using the term “final conclusion” in this way is perfectly fine for most arguments. The reason we do not use this definition of “final conclusion” is as follows. Our definition of “argument” requires that every argument has a final conclusion. But not every argument can be arranged into a sequence with a last proposition if the steps are arranged on the basis of which are supposed to entail which. Consider circular arguments. Arrange the propositions on the basis of represented entailments. The result will be a circle, not a sequence with a last proposition. If we define “final conclusion” in terms of the last proposition in the sequence, we would have to say that circular arguments had no final conclusion.

Of course, there is a simple solution to this problem. In the case of circular arguments, we might just require that one of the propositions be designated as “the final conclusion”. But if we are going to require this of some arguments, it will be simpler to require it for all arguments. This brings us back to our definition, which is that the “final conclusion” of an argument is simply a proposition in the argument that has been selected to be called “the final conclusion”.

No last proposition? Problem solved.

No need for a selector

We said that the final conclusion of an argument is whatever proposition has been “selected” to be called “the final conclusion”. One might wonder: selected by whom? Do we need to posit a selector for each argument? Our answer is no, we do not need to posit selectors. Instead, we should simply conceive of arguments as having their final conclusions built into them. If you take an argument and try to designate a new proposition in that argument as its new final conclusion, you’ve really just changed which argument you’re talking about.

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Written by Geoff Anders

May 29, 2011 at 12:10 am

Posted in Uncategorized

What Are Concepts And Propositions?

We can divide all representations into two types: propositions and concepts. What is a proposition? What is a concept?

Definition by paradigm cases

We will define both “concept” and “proposition” by means of paradigm cases. A “concept” is any of the examples we give in the “paradigm cases of concepts” section below or any representations that are relevantly similar. A “proposition” is any of the examples we give in the “paradigm cases of propositions” section below or any representations that are relevantly similar.

Paradigm cases of concepts

Each of the following examples is a paradigm case of a concept:

  • <square>
  • <an action being good>
  • <non-red>
  • <a bridge spanning a river>
  • <Socrates being next to Plato>

From this and our definition of “concept”, it follows that these representations are concepts, as are any representations that are relevantly similar to them.

Paradigm cases of propositions

The following examples are paradigm cases of propositions:

  • <I exist>
  • <all bachelors are unmarried>
  • <something exists or nothing exists>
  • <the sun will rise tomorrow>
  • <Socrates is next to Plato>

From this and the definition of “proposition”, it follows that these representations are propositions. Likewise with any representations relevantly similar to them.

The difference between concepts and propositions

We have defined “concept” and “proposition” in terms of representations that are relevantly similar to various paradigm cases. Similar in what regard? One way to indicate the relevant dimension of similarity is to show how concepts and propositions differ from one another. If you know how concepts and propositions differ from one another, then you should be able to reliably distinguish between concepts and propositions and correctly classify any new cases you encounter.

How do concepts and propositions differ? We could point out that words and phrases tend to call concepts to mind, while statements tend to make us think of propositions. But this does not show us the intrinsic difference between concepts and propositions, if there is one. To see the intrinsic difference, it is useful to examine various pairs of representations. Consider the last example of a concept and the last example of a proposition given above. These representations are extremely similar. In fact, it may that the only difference between them is whatever it is that distinguishes concepts from propositions. There are a very large number of pairs of concepts and propositions like this. For example:

  • Concept: <myself existing>
  • Proposition: <I exist>
  • Concept: <an action being good>
  • Proposition: <an action is good>
  • Concept: <something existing or nothing existing>
  • Proposition: <something exists or nothing exists>
  • Concept: <a bridge spanning a river>
  • Proposition: <a bridge spans a river>
  • Concept: <Socrates being next to Plato>
  • Proposition: <Socrates is next to Plato>

Examine pairs of representations like these. This will show you the difference between concepts and propositions.

 

No problem.

Now, having examined the relevant representations, different philosophers have come to different opinions on the difference between concepts and propositions. Some maintain that there is no difference and that the “pairs” are really the same representation expressed in two ways. Others maintain that there is a difference, and that that difference is a matter of representational content. According to these philosophers, there is something in the representational content of a proposition that is not present in the associated concept. Other philosophers maintain that the difference is something else. Whatever the truth is, the above pairs of representations display clearly the difference between concepts and propositions if there is one.

