Truth & ConsistencyStandards for Critical Thinking
Truth
Matters of Taste or Opinion
Matters of Convention
Matters of Fact
Matters of Necessity
Four Types of Truth
Does this exhaust all truths?
What is the difference between
the truth, an honest mistake,
and a lie?
Truth
Matters of Taste or Opinion
Matters of Convention
Matters of Fact
Matters of Necessity
Four Types of Truth
Truth
Matters of Taste or Opinion
Matters of Convention
Matters of Fact
Matters of Necessity
Four Types of Truth
The ocean is prettier than the desert &The desert is prettier than the woods.
Truth
Matters of Taste or Opinion
Matters of Convention
Matters of Fact
Matters of Necessity
Four Types of Truth
The desert is prettier than the woods &The woods are prettier than the ocean.
Truth
Matters of Taste or Opinion
Matters of Convention
Matters of Fact
Matters of Necessity
Four Types of TruthCan be indexed to a person, place, time or culture:
• According to Alex pizza is better than pot stickers.
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Does this exhaust all truths?
Truth
Matters of Taste or Opinion
Matters of Convention
Matters of Fact
Matters of Necessity
Four Types of Truth
Does this exhaust all truths?
Consider someone who honestly
believes red means go and green means
stop. Is his belief true, or an honest
mistake?
Truth
Matters of Taste or Opinion
Matters of Convention
Matters of Fact
Matters of Necessity
Four Types of Truth
Steering wheels are on the left.
Truth
Matters of Taste or Opinion
Matters of Convention
Matters of Fact
Matters of Necessity
Four Types of Truth
Steering wheels are on the right.
Truth
Matters of Taste or Opinion
Matters of Convention
Matters of Fact
Matters of Necessity
Four Types of Truth
Women wear skirts.
Truth
Matters of Taste or Opinion
Matters of Convention
Matters of Fact
Matters of Necessity
Four Types of Truth
Men wear kilts.
Truth
Matters of Taste or Opinion
Matters of Convention
Matters of Fact
Matters of Necessity
Four Types of Truth
Can be indexed to a convention, culture or society:
• According to the music business, Tupac is gangsta is while My Chemical Romance is emo.
Does this exhaust all truths?
Truth
Matters of Taste or Opinion
Matters of Convention
Matters of Fact
Matters of Necessity
Four Types of Truth
Does this exhaust all truths?
Consider a world without
people or conventions,
would water still boil at 212º Fahrenheit,
ceteris paribus?
Truth
Matters of Taste or Opinion
Matters of Convention
Matters of Fact
Matters of Necessity
Four Types of Truth
The earth is 93 million miles from the sun.
Truth
Matters of Taste or Opinion
Matters of Convention
Matters of Fact
Matters of Necessity
Four Types of Truth
Water boils at 212º fahrenheit.
Truth
Matters of Taste or Opinion
Matters of Convention
Matters of Fact
Matters of Necessity
Four Types of Truth
Such truths as often expressed ceteris paribus:
• The earth is about 93 million miles from the sun on average.
• Water boils at 212º fahrenheit at standard barometric pressure.
Does this exhaust all truths?
Truth
Matters of Taste or Opinion
Matters of Convention
Matters of Fact
Matters of Necessity
Four Types of Truth
Does this exhaust all truths?
Consider a cosmos without
earth, would Jupiter still be
larger than Mars, ceteris
paribus?
Truth
Matters of Taste or Opinion
Matters of Convention
Matters of Fact
Matters of Necessity
Four Types of Truth
1 + 1 2=
Truth
Matters of Taste or Opinion
Matters of Convention
Matters of Fact
Matters of Necessity
Four Types of Truth
∏ = 3.141592...
Truth
Matters of Taste or Opinion
Matters of Convention
Matters of Fact
Matters of Necessity
Four Types of Truth
∏ = 3.141592...
What is Truth?
The puppy is on the rug.
When a claim matches what is
The Claim What is: reality
Truth
((The puppy) is on the rug.)
When a claim matches what is
The Claim What is: reality
((Subject) predicate)
Truth
((The puppy) is on the rug.)
When a claim matches what is
The Claim What is: reality
((Subject) predicate)
((Designates) expresses)
Truth
((The puppy) is on the rug.)
When a claim matches what is
The Claim What is: reality
((Subject) predicate)
((Designates) expresses)
<<Thing> property>
Truth
((The puppy) is on the rug.)
When a claim matches what is
The Claim What is: reality
((Subject) predicate)
((Designates) expresses)
<<Thing> property>
Truth
The puppy is on the rug.
When a claim matches what is
The Claim What is: reality
((The puppy) is on (the rug.))
<<Thing> relation<thing>>
((Subject) verb (Object))
<<puppy> being on<the rug>>
TruthWhen a claim matches what is
The Claim What is: reality
((The fire) is out.)((Subject) predicate)
<<Thing> property><<fire> being extinguished>≠
Not true False
TruthWhen a claim matches what is
The Claim What is: reality
((Photosynthesis) is a process by which light energy is converted into
chemical energy.)
<< Photosynthesis > being a process by which light energy is converted
into chemical energy >
=
TruthWhen a claim matches what is
Eleven is a prime number.
