Using Logic And Philosophy A Modern Introduction
Most students pick up Logic And Philosophy A Modern Introduction by Hurley and others and immediately drown in the formal notation. The book is dense but not impenetrable. It covers propositional logic, predicate logic, informal fallacies, and basic philosophical reasoning all in one volume. The real challenge is getting through it without losing your mind. I want to talk about how to actually use this book rather than just reading it cover to front, which most people do and regret. Here is what works. The text is split into three main sections. The first covers informal fallacies and basic critical thinking. The second moves into propositional logic with truth tables and natural deduction. The third handles categorical and predicate logic. Each section builds on the last, so do not skip ahead. I have seen students jump into natural deduction before they fully understand truth tables. They end up confusing material implication with logical equivalence and spend weeks untangling it.
The book also includes brief philosophical applications at the end of chapters. These are not fluff. They show why the formal tools matter. A lot of people skip them. That is a mistake.
How to study each chapter
Read the chapter once without stopping to take notes. Get the lay of the land. Then read it again slowly, doing every worked example. Close the book and redo them on your own. This is where most people cut corners. They think recognizing a solution means they can produce one. They cannot. After the examples, do the exercises. Start with the easier ones to build confidence, then move to the harder set. If you get stuck on a proof, do not just look at the answer key. Write down where you got lost. That gap in understanding is what you need to fix. I spent an hour one evening trying to construct a conditional proof using Indirect Proof when a Direct Proof would have been two steps. I kept forcing the wrong method because the chapter introduced it later. I should have just flipped ahead and checked what tool was available.
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Natural deduction pitfalls
This is the part that trips people up. The inference rules like Modus Ponens, Hypothetical Syllogism, and Disjunctive Syllogism are straightforward. The problem comes with the replacement rules and the three rules of conditional proof. Students miss that you can only apply certain rules to whole statements or to specific components. You cannot pull out a subformula from inside a conjunction unless you use Simplification first. Another issue: line numbering. When you start a subproof for Conditional Proof or Reductio, you indent and renumber. Many people forget to discharge the assumption correctly at the end. If your final line is inside the subproof, the proof is invalid. Check your scope lines.
Categorical logic and Venn diagrams
The categorical syllogism section uses Venn diagrams to test validity. Draw them carefully. The order of shading and filling dots matters. Shade first, then place Xs. If you do it backwards, you can mark the diagram incorrectly and get the wrong answer. There is a distribution rule shortcut you can use instead of diagrams once you are comfortable. It is faster but easier to mess up under time pressure. The six rules for categorical syllogisms are:
- Must have exactly three terms
- Middle term distributed at least once
- Terms distributed in the conclusion must be distributed in the premises
- No two negative premises
- If one premise is negative, the conclusion must be negative
- No drawing affirmative conclusions from negative premises
Memorize these. They catch errors faster than diagrams in most cases. This section is harder than propositional logic for most people. You are translating English sentences into quantified formulas. The main trap is scope of the quantifier. "Every student admires some professor" is not the same as "Some professor is admired by every student." The first is x(Sx y(Py Ax y)). The second is y(Py x(Sx Ax y)). Switching the order changes the meaning entirely. I wrote these out on paper twice to make sure I had them right before trusting myself on a practice test. The textbook itself is expensive new. You can often find older editions for free through your university library or on open educational resource sites. Ninth and tenth editions cover the same core material. The exercises change slightly but the logic does not. Check your course syllabus to see if the edition matters for your class.
There are also free companion sites and YouTube lectures that walk through specific chapters. Paul's Online Math Notes has a decent logic section. The Stanford Encyclopedia of Philosophy entries on formal logic supplement the book well if you want deeper philosophical context.
When this approach fails
If you are working through this book and still struggling after two attempts at each chapter, the problem might not be the book. It might be that you need more foundational practice before tackling the formal systems. Khan Academy offers free propositional logic exercises. Doing those first can save you weeks of frustration. Also, if your course requires a specific edition for online homework platforms like Cengage MindTap, older editions will not match the problem sets. In that case you are stuck with whatever the publisher requires. I wish there were a better workaround for that, but there is not.
What to focus on for exams
Truth table construction. Symbolizing arguments. Proving validity with natural deduction. Testing categorical syllogisms. These four skills make up most of any standard exam for this material. The philosophical discussion questions are usually easier points if your professor includes them. Do not ignore them entirely, but do not spend more than ten percent of your review time on them. Practice proofs under timed conditions. Most students can do them when there is no pressure. Under a clock, they rush and make silly mistakes like dropping a line or misapplying a rule. Set a timer for twenty minutes and do three proofs back to back. It makes the real exam feel slower by comparison.