The angle brackets convention

When we mention specific concepts or propositions, we will use angle brackets (< … >). This will allow us to distinguish propositions, which we mark with angle brackets, and statements, which we mark with quotation marks (“ … ”).

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Written by Geoff Anders

May 28, 2011 at 7:26 pm

Posted in Uncategorized

What Is Immediate Entailment?

One of the most important and most fundamental concepts in philosophy is the concept of immediate entailment. Understanding immediate entailment is essential for understanding what an argument is, validity, transparent validity and how to assess arguments. What is immediate entailment?

What immediate entailment is

It is very difficult to define “immediate entailment”. It may be impossible. So we will not try to define it here. Instead, we will attempt to convey it by giving a bunch of examples and by stating some general truths about it.

Several examples

Here are some examples of immediate entailment. They are organized into various categories. Keep in mind that these are just some examples. It is possible to generate many, many more.

  • Logical Connectives: And, Or, Not, If/Then
    • <Steve is happy and Steve is friendly> immediately entails <Steve is happy>.
    • <Julia is clever> immediately entails <Julia is a cube or Julia is clever>.
    • <Xenophanes is at home or Xenophanes is abroad> and <it is not the case that Xenophanes is abroad> together immediately entail <Xenophanes is at home>.
    • <All cubes are red or green> and <no cubes are red> together immediately entail <all cubes are green>.
    • <It is not the case that it is not the case that everyone is benevolent> immediately entails <everyone is benevolent>.
    • <Some people are cruel> immediately entails <it is not the case that it is not the case that some people are cruel>.
    • <If all cats are dogs, then all dogs are rabbits> and <if all dogs are rabbits, then all rabbits are elephants> together immediately entail <if all cats are dogs, then all rabbits are elephants>.
  • Modus Ponens
    • <Plato is cryptic> and <if Plato is cryptic, then Plato does not tell us everything he knows> together immediately entail <Plato does not tell us everything he knows>.
    • <Some triangles are green> and <if some triangles are green, then some triangles are visible> together immediately entail <some triangles are visible>.
  • Modus Tollens
    • <if Aristotle wrote The Republic, then Aristotle is Plato> and <it is not the case that Aristotle is Plato> together immediately entail <it is not the case that Aristotle wrote the The Republic>.
    • <if Aquinas was an atheist, then he did not argue for the existence of God> and <it is not the case that Aquinas did not argue for the existence of God> together immediately entail <it is not the case that Aquinas was an atheist>.
  • Various
    • <the box is red> immediately entails <the box is some color>.
    • <A is identical to B> and <B is identical to C> together immediately entail <A is identical to C>.
    • <<Socrates is wise> is true> immediately entails <Socrates is wise>.
    • <Kant is a philosopher> immediately entails <Kant is a philosopher>.

Some general truths

Here are some general truths about immediate entailment. By themselves, these truths are not enough to convey the concept fully. But they can help you check to make sure you have picked out the right idea.

  • Immediate entailment is a relation between propositions. It relates one more more propositions to a given proposition.
  • While false propositions can immediately entail true propositions or false propositions, true propositions can only immediately entail true propositions. In other words, immediate entailment is truth-preserving.
  • Whether one or more propositions entail some propositions depends only on the intrinsic properties of those propositions.
  • If you possess the concept of immediate entailment, then if one or more propositions immediately entail some proposition, it is possible for you to recognize this merely by examining the propositions in question.
  • If you know that some proposition is true and you know that that proposition immediately entails some proposition, then you can know that the latter proposition is true as well.
  • The fact that proposition A immediately entails proposition B and proposition B immediately entails proposition C is not enough by itself to ensure that proposition A immediately entails proposition C.
  • Every proposition immediately entails itself.

How to test for immediate entailment

As stated above, if you possess the concept <immediate entailment>, then it is possible to recognize whether some propositions immediate entail a proposition merely by considering the propositions in question. This means that the best way to test for immediate entailment is simply to examine the propositions in question and see whether they fall under the concept <immediate entailment>.

Apart from this, there is another test you can use. This test will not show that any purported immediate entailments do hold, but it will show in some cases that the purported immediate entailments do not hold. The test is as follows. Consider the propositions that are supposed to immediately entail the proposition in question. Pretend that those propositions are true. Now try to conceive of those propositions as being true and the proposition supposedly entailed as being false. Can you do this without overtly contradicting yourself? If you succeed, then the supposed immediate entailment does not hold. If you do not, there may be various reasons for this. As a result, no definitive conclusion can be drawn.

