Introduction to PhilosophyLecture 3

Formalizing an argument

By David Kelsey

Evaluating an argument

• Evaluate the argument: – To evaluate an argument is to critique it.

• Understand the argument: – Before evaluating an argument you must understand it as it’s author does.

– Formalize it

A summary of the process

• To formalize an argument: – to break that argument down into its most simplified form.

• The process (of formalizing) includes several steps:– Write:

– Structure:

– Evaluate:

The principle of charity

• Write what the author intends:

– Abide by the principle of charity.

– The Bloodhounds example again

Simplify and number

• Simplify and Number:

– Now Simplify the Propositions of the argument

– Number the propositions

• Any inference the argument makes must follow what it is inferred from.

The structureof an argument

• The structure rule: – any inference the argument makes follows what it is inferred from.

– How do we clarify an argument’s structure?

• An argument’s structure: its pattern of reasoning from the first premise to the conclusion.

Clarifying an argument’s structure: #s and symbols

• First, – Number the propositions of the argument according to the order in which

they fall in the text itself.

• Second,– Clarify the structure with the numbers

Symbols

• When one proposition Q is inferred from another P we write:

Symbolizing Dependent Premises

• Dependent Premises: When you have two or more propositions, P and Q, that dependently support some other proposition of the argument, R:

Symbolizing Independent premises

• Independent Premises: when we have two or more propositions, P and Q, that independently support some third proposition of the argument, R:

–

1 proposition supporting more than one or vice versa.

• 1 Proposition Supporting 2: When we have a proposition, P, that supports more than one proposition of the argument, Q and R, we write:

• •

• Dependent & Independent Premises: When we have two propositions, P and Q, that dependently support another, S, and we also have a fourth proposition, R, that independently supports S we write:

–

Counter-arguments

• Symbolizing counter Reasons: – When we have a proposition, P, that is a reason against some other

proposition of the argument, Q, we write a downward arrow from P to Q. We then put a slash mark through the arrow.

– Like this:

• Counter reason: – A reason that is evidence against some premise of an argument.

Defending against Counter-arguments

• Defending against a Counter Argument: – Counter argument: an argument that makes use of a counter reason to show some

other argument unsound.

• Show the counter argument is unsound: – You can defend your own argument by showing a counterargument is unsound.

The Carlos example

• The passage:– I don’t think we should get Carlos his own car. As a matter of fact, he is not

responsible because he doesn’t care for his things. And anyway, we don’t have enough money for a car, since even now we have trouble making ends meet. Last week you yourself complained about our financial situation, and you never complain without really good reason.

• Find the sentences in which the premises and the conclusion are contained.– premise indicators

Listing the Propositions

• Let us now just compose a list of the propositions of the argument. – Follow the order of the text for now

• The List:– I don’t think we should get Carlos his own car.

– As a matter of fact, he is not responsible.

– He doesn’t care for his things

– And anyway, we don’t have enough money for a car.

– Since even now we have trouble making ends meet.

– Last week you yourself complained about our financial situation.

– You never complain without really good reason.

Simplify and number

• Simplify and number:

– 1) We shouldn’t get Carlos his own car.– 2) Carlos is not responsible.– 3) Carlos doesn’t care for his things– 4) We don’t have enough money for a car.– 5) We have trouble making ends meet.– 6) Last week you complained about our financial situation.– 7) You never complain without really good reason.

Structuring the Carlos argument

• Now clarify the structure of the argument: – What is the relationship between 2 and 3? What does ‘because’ indicate about 2 and

3?

– What is the relationship between 2 and 1?

– What about 5 and 4? What does ‘since’ indicate about 4 and 5?

– What is the relationship between 6, 7 and 4?

The finished structure

• Propositions 6, 7 and 5 are all related to 4. So lets combine the symbolization:

• But what is the relationship between 4 and 1?

• So what does the final structure look like?

The finished formalization

• Now Renumber the propositions of the argument to map onto its structure.

• The argument after renumbering:– 1) Carlos doesn’t care for his things.– Thus, 2) Carlos isn’t responsible.

