Universal instantiation can be used to prove one of the classical "syllogisms" of the Greek philosopher and scientist Aristotle, who lived from 384 to 322 B.C.E. and who first developed a system of formal logic. The argument has the form, "All humans are mortal. Socrates is human. There- fore Socrates is mortal." Using the notation H(x) is “x is human." s is a constant symbol (Socrates) M(x) is "x is mortal." the argument is (Vx)[H(x) → M(x)] ^ H(s) → M(s) and a proof sequence is (Vx)(H(x) → M(x)) hyp Но) һyp H(s) → M(s) 1, ui M(s) 2, 3, mp In step 3, a constant symbol has been substituted for x throughout the scope of the
Universal instantiation can be used to prove one of the classical "syllogisms" of the Greek philosopher and scientist Aristotle, who lived from 384 to 322 B.C.E. and who first developed a system of formal logic. The argument has the form, "All humans are mortal. Socrates is human. There- fore Socrates is mortal." Using the notation H(x) is “x is human." s is a constant symbol (Socrates) M(x) is "x is mortal." the argument is (Vx)[H(x) → M(x)] ^ H(s) → M(s) and a proof sequence is (Vx)(H(x) → M(x)) hyp Но) һyp H(s) → M(s) 1, ui M(s) 2, 3, mp In step 3, a constant symbol has been substituted for x throughout the scope of the
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.1: Real Numbers
Problem 29E
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![Universal instantiation can be used to prove one of the classical "syllogisms" of
the Greek philosopher and scientist Aristotle, who lived from 384 to 322 B.C.E. and
who first developed a system of formal logic.
The argument has the form, "All humans are mortal. Socrates is human. There-
fore Socrates is mortal." Using the notation
H(x) is “x is human."
s is a constant symbol (Socrates)
M(x) is "x is mortal."
the argument is
(Vx)[H(x) → M(x)] ^ H(s) → M(s)
and a proof sequence is
(Vx)(H(x) → M(x)) hyp
Но)
һyp
H(s) → M(s)
1, ui
M(s)
2, 3, mp
In step 3, a constant symbol has been substituted for x throughout the scope of the](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2c3fa8a0-4ae2-4dd9-a1f0-37df71613cb3%2F810ad234-7f96-40d8-b2dd-40fe30d2b050%2Fyimzqtn.png&w=3840&q=75)
Transcribed Image Text:Universal instantiation can be used to prove one of the classical "syllogisms" of
the Greek philosopher and scientist Aristotle, who lived from 384 to 322 B.C.E. and
who first developed a system of formal logic.
The argument has the form, "All humans are mortal. Socrates is human. There-
fore Socrates is mortal." Using the notation
H(x) is “x is human."
s is a constant symbol (Socrates)
M(x) is "x is mortal."
the argument is
(Vx)[H(x) → M(x)] ^ H(s) → M(s)
and a proof sequence is
(Vx)(H(x) → M(x)) hyp
Но)
һyp
H(s) → M(s)
1, ui
M(s)
2, 3, mp
In step 3, a constant symbol has been substituted for x throughout the scope of the
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