For instance, consider the proposition <every spatial object has a shape>. Does this proposition immediately entail the proposition <every spatial object has a color>? Clearly not. We can conceive of objects existing in space while being perfectly colorless and hence invisible. This means we can conceive the supposedly immediately entailing proposition being true while the supposedly immediately entailed proposition is false. It follows that the immediate entailment in question does not hold.

Invisible pile of gold. Counterexample conceived.

Immediate entailment and logical form

We gave several cases of immediate entailment above. Now some people will only want to refer to some of those cases as being cases of “immediate entailment”. This is because some people want to use the term “immediate entailment” to refer only to cases of immediate entailment that fit a particular logical form. For instance, some will want to only use the term “immediate entailment” to refer to cases of modus ponens. Others will want to use the term “immediate entailment” to refer to all of the cases above except for the first one in the “Various” category.

Who is right? People are free to use terms however they would like. Thus people are free to use the term “immediate entailment” however they would like. There are various reasons to select one terminology over another. In this case, though, we believe that all of the options mentioned are perfectly fine. One can use the term “immediate entailment” as we initially presented it, or one can restrict it so that it only refers to cases of immediate entailment that fit a particular logical form. As for ourselves, we will use the term as we initially presented it, and thus will consider all of the above examples to be cases of immediate entailment.

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Written by Geoff Anders

May 27, 2011 at 2:16 pm

Posted in Uncategorized

What Is Entailment?

In order to understand what an argument is, you need to understand entailment. What does it mean to say that one or more propositions entails some proposition?

What entailment is

The concept of entailment depends on a more fundamental concept, the concept of immediate entailment. Once you grasp the concept <immediate entailment>, the concept <entailment> is easy to understand.

In particular, to say that one or more propositions “entail” some proposition Q is to say that those propositions are related to proposition Q by a chain of immediate entailments. This means that like immediate entailment, entailment is a relation between propositions and relates one or more propositions to a given proposition.

Some examples

Consider the following list of propositions:

A.  <Socrates is a person>
B.  <all people are mortal>
C.  <Socrates is mortal>
D.  <all mortal things have parts>
E.  <Socrates has parts>
F.  <all things that have parts are made of particles>
G.  <Socrates is made of particles>

Here, propositions A and B immediately entail proposition C. This is a chain of immediate entailment one link long, so propositions A and B entail proposition C. Similarly, propositions C and D immediately entail proposition E and propositions E and F immediately entail proposition G. It follows that propositions C and D entail proposition E and that propositions E and F entail proposition G. It also follows that propositions A, B, D and F are linked to proposition G by a chain of immediate entailments. So it follows that propositions A, B, D and F together entail proposition G.

Next, consider these propositions:

H.  <all cats are animals>
I.  <all dogs are animals>
J.  <all cats are dogs>

Here, none of the propositions entail any of the others. How do we know? It is not because we cannot see how any of them entail any of the others. The axioms of geometry and arithmetic entail a very large number of propositions, including many propositions we cannot tell that the axioms entail. So our merely not seeing the entailments is not enough to show that the entailments are not there.

Non-obviously entailed by the axioms of geometry.

There are various ways to figure out which propositions entail one another and which do not. For instance, as we will note in a moment, entailment is truth-preserving. This means that true propositions never entail false propositions. From this it follows that propositions H and I do not entail proposition J, as <all cats are animals> and <all dogs are animals> are true while <all cats are dogs> is false.

Properties of entailment

The relation of entailment has a number of important properties. As we just said, entailment is truth-preserving. False propositions can entail true propositions or false propositions, but true propositions can only ever entail other true propositions. Entailment has other important properties as well.

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Written by Geoff Anders

May 27, 2011 at 2:25 am

Posted in Uncategorized

The Quality Of An Argument

We are examining arguments. We want to know how good they are. How should we proceed? One might think that the answer will differ from argument to argument, with some criteria applying to some arguments and different criteria applying to others. But that’s not true. For all finite, non-circular arguments, there is just one set of criteria to apply. This makes assessing arguments a relatively straightforward task.

Two criteria

Let’s consider just finite, non-circular arguments. The quality of this type of argument is determined by two criteria:

When assessing an argument, these are the only factors that matter. Everything else can be ignored.

How do transparent validity and quality of premises work together to determine the quality of an argument? First, for an argument to be good, it must be transparently valid. If it is not transparently valid, it is automatically a bad argument. This is not to say that transparent validity makes an argument good. By itself, it doesn’t. It is just a necessary condition, not a sufficient one.