(from 1)– 3) Last week you complained about

our financial situation.– 4) You never complain without really

good reason.– 5) We have trouble making ends

meet now.– Thus, 6) We don’t have enough

money for a car. (from 3&4 and 5.)– Thus, 7) We shouldn’t get Carlos his

own car. (from 2 and 6.)

• After the finished formalization now evaluate it.

Evaluating formalizations, generally speaking

• In evaluating a formalization: determine if the argument is good.– Is the argument valid or strong?

– Are the premises of the argument reasonable?

Step #2

• Are the premises are reasonable?– Evaluate the support given for each premise.

– The premises of a well supported argument are sub-conclusions

Premises as sub-conclusions

• To evaluate an argument in favor of a sub-conclusion

• Tips for quick evaluations of the premises of an argument:– Does the claim conflict with other credible sources or your own observation or

background info?

• What if the argument is valid or strong and it’s premises reasonable?

4 Simple steps to formalizing

• Here is a quick 4 step process to formalizing arguments:• 1. What is the issue of the passage?

• 2. Find the conclusion.

• 3. Find the premises– Work backwards:

• 4. Arguments for premises?

The Ontological Argument

• Let us now look at “The Ontological Argument” by Saint Anselm.

• So Lord--you who reward faith with understanding--let me understand, insofar as you see fit, whether you are as we believe and whether you are what we believe you to be. We believe you to be something than which nothing greater can be conceived. The question, then, is whether something with this nature exists, since “the fool has said in his heart that there is no God” [Ps. 14:1, 53:1]. But surely, when the fool hears the words “something than which nothing greater can be conceived,” he understands what he hears, and what he understands exists in his understanding--even if he doesn’t think that it exists. For it is one thing for an object to exist in someone’s understanding, and another for him to think that it exists.

• And the passage continues:• This should convince even the fool that

something than which nothing greater can be conceived exists, if only in the understanding--since the fool understands the phrase “that than which nothing greater can be conceived” when he hears it and whatever a person understands exists in his understanding. And surely that than which a greater cannot be conceived cannot exist just in the understanding. If it were to exist just in the understanding, we could conceive it to exist in reality too, in which case it would be greater. Therefore, if that than which a greater cannot be conceived exists just in the understanding, the very thing than which nothing greater can be conceived is something than which a greater can be conceived. But surely this cannot be. Without doubt, then, something than which a greater can’t be conceived does exist--both in the understanding and in reality.

Premise Indicators

• Now that we have the passage let’s look for premise and conclusion indicators:

– ‘But surely’

– ‘This should convince’

– ‘Therefore’

– ‘Without doubt then’

The Anselm argument

• The argument:

– When one hears the words ‘something than which nothing greater can be conceived’, he understands what he hears.

– Whatever a person understands exists in his understanding.– Something than which nothing greater can be conceived exists in the

understanding.– If something than which nothing greater can be conceived were to exist just

in the understanding, we could conceive it to exist in reality too, in which case it would be greater.

– Therefore, if that than which a greater cannot be conceived exists just in the understanding, the very thing than which a greater cannot be conceived is something than which a greater can be conceived.

– Without doubt, then, something than which a greater can’t be conceived does exist.

Simplify and Number

• Once we have simplified our premises and conclusion number them– Follow the Structure Rule

1) When one hears the words ‘something than which nothing greater can be conceived’, (or GOD) he understands what he hears.

2) Whatever a person understands exists in his understanding.

3) Thus, GOD exists in the understanding.

4) If GOD were to exist just in the understanding, we could conceive it to exist in reality too.

5) If GOD were to exist in reality too, it would be greater.

6) Thus, if GOD exists just in the understanding, it is something than which a greater can be conceived.

7) Thus, GOD does exist in reality.

Evaluating the argument

• Now that our argument is formalized we must evaluate it– 1- determine if it is a good argument.

– 2-Examine the premises:

Evaluating Anselm’s argument

• What about the Anselm argument.– Premise 1?

– Premise 4?

– Premise 5?