Where is the fallacy in Seth Yalcin’s counterexample to the modus tollens?

What is fallacy of modus tollens?

Modus Tollens. Latin for “method of denying.” A rule of inference drawn from the combination of modus ponens and the contrapositive. If q is false, and if p implies q (p q), then p is also false. Fallacy. An error in reasoning.

Is modus tollens valid?

MT is often referred to also as Denying the Consequent. Second, modus ponens and modus tollens are universally regarded as valid forms of argument.

Is denying the consequent modus tollens?

In propositional logic, modus tollens (/ˈmoʊdəs ˈtɒlɛnz/) (MT), also known as modus tollendo tollens (Latin for “method of removing by taking away”) and denying the consequent, is a deductive argument form and a rule of inference. Modus tollens takes the form of “If P, then Q.

What is the difference between denying the antecedent and modus tollens?

While modus tollens denies the consequent of a conditional statement, denying the antecedent denies the antecedent of a conditional statement.

What is the counterexample method and how is it applied to arguments?

The “counterexample method” is a powerful way of exposing what is wrong with an argument that is invalid. If we want to proceed methodically, there are two steps: 1) Isolate the argument form; 2) Construct an argument with the same form that is obviously invalid. This is the counterexample.

What is modus tollens with example?

Modus tollens is a valid argument form in propositional calculus in which and are propositions. If implies , and is false, then. is false. Also known as an indirect proof or a proof by contrapositive. For example, if being the king implies having a crown, not having a crown implies not being the king.

Can a modus tollens argument have false premises and a true conclusion?

A valid argument can have false premises; and it can have a false conclusion. But if a valid argument has all true premises, then it must have a true conclusion.

How do you prove modus tollens?


And this is going to provide a nice opportunity to do that using modus ponens to prove modus tollens. So remember that we have two premises that allow us to use modus tollens which are P implies Q.

What is fallacy of affirming the consequent?

Affirming the consequent, sometimes called converse error, fallacy of the converse, or confusion of necessity and sufficiency, is a formal fallacy of taking a true conditional statement (e.g., “If the lamp were broken, then the room would be dark”), and invalidly inferring its converse (“The room is dark, so the lamp

How do you find a counterexample?

When identifying a counterexample,

  1. Identify the condition and conclusion of the statement.
  2. Eliminate choices that don’t satisfy the statement’s condition.
  3. For the remaining choices, counterexamples are those where the statement’s conclusion isn’t true.


What is a counterexample example?

An example that disproves a statement (shows that it is false). Example: the statement “all dogs are hairy” can be proved false by finding just one hairless dog (the counterexample) like below.

What is the counterexample method example?

The Counter-Example Method: Once you determine the form that an argument has, if you can find an example of an argument with that same form where the premises are true and the conclusion is false, then that argument form is invalid.