1. Critical Thinking Lecture 2 Arguments
By David Kelsey

2. Arguments Arguments: A position supported by reasons for its truth
Always have a conclusion and at least one premise

3. Dependent & Independent Premises
Types of premises: the premises of an argument can support its conclusion in two ways: dependently or independently.
This distinction is one that is a distinction in type of support provided…

4. Dependent Premises
Dependent premises support the conclusion of an argument only together with and dependent on some other dependent premise.
A dependent premise:
cannot support the conclusion of an argument by itself.

5. Independent Premises
Independent premises, on the other hand, support the conclusion of an argument on their own.
An independent premise:
doesn’t need any other premise to support its conclusion.
has enough power and justification to support the conclusion on its own.

6. More on Dependent Premises
So Dependent premises must and always support a conclusion along with another dependent premise.
In addition, if there are dependent premises in support of a conclusion and one is false you no longer have an argument at all!
So any support dependent premises offer for a conclusion is cancelled or destroyed if one of those premises is false.

7. Dependent Premises, an example
An Example of an argument with Dependent Premises:
1) Socrates is human.
2) All humans are mortal.
Thus, 3) Socrates is mortal.
As you can see to get to the conclusion that Socrates is mortal, you need both premises.
Note also if it just so happened that, say, it was false that All humans are mortal, then this argument no longer supports the conclusion that Socrates is mortal.

8. More on Independent Premises
While Dependent Premises always support a conclusion with another premise, an independent premise supports a conclusion on its own.
Note also that if you have 2 independent premises in favor of the same conclusion and one is false, the argument is not destroyed!

9. Independent Premises, an example
An example of an argument with Independent Premises:
1) The weather forecast predicts rain tomorrow.
2) It has rained all week.
Thus 3) it will rain tomorrow.
Notice here that if it happens to be false that it has rained all week we still have good reason for thinking it will rain tomorrow for the weather forecast says it will!

10. Valid arguments
Valid arguments are defined as those arguments in which it is the case that if the premises are true then the conclusion must be true.

11. Valid arguments and the necessary connection
Valid arguments: a necessary connection
With Valid arguments there is a necessary connection between the premises and the conclusion
So the conclusion of a valid argument must follow from its premises.
And the conclusion of a valid argument is the only possible claim that can follow necessarily from the premises. No other claim will do.

12. Socrates is Mortal Socrates is mortal: 1. Socrates is human.
2. All humans are mortal.
Thus, 3. Socrates is mortal.

13. More on Socrates Thinking about the Socrates is mortal example:
From the claim that Socrates is human and that all humans are mortal, it doesn’t follow that I am mortal or that you are mortal because those claims aren’t about you or I.
The only claim that could possibly follow these premises is that Socrates is mortal…

14. Barack Obama
We can have a valid argument with a false premise and a false conclusion.
Barack Obama example:
1) Barack Obama is a robot.
2) If Barack Obama is a robot then he cannot be the president.
Thus, 3) Barack Obama cannot be president.

15. The moon is made of green cheese
And we can have a valid argument with false premises and a true conclusion:
The moon is made of green cheese example:
1) The moon is made of green cheese.
2) All things made of green cheese orbit the Earth.
Thus, 3) The moon orbits the Earth.

16. The puzzle metaphor The puzzle metaphor:
As a metaphor to describe a valid argument picture a jigsaw puzzle.
Imagine that the puzzle is complete except for one final piece.
Think of the puzzle, missing one final piece, as the premises and the final missing piece as the conclusion.

17. Sound Arguments A sound argument is valid and has true premises.
Thus, the conclusion of a sound argument is also true.
A sound argument is ideal.
Perfect reasoning with true premises and conclusion!

18. Dreaming example Dreaming example:
1) Either I am giving this lecture right now or I am dreaming it.
2) I am not dreaming it.
Thus, 3) I am giving this lecture right now.

19. The Superbowl example The Superbowl example:
1) The Broncos won the Superbowl in 2016.
2) If a team loses a playoff game, then they cannot win the Superbowl.
Thus, 3) The Broncos didn’t lose a playoff game in 2016.

20. Strong arguments
Strong arguments are defined as those arguments in which it is the case that if the premises are true then the conclusion is likely to be true.

21. Strong arguments and the connection of likelihood
Strong arguments: a connection of probability
While Valid arguments have a necessary connection between the premises and the conclusion Strong arguments have a connection that is built on probability or likelihood.
So the conclusion of a strong argument is made to be more likely given its premises.
Lets look at an example…

22. Rain today
Rain today:
1. It has rained all week.
Thus, 2. It will rain today.
Note that because it has rained all week it does seem more likely that it will rain...
But also note that even though it has rained all week this in no way guarantees that it will rain today. So the conclusion could still be false.

23. The Swan example
So with Strong arguments we see that even if the premises of the argument are true, the conclusion could still be false.
Here is an example:
1. Every swan I’ve ever seen is white.
Thus, 2. All swans are white.
Although it is true that I have only seen white swans in my life, in some parts of the world there are black or even blue swans!

