By this, we mean forms or types of Logic – deductive reasoning and inductive reasoning
From inductive reasoning we get inductive inferences or inductive argument and from deductive reasoning will get deductive inferences or argument. Hence, reasoning can be in two forms: deductive & inductive reasoning. Formal logic is more interested in deductive reasoning because we can only get certainty in deductive reasoning.
Inductive Reasoning
An inductive argument is an argument that given the premises, it is possible that the conclusion is true. For example, it rained in July 2014, it rained in July 2015, it rained in July 2016, it rained in July 2017, it rained in July 2018, and therefore it will rain in July 2019.
The relationship between the premises and the conclusion of an inductive argument is that of probability. (Science relies on Induction, inductive reasoning is part of everyday life). (Note: Sometimes induction can fail but with some other factors it is most reliable).
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An inductive arguments is strong when given the premises, the probability that the conclusion will follow is high.
For example,
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In this case, although it is possible that the speaker might go to the restaurant one more time and the food will not be delicious. Given the information in the premises, it is likely the food will be delicious.
In other words, the probability that the claim or conclusion is true given the premises is quite high.
An inductive argument is weak when given the premises, the probability that the conclusion will follow is low. For example,
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In this case, although it is possible that the next time the speaker will use paracetamol it will work, but it will not be much of a surprise if it does not, given the information in the premises.
In other words, the probability that the claim is true given the premises is quite low.
Assignment
Write out five strong and weak inductive arguments.
For Example,
1.
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2.
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3.
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(Note) a weak argument can be strengthened by adding information to the premises. Formal logic is more interested in deductive argument because it interest is in certainty not probability
Deductive Argument
A deductive argument is an argument in which the conclusion seems to or appears to follow necessarily from the premises. In other words, the premises appears to give conclusive support to the claim. For example:
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In this argument the conclusion seems to follow necessarily from the premises. When the claim of a deductive argument actually follows from the premises; the argument is a valid deductive argument. In this case, it is accepted that if the premises can be true, the conclusion will also be true. When the premises of a deductive argument appears to give a conclusive support to it claim but does not; it is an invalid deductive argument. In this case although it seems the claim follows conclusively from the premises; it does not.
For example,
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Distinguishing between a valid and invalid deductive argument without using a method in logic can be tricky. This is because validity of a deductive argument does not lie in the truth of it context but in it structure. It is possible to have a deductive argument, where although all it statement are false, the argument is valid. Likewise, it is possible to have a deductive argument that has true statement yet it is an invalid deductive argument. A valid deductive argument is either sound or not sound (it means an invalid argument cannot have the property of soundness. Validity cannot come in inductive argument, inductive argument has no business with validity or otherwise). When a deductive argument is valid and all it statement are true, then it is a sound deductive argument. When a deductive argument is valid but at least one of its statement is false, then it is not a sound deductive argument. For example:
1.
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2.
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Although this deductive argument is valid, at least one of its statement is false, hence it is not a sound deductive argument. A deductive argument is therefore valid or invalid and a valid deductive argument is either sound or not sound.
Identify Valid and Invalid Argument in the following:
1.
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2.
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3.
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4.
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5.
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6.
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7.
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8.
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9.
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10.
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Test for Validity
When testing for validity using refutation by logical analogy, note the following:
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NOTE; without using a controversial example, you cannot refute a valid argument by the method of logical analogy. So when an argument is invalid, it would not take much time to be able to find an example which the premises will be true in the real world, and your conclusion will be false in the real world, but when an argument is valid, trying to refute it by method of logical analogy will lead to controversial example. So this argument:
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It’s an example of a valid argument, any attempt to refute it by method of logical analogy will lead to controversial example. Note; in test and exam we will not ask you to refute a valid argument in order avoid wasting your time. If we ask you to refute an argument, just know that, that argument is invalid.
Let look at number 3:
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This is valid argument and cannot be refuted.
Let’s look at number 4:
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The argument above is invalid, you can refute it with the following examples;
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Another example to refute the number 4 argument:
It is possible for technology to create a chair that can also act as a table, not just to sit on it but to serve as multipurpose. For example,
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Or let look at this:
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Note it is possible to have a wild goat but is not possible to have a goat that is a lion. So this will show that the argument is invalid.
Note; in logic you don’t imply what is not said, for example if I tell you some women are human; you don’t imply that some women are not human. If I tell you that some women are human; it simply means that there is at least one object that is a woman and has the property of being human. That is, both a woman has the property of being human. It means the person is a woman and human. So when I say some, it does not implies some are not. For example, if I tell you that if you pass Phil 201, I will give you #20,000, and then you failed Phil 201 and you come to me and I still give you the #20,000. Did I lie? No! I only told you what I will do if you pass, I didn’t tell you what I will not do if you didn’t pass. So in logic, you didn’t implies what is not said.
Let’s look at number 5:
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Note that validity of the original argument doesn’t depends on it truth or falsity but on it structure. It is the caricature that you will check whether it is true or not. So the original statement can have false elements and still be valid giving it structure. So it is the caricature you will check whether its premises are true but the conclusion is false.
In the number argument 5 above, it caricature/refutation will be:
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Another example:
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Another example:
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Let try Argument 6:
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Refutation:
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Assignment:
Practise example 8 & 9 on your own, write out it refutation.