Class notes
Square of Opposition: Categorical Logic
- Course
- Institution
This lecture notes discusses the topic "square of opposition" in Categorical Logic.
[Show more]
2 reviews
By: guerrerolili00 • 2 year ago
By: javeriakhalid025 • 3 year ago
By: jeffocs • 3 year ago
Thank you so much, mate, for your very generous review! Best wishes!
By: jeffocs • 3 year ago
Thank you so much, mate!
Seller
Follow
jeffocs
Reviews received
Content preview
Square of Opposition: Categorical LogicIn my other notes on terms and propositions used in categorical logic, we learned that
there are four (4) types of categorical propositions, namely:
1) Universal affirmative (A),
2) Universal negative (E),
3) Particular affirmative (I), and
4) Particular negative (O).
Now, the relationship between and among these four types of categorical propositions
is what logicians call the “square of opposition”.
There are four types of relations in the square of opposition, namely:
1) Contrary,
2) Subcontrary,
3) Subalternation, and
4) Contradiction.
Please see the two models of a square of opposition below.
, Contrary
Contrary is the relationship between universal affirmative (A) and universal negative (E)
propositions. Hence, there is only one pair in contrary (that is, A-E), and the pair differs
only in quality. As we can see, both are universal propositions, but one is affirmative and
the other negative.
Example 1:
All philosophers are deep thinkers. (A)
No philosophers are deep thinkers. (E)
Example 2:
No pastors are corrupt. (E)
All pastors are corrupt. (A)
Rules in Contrary: If one of the contraries is true, then the other is false. But if one is
false, then the other is doubtful, that is, its truth-value cannot be determined; this is
because contraries cannot be both true but can be both false. Let us consider the
examples above and assign truth-value to them.
If we assume that the proposition “All philosophers are deep thinkers” is true, then
obviously its contrary “No philosophers are deep thinkers” is absolutely false. Of course,
if it is already assumed that all philosophers are indeed deep thinkers, then it is
impossible for philosophers to be not deep thinkers.
However, if we assume that the proposition “No pastors are corrupt” is false, then we
cannot absolutely say that its contrary “All pastors are corrupt” is true. For sure, it’s
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller jeffocs. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for CA$6.39. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
81311 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy study notes for 14 years now