PROPOSISI DAN PREMIS

Summary

This script offers an insightful exploration into mathematical logic, focusing on the concepts of propositions and premises. It defines mathematical logic as the study of principles behind valid argumentation. Propositions are declarative statements with a definite truth value, either true or false, supported by valid data like research or observation. Premises, conversely, are statements whose truth values cannot be determined due to incomplete data, often leading to questions. Examples are provided to differentiate between the two, highlighting the necessity of complete data for a statement to be considered a proposition. The script concludes by discussing how propositions and premises can be transformed based on the presence or absence of comprehensive data.

Takeaways

• 🧠 Mathematics Logic is a discipline that studies the principles of valid argumentation.
• 🔍 An argument is an effort to find the truth of a statement, supported by evidence like proofs from research or observations.
• 📚 The purpose of propositional logic is to explain different forms of arguments and their validity.
• 🗣️ A proposition is a declarative statement with a definite truth value, either true or false.
• 🔑 Propositions must be supported by valid data to be considered true or false.
• 🚫 Premises are statements that cannot have their truth value determined due to lack of complete or valid data.
• 🌐 Premises often contain words like 'now', 'today', or proper nouns that are not well-known figures, leading to ambiguity.
• 🔄 The transformation between propositions and premises can occur by adding or removing complete data.
• 📈 Examples of propositions include statements about definite facts like 'Borobudur is in Yogyakarta' or 'Joko Widodo is the second president of Indonesia'.
• 📉 Examples of premises include statements that are vague or incomplete like 'There are two seasons in Indonesia' or commands like 'Close the door'.
• 🔗 Propositions can also contain both true and false values in a single statement, connected by conjunctions like 'and', 'or', 'but'.

Q & A

What is the definition of Mathematical Logic?

Mathematical logic is a branch of knowledge that studies principles related to reasoning and valid arguments. It involves analyzing arguments to determine their validity through supportive data, research, or observation.

What is the purpose of studying propositional logic?

The purpose of propositional logic is to explain different forms of arguments and determine their validity, which can be proven with research or observational data. It also introduces valid arguments that can be supported by data or evidence.

What is a propositional statement?

A propositional statement is a declarative sentence that contains a single truth value—either true or false. It is a statement that can be verified as either true or false based on supporting data.

What are the characteristics of a propositional statement?

The characteristics of a propositional statement are: (1) it contains a single truth value (either true or false) unless it includes conjunctions like 'and' or 'but', and (2) its truth value must be supported by valid data or research.

How can a sentence have both true and false truth values?

A sentence can have both true and false truth values if it contains conjunctions such as 'and', 'but', or 'although'. These words connect multiple statements, each of which may have different truth values.

What is a premise, and how is it different from a proposition?

A premise is a declarative statement that cannot be determined as true or false due to incomplete or missing data. In contrast, a proposition is a statement that can be verified as true or false because it is supported by valid data.

What are the characteristics of a premise?

The characteristics of a premise are: (1) it lacks supporting facts or data, making it uncertain, (2) it generates questions from readers or listeners, and (3) it lacks a definite truth value.

Can a premise be turned into a proposition? If so, how?

Yes, a premise can be turned into a proposition by providing complete and valid data to support the statement. For example, adding specific details, such as dates or names of places or people, can turn a vague statement into a verifiable one.

What are examples of propositional statements?

Examples of propositional statements are: (1) 'Borobudur Temple is not located in Yogyakarta,' which is false, (2) 'Banjarmasin is known as the city of a thousand rivers,' which is true, and (3) 'Indonesia has two seasons: dry and rainy,' which is true.

What are examples of premise statements?

Examples of premise statements are: (1) 'Today is Wednesday,' because 'today' can vary, making it unclear, and (2) 'Tono went to college today,' because Tono is not a well-known figure, making the statement unverifiable.