Jacqui thinks black is more alluring than pink.The music is loud.
Jupiter is bigger than Mars.
The Constitution of the United States was adopted on September 17, 1787
Romeo and Juliette is a tragedy.New York is the largest city in the US.
Hockey is better than basketball.
ConsistencyA Truth of Necessity in Logic
The Principle of Noncontradiction — No thing can, at the same time and in the same manner, both have and not
have the same property.
Let’s define ‘this square’ as the thing depicted below at x-position 303 px and y-position 318 px and of the dimensions 242 px by 242 px.
this square
ConsistencyA Truth of Necessity in Logic
Next let’s define ‘white’ as the color depicted below of the RGB values Red = 255, Green = 254, Blue = 235.
white
ConsistencyA Truth of Necessity in Logic
Now pay attention to your mental processes as we make the following claim:
ConsistencyA Truth of Necessity in Logic
Now pay attention to your mental processes as we make the following claim:
>>This square is white and this square is not white.<<
ConsistencyA Truth of Necessity in Logic
What was your reaction?
ConsistencyA Truth of Necessity in Logic
What was your reaction?
ConsistencyA Truth of Necessity in Logic
No thing can, at the same time and in the same manner, both have and not have the same property.
General:
No claim, adequately defined, can be both true and not true.
Special:
ConsistencyA Truth of Necessity in Logic
The Principle of Noncontradiction
p and not p
The Standard Form of a Contradiction:
ConsistencyA Truth of Necessity in Logic
The Principle of Noncontradiction
Eleven is a prime number andeleven is not a prime number.
Jacqui thinks black is more alluring than pink andshe doesn’t.
The music is loud and the music is quiet.*
Jupiter is bigger than Mars and it is not bigger than Mars.
The Constitution of the United States was adopted on September 17, 1787 and The Constitution of the United States was adopted on July 4, 1776.*
Romeo and Juliette is a tragedy and it is not a tragedy.*New York is and isn’t the largest city in the US.*
Hockey is better than basketball but it is not better than basketball.*
The Standard Form of a Contradiction: p and not p
ConsistencyA Truth of Necessity in Logic
The Principle of Noncontradiction
From Plato’s Republic
Plato on ContradictionSocrates said: It is obvious that the same thing will never do or suffer opposites with respect to the same part and in relation to the same thing at the same time. So if ever we find such contradictions we shall know that it was not the same thing but many.Socrates: For example, can the same thing be at rest and in motion in the same respect at the same time? Glaucon: Impossible. Socrates: Still, let's have a still more precise agreement so that we won't have any grounds for dispute as we proceed. Imagine the case of a man who is standing and also moving his hands and his head, and suppose a person to say that one and the same person is in motion and at rest at the same moment — we would respond that one part of him is in motion while another is at rest. Glaucon: Very true. Socrates: And suppose someone says that tops as wholes stand still and move at the same time — we wouldn't accept it because it's not with respect to the same part being at rest and in motion. Instead we'd but reply that it has an axis and a circumference and moves with respect to the circumference, as it spins, but with respect to the axis it is standing still.Glaucon: That's right. Socrates: Then such objections won't confuse us into holding that the same thing at the same time, in the same part or relation, can act or be acted upon in contrary ways. Glaucon: Certainly not. Socrates: Yet, instead of examining every objection and proving them untrue one by one, let us assume that no objects hold. But if this assumption is wrong, then none of our conclusions would hold. Glaucon: Yes.
The Principle of [Non]contradiction
Based on an excerpt from Plato’s The Republic
The Principle
How does Socrates intend to use this principle?
Socrates give the example of tops moving (spinning) and not moving (being stationary) at the same time—how does he show this is not a counter example to the Principle?
What is the main issue question?
From Plato’s Republic
Plato on Contradiction
Socrates: Just as the hands of the archer can't push and pull the bow at the same time — one hand pushes and the other pulls. Glaucon: Exactly. Socrates: Can it be that someone is thirsty and yet unwilling to drink? Glaucon: It happens all the time. Socrates: Would you say that part of the soul bidding them to drink, while another part masters the desire to drink by denying the unhealthy drink? Glaucon: Fair enough. Socrates: And such denial comes from the calculations of reason while the attraction proceeds from desire? Glaucon: Clearly. Socrates: So can we assume that they are two parts and different from each other — naming that in the soul whereby it reckons and reasons the rational and the other which lusts, hungers, thirsts, and feels desires the appetitive?
My Cousin VinnyWhat contradiction does Socrates reveal? List the contradiction in standard form (p and NOT p).
How is the contradiction related to the issue question?
Which side of each contradiction does Socrates take? What reasons could he give to show that the side he takes is true?
What about the other side of the contradiction? What reasons could you give to show that the side is true?
The Tripartite Soul
Assignment: Write a brief paper (1,000 words) answering what you take the MAIN ISSUE QUESTION to be in the reading, explaining how Socrates uses the principle of [non]contradiction to refute opposing claims. Be specific as to the claims being contradicted and the claims and arguments being rejected. Evaluate the Socrates' arguments—do they work? List your reasons why they do, or don’t. DUE IN 2 WEEKS.