Geometry
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Unit 2: Reasoning & Proof
Lesson 2.4:
What is Deductive Reasoning and How Can We Use It?
"Deductive reasoning is a logical process in which a conclusion
is based on the concordance of multiple premises
that are generally assumed to be true.
Deductive reasoning is sometimes referred to as top-down logic."
--whatis.com
is based on the concordance of multiple premises
that are generally assumed to be true.
Deductive reasoning is sometimes referred to as top-down logic."
--whatis.com
We will spend most of our time in this class using deductive reasoning.
We will be looking at two laws:
1) The Law of Detachment
2) The Law of Syllogism
What is true? How can we definitively say that there is something
that is perfectly, totally, and unavoidably true? How can we prove it?
We are going to look at some very basic truths and use these as foundations for all sorts of truths.
We are going to be using deductive reasoning each step of the way.
Let's start with the law of detachment, which in essence tells us that we are allowed to make new conclusions in the first place:
We will be looking at two laws:
1) The Law of Detachment
2) The Law of Syllogism
What is true? How can we definitively say that there is something
that is perfectly, totally, and unavoidably true? How can we prove it?
We are going to look at some very basic truths and use these as foundations for all sorts of truths.
We are going to be using deductive reasoning each step of the way.
Let's start with the law of detachment, which in essence tells us that we are allowed to make new conclusions in the first place:
If we have a conditional t (If p, then q) that is true, and the hypothesis is true, then the conclusion is true.
For example:
Conditional: If you earn a score that is 90% or above, you have earned an A in this class.
Hypothesis: You earned a 94.8%.
What conclusion can we draw from this true conditional and this true hypothesis?
...
You have earned an A in this class! Way to go!
For example:
Conditional: If you earn a score that is 90% or above, you have earned an A in this class.
Hypothesis: You earned a 94.8%.
What conclusion can we draw from this true conditional and this true hypothesis?
...
You have earned an A in this class! Way to go!
Let's take a second to remind ourselves of the difference between inductive and deductive reasoning,
and also look at The Law of Syllogism:
and also look at The Law of Syllogism:
As stated in the video, inductive reasoning is a bottom-up approach.
You gather facts and patterns and predict what will happen next.
You do this a lot in science, with the aid of the scientific method to keep out human bias.
Deductive reasoning is a top down approach.
We start with basic truths and make a case for new truths.
With deductive reasoning, we have certainty.
We know certain things to be true.
You gather facts and patterns and predict what will happen next.
You do this a lot in science, with the aid of the scientific method to keep out human bias.
Deductive reasoning is a top down approach.
We start with basic truths and make a case for new truths.
With deductive reasoning, we have certainty.
We know certain things to be true.
If you live in Palo Alto, you live in California.
If you live in California, you live in the United States.
Hypothesis: Herbert lives in Palo Alto.
Conclusion: Herbert lives in the United States.
I found a few videos of The Law of Syllogism made by students (probably) your age:
If you live in California, you live in the United States.
Hypothesis: Herbert lives in Palo Alto.
Conclusion: Herbert lives in the United States.
I found a few videos of The Law of Syllogism made by students (probably) your age:
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