If an argument is transparently valid, its quality is then determined by the quality of its premises. In particular, an argument is at best as good as its worst premise. If an argument has zero or one imperfect premises, then the argument is exactly as good as its worst premise. If an argument has two or more imperfect premises, then it is worse than its worst premise. How much worse? This depends on how bad the various premises are.

In this regard, an argument is like a chain. A chain is at most as strong as its weakest link. If it has just zero or one imperfect links, then the chain is exactly as strong as its weakest link. If it has two or more imperfect links, the chain is weaker than its weakest link – so long as we suppose that the links do not always fail in order of weakness. How much weaker? This depends on how weak the various links are.

At most as strong as the weakest link.

Some examples

Let’s consider a few examples.

  1. Socrates is a person.
  2. All people are mortal.
  3. Therefore, Socrates is mortal. [1,2]
  4. All mortal things have parts.
  5. Therefore, Socrates has parts. [3,4]
  6. All things that have parts are made of particles.
  7. Therefore, Socrates is made of particles. [5,6]

To assess this argument, first we consider whether it is transparently valid. In fact, it is transparently valid. So it passes the first test. Next we consider its premises. How good is each? Answering this question is difficult. In fact, answering it may require us to answer the central question of philosophical methodology. Since that is its own topic, for now we will just answer from our pre-theoretical perspective. Pre-theoretically, we might say that step 1 is extremely plausible and steps 2, 4 and 6 are very plausible. If we say these things, then we should conclude that the argument is somewhat plausible. We could not say it is very plausible, as the argument has four imperfect premises and thus is worse than its weakest premise. But pre-theoretically we would not say that it was a weak argument either. As far as things go, one extremely plausible premise and three very plausible premises is pretty good.

Next, consider this:

  1. All cats are animals.
  2. All dogs are animals.
  3. Therefore, all cats are dogs. [1,2]

As before, we begin by checking transparent validity. Is the argument transparently valid? The answer is no. This makes assessment easy: the argument is automatically bad, just like every argument that is not transparently valid. We do not even need to assess the quality of the argument’s premises.

Finally, consider this argument:

  1. All rabbits are cubes.
  2. All cubes are spatial.
  3. Therefore, all rabbits are spatial. [1,2]

Again, first we consider transparent validity. Is this argument transparently valid? The answer is yes. So we move on to the premises. How good is each? Sticking with our pre-theoretical perspective, step 1 is deeply, deeply implausible. Step 2, on the other hand, is perfect or nearly so. It follows that from our pre-theoretical perspective, this argument is at best really bad. If we judge step 2 to be perfect, then the argument has only one imperfect premise and thus is exactly as strong as its weakest premise. Which is to say, exactly really bad.

Precision in assessment

We said that the first argument above was, speaking pre-theoretically, better than weak but worse than very plausible. This might seem preposterously imprecise. In fact, the question of whether and how we can make argument assessment more precise is itself an important philosophical question.

The permissibility of abbreviation?

We said that the goodness of an argument requires that it be transparently valid. Some people will object to this, saying that it is sometimes okay to abbreviate arguments and leave out some of the more obvious steps. Of course, in almost every case abbreviating an argument will render it no longer transparently valid.

It is true that in practice it is often fine to abbreviate arguments and leave out obvious steps. However, it is also true that in practice, people very frequently abbreviate arguments and leave out crucial steps that should not have been left out. We don’t want to leave out crucial steps. We don’t want others to leave out crucial steps. People have been leaving out crucial steps for thousands of years and we’d like that to stop. That is why we require that arguments be transparently valid.

An “abbreviated” argument.

There are benefits to working with abbreviated arguments. They are easier to write down, for instance. If people would like to work with abbreviated arguments, that is fine. Our attitude is just that when it comes time to officially assess an argument, that argument should be presented in its full form. At that point, no step should be skipped.

More on the assessment of arguments

There is more to be said about how we assess arguments. First, we can explain why we assess arguments the way we do. Second, we can contrast the criteria we use with other potential criteria and explain why those other criteria are wrong. Third, above we restricted conversation to finite, non-circular arguments. How should we assess infinite arguments? How should we assess circular arguments? Follow the links to read more.

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Written by Geoff Anders

May 26, 2011 at 10:39 am

Posted in Uncategorized