24. Strength and Validity
So it is possible to have a strong argument with true premises and a false conclusion.
This is precisely why strong arguments are not valid arguments.
For if an argument is valid and its premises true, its conclusion must be true.
But a strong argument can have true premises and a false conclusion…

25. Stronger arguments Some Strong arguments are stronger than others.
For the more evidence you have in favor of your conclusion the more likely your conclusion is to be true.
Lets look at an example…

26. Stronger arguments again
Lets look back at the swan example to see the point:
1. Every swan I’ve ever seen is white.
Thus, 2. All swans are white.
Imagine in this case that you have seen 10 swans in your life. So you conclude all swans are white.
Now imagine, differently, that you have seen 50,000 swans in your life and they have all been white and so you conclude that all swans are white.

27. Reverse Gravity example
Imagine for this example that gravity is reversed and when you drop something it actually floats up and not down. Now imagine you have a pen in your hand…
The Reverse Gravity example:
1. Every time I have ever let go of something from my hand it floats up to the sky.
Thus, 2. If I let go of a pen from my hand at this moment it will float up to the sky.
Notice that although the premise and conclusion here are false that if this premise was true the conclusion would be really likely.

28. Cogent Arguments A Cogent Argument is strong and has true premises.
Thus, the conclusion of a Cogent argument is likely to be true.

29. The Sun rises and sets The sun rises and sets:
1) Every day of my life the sun has risen in the morning and set in the evening.
Thus, 2) Tomorrow the sun will rise in the morning and set in the evening.
Notice that this is about as strong an argument as we can make! My evidence for this one is every day of my life!
But also notice that it is still possible that the conclusion turns out false for we cannot know what will happen tomorrow.

30. Strength, Cogency and Prediction
Notice as in the Sun Rises example, in most cases strong and cogent arguments will look a lot like a prediction into the future!
In the Sun rises example I predict that tomorrow the sun rises.
In the reverse gravity example I predict what will happen when I let go of a pen from my hand.
In the Rain Today example I predict it will rain today.
And in the Swans example I predict the color of all swans.
So strong and cogent arguments are based on prediction. This creates uncertainty, hence, strong arguments have a connection based on likelihood.

31. Deduction versus Induction
Deductive Arguments are those that are valid and sound.
Thus, there is a necessary connection...
Inductive Arguments are strong and cogent.
Thus, the connection is based on probability or likelihood.

32. Socrates is Mortal Socrates is mortal: 1. Socrates is human.
2. All humans are mortal.
Thus, 3. Socrates is mortal.
This example is deductive.
Notice the necessary connection.

33. Rain Tomorrow Rain Tomorrow: This example is inductive.
1. The weather forecast is for rain tomorrow.
2. It has rained all week.
Thus, 3. It will rain tomorrow.
This example is inductive.
Notice the connection here is one of probability or likelihood.
Since we cannot predict the future, from the premises its just likely that it will rain tomorrow, not necessary.

34. Induction and Prediction
Inductive arguments tend to make predictions.
Consider the Rain Tomorrow example:
1. The weather forecast is for rain tomorrow.
2. It has rained all week.
Thus, 3. It will rain tomorrow.
Notice that this inductive argument makes a prediction about the weather.

35. The Sun Rises and Swans are White
The Sun Rises and Sets:
1. Every day of my life the Sun has risen in the morning and set in the evening.
Thus, 2. Tomorrow the Sun will rise in the morning and set in the evening.
All Swans are White:
1. Every swan I have ever seen was white.
Thus, 2. All swans are white.
Notice the prediction that occurs in both examples.

36. Inductive Arguments The Sun Rises and Sets:
1. The Sun has risen and set every day of my life.
Thus, 2. the Sun will rise and set tomorrow.
We see that in this Inductive argument the conclusion is interesting and new information.
It looks a bit like a guess.
And it might turn out false.

37. Deductive Arguments Socrates is mortal:
1. Socrates is human.
2. All humans are mortal.
Thus, 3. Socrates is mortal.
Notice that the conclusion in this deductive argument is not really that interesting.
It is also not really new information. In fact, you kind of see the conclusion coming.
This is because in deductive arguments like this the conclusion is built out of the premises.

38. Induction and the future
Lets take a look at one last example of Induction for one final point.
April 10:
1. It has rained every April 10 I can remember.
Thus, 2. It will rain this April 10.
As we discussed, inductive arguments like this make predictions about the future, in this case about the coming April 10.
Notice though, in making a prediction about the future this argument assumes that the future will resemble the past.

39. The Future Resembles the Past
We can formalize our April 10 example like this then:
1. It has rained every April 10 I can remember.
2. The future resembles the past.
Thus, 3. It will rain this April 10.
We tend to assume that the future resembles the past because it usually does.
But now notice though that the future needn’t always resemble the past! Sometimes the future changes!
Thus, although its rained every April 10 I can remember, this April 10 might be different!