How can I improve my understanding of predicate logic?

  • Context: Undergrad 
  • Thread starter Thread starter bonfire09
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Discussion Overview

The discussion revolves around improving understanding of predicate logic, particularly focusing on existential and universal quantifiers. Participants express their struggles with translating sentences into predicate symbols and the foundational knowledge required for mastering these concepts. The scope includes theoretical understanding and practical application in mathematical contexts.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Homework-related

Main Points Raised

  • One participant mentions difficulty with section 2.1 of Velleman's book, specifically regarding existential and universal quantifiers, and seeks input on improving understanding of predicate logic.
  • Another participant questions whether the goal is to learn predicate calculus or if it is perceived as necessary for understanding higher mathematics, suggesting that studying higher math may enhance understanding of logical expressions.
  • A participant expresses concern about missing background knowledge if they struggle with the material, debating whether to move on or stay focused on challenging concepts.
  • One participant highlights the importance of formal definitions in mathematics and suggests that students often substitute personal interpretations for these definitions, which can hinder understanding.
  • Another participant indicates that their motivation for reading the book is to gain exposure to writing proofs, noting that quantifiers are a particular area of difficulty.
  • A later reply mentions finding a different resource, Schaum's outline of logic, which is said to explain both propositional and predicate logic effectively.

Areas of Agreement / Disagreement

Participants express various viewpoints on the necessity of foundational knowledge for understanding predicate logic, with some suggesting that moving on to higher mathematics may be beneficial. There is no consensus on whether to persist with the current material or to advance, indicating ongoing uncertainty in the discussion.

Contextual Notes

Some participants note potential gaps in background knowledge that may affect comprehension of predicate logic, as well as the challenge of reconciling personal interpretations with formal mathematical definitions.

bonfire09
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Apparently I've read through Velleman's book halfway a few times and section 2.1 gets me all the time. Its on existential and universal quantifiers. I still don't know how to take a sentence and convert it using predicate symbol quite well. I'm not sure what other sorts of skills i am missing. I need some input on how to better understand predicate logic?
 
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bonfire09 said:
Apparently I've read through Velleman's book halfway a few times and section 2.1 gets me all the time. Its on existential and universal quantifiers. I still don't know how to take a sentence and convert it using predicate symbol quite well. I'm not sure what other sorts of skills i am missing. I need some input on how to better understand predicate calculus?

Is your main goal to learn the predicate calculus? - or are you under the mis-impression that you must learn the predicate calculus in order to understand higher mathematics?

If your objective is learn higher mathematics such as abstract algebra, advanced calculus, topology and other branches of math that don't focus on "foundations", such as logic and set theory, then my advice is proceed onward to those branches of higher mathematics. It is commendable to study logic as a foundation for understanding math, but your ability to translate sentences into logical expressions with quantifiers will be sharpened by studying higher math because the sentences about mathematical topics will be more precise than common speech.

As to "other skills", I haven't studied your posts. In my opinion, the most glaring weakness that students have is that they substitute their own private ideas about mathematical objects for the formal definitions. (For example, they have their own notions about whether "dy" and "dx" are numbers, or whether .9999... = 1 or whether [itex]\frac{ \infty}{\infty} = 1[/itex]) As a consequence, they don't understand how to employ the formal definitions in proofs and they start expressing opinions about symbolic expressions like [itex]\infty[/itex] without considering whether these scribblings have formal mathematical definitions.
 
I'm under the impression that if i don't understand something in this book than I'm missing some other background knowledge. I'm not sure if i should just move on with the rest of the book or stay stuck until I get it.But this is one of the few things that is not clicking in my head.
 
bonfire09 said:
I'm under the impression that if i don't understand something in this book than I'm missing some other background knowledge. I'm not sure if i should just move on with the rest of the book or stay stuck until I get it.But this is one of the few things that is not clicking in my head.

You didn't say why you are reading the book. Have you studied calculs yet? If so, do you see how the definitions of the various kinds of limits involve quatifiers and how the proofs involve the logic of quantifiers?
 
The reason why I am reading this book is because I don't have much exposure to writing proofs. I'm reading it over again because I feel that some of it I don't have a good grasp of and quantifiers is one of them. This is the only book I read so far that deals with proofs. I haven't read any other books on proofs.
 
Never mind I found a good book called Schaum's outline of logic. It explains both propositional and predicate logic quite well.
 

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