Basic Argumentation.

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Basic Argumentation

What is an ARGUMENT? A group of statements, in which some of them (the premises) are intended to support another statement (the conclusion). An Argument is NOT: a quarrel, bickering or verbal fighting of any kind. When we use the word “Argument” in logic, this is NOT what we mean.

Introduction to LOGIC Deductive Arguments
An argument whose conclusion necessarily follows from the truth of the premises A D.A. is “valid” if it is successful in providing logical support for its conclusion A “valid” D.A. is such that if all its premises are true, it is guaranteed that the conclusion must be true. This means that if all the premises are true, there is NO possible way that the conclusion could be false. We say that a D.A. is “invalid” if the truth of the premises does NOT guarantee that the conclusion must be true.

Introduction to LOGIC Deductive Arguments VALID does NOT equal TRUE
These are NOT synonyms It is entirely possible for a valid D.A. to be FALSE. To claim that an argument is a “deductively valid argument” only means that the argument has necessary logical STRUCTURE Logical structure doesn’t refer to the actual contents of an argument, but to its construction: The particular way the premises and conclusion fit together. The logical structure of a D.A. is “truth preserving” which means the truth of the premises are preserved onto the conclusion

Introduction to LOGIC Simple Deductive Arguments
Premise 1 – All politicians are liars Premise 2 – Jim is a politician Conclusion – Therefore it follows that Jim is a liar Premise 1 – All men are mortal Premise 2 – Socrates is a man Conclusion – Therefore, Socrates is mortal

Introduction to LOGIC Logic is ABSOLUTE
In each of these following arguments, if the premises are true, the conclusion MUST be true. It is impossible for the premises to be true and the conclusion to be false. The conclusion follows directly from the premises, and the order of the premises makes no difference

Introduction to LOGIC Deductively INVALID Arguments
Premise 1 – All politicians are liars Premise 2 – All used car salesmen are liars Conclusion – Therefore if follows that all used car salesmen are politicians Premise 1 – If Socrates has no teeth, then he is mortal Premise 2 – Socrates is mortal Conclusion – Therefore, Socrates has no teeth *These Conclusions do not logically follow from the Premises

Introduction to LOGIC INDUCTIVE Arguments
An argument that is intended to provide “probabilistic” support for its conclusion. An I.A. is such that if all its premises are true, the conclusion is possibly true, or highly likely to be true, but not necessarily true If an I.A. succeeds in providing probable (but not logically necessary) support for its conclusion, then it is said to be “strong.” If an I.A. fails to provide good support for its conclusion, we call it “weak.” The structure of an I.A. does NOT guarantee that if all the premises are true, the conclusion must necessarily be true. However, if the conclusion is “highly probable” then it should be generally accepted. When a good Inductively strong argument has true premises, it is “cogent.” Bad inductive arguments are NOT cogent.

Introduction to LOGIC INDUCTIVE Arguments
Due to the fact that the truth of an inductive argument's conclusion cannot be guaranteed by the truth of its premises, inductive arguments are NOT “truth preserving.”

Introduction to LOGIC Strong INDUCTIVE Arguments
Premise 1 – Most dogs have fleas Premise 2 – Bowser is a dog Conclusion – Therefore it follows that Bowser probably has fleas Premise 1 – 98% of snails are slimy Premise 2 – There is a snail in my garden Conclusion – Therefore, the snail in my garden is highly likely to be slimy

Introduction to LOGIC Strong INDUCTIVE Arguments
Be aware that it is entirely possible for all the premises to be true in these I.A.s, and for the conclusion to be false. After all, just because most dogs have fleas, doesn’t mean that Bowser does, because it is possible that he is one of the few dogs that don’t. Also, just because 98% of snails are slimy, doesn’t mean the one in my garden is necessarily slimy, because he might be part of the 2% that is not.

Introduction to LOGIC Strong INDUCTIVE Arguments
Be aware that it is entirely possible for all the premises to be true in these I.A.s, and for the conclusion to be false. After all, just because most dogs have fleas, doesn’t mean that Bowser does, because it is possible that he is one of the few dogs that don’t. Also, just because 98% of snails are slimy, doesn’t mean the one in my garden is necessarily slimy, because he might be part of the 2% that is not. Good D.A.s definitely have a valid logical structure. However, there is more to good deductive arguments than good logical structure. Good D.A.s also have true premises. EXAMPLE: Deductively Valid (but FALSE) Argument Premise 1 – All pigs can fly Premise 2 – Charles is a pig Conclusion – Therefore it follows that Charles can fly

Introduction to LOGIC A good D.A. must have true premises
We say that a deductively valid argument with true premises is “sound.” A SOUND argument is a good argument which gives you good reasons for accepting its conclusions. Deductively valid arguments can have TRUE or FALSE premises and TRUE or FALSE conclusions Deductive valid arguments can have: False premises and a false conclusion False premises and a true conclusion True premises and a true conclusion

Introduction to LOGIC False Premises and False Conclusion
All fish have wings All fish are dogs Therefore it follows that all dogs have wings False Premises and True Conclusion All crows don’t have wings Everything that doesn’t have wings is black Therefore, all crows are black

Introduction to LOGIC True Premises and True Conclusion
I have two feet On each foot I have five toes Therefore, I have ten toes The support a D.A. gives for its conclusion is “absolute.” Either it is demonstrably true, or it is not. There is no possible “sliding scale” of truth or falsity. However, as the support an I.A. gives is probabilistic, the likelihood of the truth of an I.A. goes on a scale from very unlikely to highly likely.