Skip to lesson

INTERACTIVE COURSE · 18 LESSONS

Logic: from arguments to evidence

A convincing conclusion is not always a justified one. Learn to tell the difference, one argument and one counterexample at a time.

Start lesson 1 No formal-logic background required

What you will be able to do

Reconstruct a claim fairly, test whether the conclusion follows, build a counterexample, justify a short proof, and separate scientific evidence from an overclaim. Examples come from everyday decisions, software, and research; AI is one application, not the whole course.

01

Read the argument

What is being claimed, and why?

  1. 01What is the argument?Separate a claim, its support, and the conclusion it is meant to support.
  2. 02True is not the same as validDistinguish statement truth, argument validity, and soundness.
  3. 03The missing bridgeExpose missing assumptions without quietly treating them as facts.
02

Make the structure visible

Which combinations does a rule allow?

  1. 04Not, and, orTranslate simple combinations without importing everyday ambiguity.
  2. 05Necessary or sufficient: is registration enough?Keep sufficient and necessary conditions pointing the right way.
  3. 06Same truth in every rowUse a complete truth table to test equivalence, not a few favorable examples.
03

Try to break the inference

Can the premises hold while the conclusion fails?

  1. 07Four similar-looking inferencesDistinguish modus ponens and modus tollens from two invalid lookalikes.
  2. 08Build the case that breaks itSearch systematically for true premises and a false conclusion.
  3. 09When the premises cannot all holdRecognize consistency, tautology, contradiction, and vacuous consequence.
04

Think in objects and relations

All of what? A witness for whom?

  1. 10All, some, and finite worldsEvaluate quantified statements in a specified, nonempty domain.
  2. 11Not all is not noneNegate quantified statements and recognize vacuous universals.
  3. 12Everyone has one, or one for everyone?See why changing quantifier order changes who may depend on whom.
05

Account for every step

What permits this step, under which assumptions?

  1. 13A proof is a chain of permissionsJustify short natural-deduction steps using stated premises and rules.
  2. 14Borrow an assumption, then return itUse conditional proof without leaking temporary assumptions.
  3. 15Cases, contradictions, and what they proveClose every case and identify exactly which assumption a contradiction rejects.
06

Reason beyond certainty

What does the evidence support, and what does it leave open?

  1. 16Support is not entailmentSeparate deduction, induction, and causal claims without dismissing empirical evidence.
  2. 17Count before you trust the percentageDistinguish P(flag | defect) from P(defect | flag) using natural frequencies.
  3. 18A conclusion you can stand behindReconstruct, test, and qualify a real-looking argument without overstating certainty.

Further reading

Does That Follow? English edition cover

English PDF · 10 short lessons · Paid ebook

Does That Follow?

An introduction to everyday logic from Fineuralab. Spot hidden assumptions, test arguments, and explore probability and causation. No prior knowledge needed.

View book on Ko-fi

The ebook is a separate purchase. The interactive courses on this site remain free.

Published by Fineuralab. Created with AI assistance in writing and layout.

What this edition does not claim

This is an introduction, not a complete university logic sequence. It does not cover a full first-order proof calculus, completeness theorems, modal logic, or a full statistics course. Practice records are not a certificate, and the course has not yet been evaluated in a learner study.

Try a problem before opening its solution. A later attempt with no hints is worth revisiting after a delay, not treating as permanent mastery. Local review reminders use a simple one- or three-day interval, not a validated adaptive-learning model.