Definition of hypothetical syllogism. 1: a syllogism consisting wholly of hypothetical propositions. — called also pure hypothetical syllogism. 2: a syllogism consisting partly of hypothetical propositions. — called also mixed hypothetical syllogism. 11 rows · Hypothetical syllogisms are short, two-premise deductive arguments, in which at least one of the premises is a conditional, the antecedent or consequent of which also appears in the other premise. I. “Pure” Hypothetical Syllogisms: In the pure hypothetical syllogism (abbreviated HS), both of the premises as well as the conclusion are conditionals. For such a conditional to be valid the .
Hypothetical Syllogisms. Hypothetical syllogisms are short, two-premise deductive arguments, in which at how to make a water level alarm one of the premises is a conditional, the antecedent or consequent of which also appears in the other premise. In the pure hypothetical syllogism abbreviated HSboth of the premises as well as the conclusion are conditionals. For such a conditional to iss valid the antecedent of one premise must match the consequent of the other.
What one may validly conclude, then, is a conditional containing the remaining antecedent as antecedent and the remaining consequent as consequent. You might simply think of the middle term — the proposition in common ayllogism the two premises — as being cancelled out. Other forms are invalid unless they can be converted into a valid form by the law of what is a hypothetical syllogism — see my notes for categorical syllogisms.
In mixed hypothetical syllogisms, one of the premises is a conditional while the other serves to register agreement affirmation or disagreement denial with either the antecedent or consequent of that conditional. There are thus four possible forms of such syllogisms, two of which are valid, while two of which are invalid.
You can perhaps see why these forms are valid or invalid by considering a very simple example. Think of the what is a standard work week four syllogisms:. While syllogisms 1. And Tweety might just happen to be one of those. Exercises: The following is a list of schematized hypothetical syllogisms. Hypothetical Syllogisms Hypothetical syllogisms are short, two-premise deductive arguments, in which at least one of the premises is a conditional, the antecedent or consequent of which also appears in the other premise.
If q, then r. So If p, then r If p, then not r. If not r, then not q. So If p, then not q Other forms are invalid unless they can be sylogism into a valid form by the law of contraposition — see my notes for categorical syllogisms. Not q. Not p. You will want to remember these rules for validity!!!
Think of the following four syllogisms: 1. Tweety is a bird. Tweety flies 2. Tweety is not a bird. Tweety flies. Tweety is a bird 4. P, if not q. Invalid DA ii. If q, then not r. If p, then not r. Valid HS 1. If p, q. P only if q. Without p, q. P, provided that q. If p, then not q. R, unless q. If p, then r. If p, then q.
If r, then q. Assuming p, q. Q only if r. P only if r. P else q. P unless q. Unless p, q. Only if p, q Not p. Not q sylloogism Given p, not q. P whenever q. Not p, should it be q. Not p Q Not p only if nypothetical. Whenever q, r. R unless p. Answers to odd exercises: 1. Invalid AC 3. Valid AA 5. Valid HS 7. Invalid AA [but wrong conclusion! Valid HS Invalid AC Valid DC Valid AA Valid HS. So If p, then r.
So If p, then not q. Invalid DA. Not p Q.
A hypothetical syllogism is a valid argument form in logic. The form of hypothetical syllogism is: “If P, then Q. If Q, then R. Therefore, if P, then R.” It may also be written as: P > Q Q > R ? P > R.
In classical logic , hypothetical syllogism is a valid argument form which is a syllogism having a conditional statement for one or both of its premises. The term originated with Theophrastus. In propositional logic , hypothetical syllogism is the name of a valid rule of inference often abbreviated HS and sometimes also called the chain argument , chain rule , or the principle of transitivity of implication.
The rule may be stated:. Hypothetical syllogism is closely related and similar to disjunctive syllogism , in that it is also type of syllogism, and also the name of a rule of inference. The rule of hypothetical syllogism holds in classical logic , intuitionistic logic , most systems of relevance logic , and many other systems of logic.
However, it does not hold in all logics, including, for example, non-monotonic logic , probabilistic logic and default logic.
The reason for this is that these logics describe defeasible reasoning , and conditionals that appear in real-world contexts typically allow for exceptions, default assumptions, ceteris paribus conditions, or just simple uncertainty.
An example, derived from Adams , . Clearly, 3 does not follow from 1 and 2. In practice, real-world conditionals always tend to involve default assumptions or contexts, and it may be infeasible or even impossible to specify all the exceptional circumstances in which they might fail to be true. For similar reasons, the rule of hypothetical syllogism does not hold for counterfactual conditionals.
The hypothetical syllogism inference rule may be written in sequent notation, which amounts to a specialization of the cut rule:. An alternative form of hypothetical syllogism, more useful for classical propositional calculus systems with implication and negation i. An example of the proofs of these theorems in such systems is given below.
The proofs relies on two out of the three axioms of this system:. The proof of the HS2 is given here. From Wikipedia, the free encyclopedia. The Logic of Conditionals. Dordrecht: Reidel. Categories : Rules of inference Theorems in propositional logic Classical logic Syllogism. Namespaces Article Talk. Views Read Edit View history. Help Learn to edit Community portal Recent changes Upload file.
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