Does transposition of the premises preserve validity in categorical syllogisms?


What are the rules for validity of categorical syllogism?

VALIDITY REQUIREMENT FOR THE CATEGORICAL SYLLOGISM

  • The argument must have exactly three terms.
  • Every term must be used exactly twice.
  • A term may be used only once in any premise.
  • The middle term of a syllogism must be used in an unqualified or universal sense.

What makes a categorical syllogism valid or invalid?

If the actual conclusion of the syllogism is equivalent to the natural conclusion or its contraposition, then the syllogism is valid. Otherwise, it is invalid.

How did you able to determine the validity of the given categorical syllogisms?

One is to draw a picture of the premises using Venn diagrams (three overlapping circles: one for each category). If the conclusion shows up as a result of drawing the premises, then we know the argument is valid, because that means that the conclusion results necessarily from the premises.

Is categorical syllogism always valid?

Yes, if the premises have been drawn, then the conclusion is already drawn. But this models a significant logical feature of the syllogism itself: if its premises are true, then its conclusion must also be true. Any categorical syllogism of this form is valid.

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What are the six rules for validity for a syllogism?

There are six rules for standard-form categorical syllogisms:

  • The middle term must be distributed in at least one premise.
  • If a term is distributed in the conclusion, then it must be distributed in a premise.
  • A categorical syllogism cannot have two negative premises.

Which of the following syllogisms is valid?

If a syllogism is valid, then it has a negative premise, if and only if it has a negative conclusion. If a syllogism is valid, then if its premises are universal, then its conclusion is universal.
Using Syllogistic Rules.

Categorical Sentence Type Distributes subject? Distributes predicate?
I no no
E yes yes
O no yes

Is syllogism a valid or invalid?

A valid syllogism is one in which the conclu- sion must be true when each of the two premises is true; an invalid syllogism is one in which the conclusions must be false when each of the two premises is true; a neither valid nor invalid syllogism is one in which the conclusion either can be true or can be false when …

Are syllogisms valid?

A syllogism is valid (or logical) when its conclusion follows from its premises. A syllogism is true when it makes accurate claims – that is, when the information it contains is consistent with the facts. To be sound, a syllogism must be both valid and true.

Can a valid syllogism have false premises?

A valid argument can have false premises; and it can have a false conclusion. But if a valid argument has all true premises, then it must have a true conclusion.

Can premises be valid?

TRUE: If an argument is sound, then it is valid and has all true premises. Since it is valid, the argument is such that if all the premises are true, then the conclusion must be true. A sound argument really does have all true premises so it does actually follow that its conclusion must be true.

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What happens if a premise is not factual?

A false premise is an incorrect proposition that forms the basis of an argument or syllogism. Since the premise (proposition, or assumption) is not correct, the conclusion drawn may be in error. However, the logical validity of an argument is a function of its internal consistency, not the truth value of its premises.

Is an argument with contradictory premises valid?

Well, if the premises are contradictory, then they cannot all be true (that’s just what contradictory means) so they can’t all be true while the conclusion is false (the necessary condition for non-validity). So the argument cannot be non-valid, it must be valid. Thus an argument with contradictory premises is valid.

Can you render an invalid argument valid by removing premises?

In classical logic no, but you can make a sound argument unsound by adding false premises. The difference between soundness and validity is usually ignored colloquially, but logical validity is neutral on the truth of the premises, it only cares whether inference would preserve that truth.

Is an argument with contingent premises valid?

The definition applies to it because it is impossible for it to have true premises and a false conclusion (since it is impossible for it to have a false conclusion at all). All other sentences–that is, all those that are neither tautologies nor inconsistent–are called CONTINGENT.
Tautologies.

P ~P P & ~P
T F F
F T F