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Ability to recognise valid arguments involving the expression "therefore (=>)" in logical expressions
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  • 1

    Various IQ tests have shown the connection between recognising valid inferences (arguments) and the level of ones intelligence; our aim here is to observe what people consider as "valid inference".

    A valid argument is said to be impossible for its premise(s) to be true and its conclusion false.

    A valid argument is free of counterexamples, that is, it is impossible to find a situation in which the premise(s) of the argument are true and the conclusion is false.

    For example:

    a valid inference (argument):
    ⁃ 1) Messi is in Germany therefore (=>) Messi is in Germany

    an invalid inference (argument):
    ⁃ 2) It is snowing in Frankfurt therefore (=>) The airport in Frankfurt is closed

     

    Inference 1 is a valid argument because there is no situation when the premise (Messi is in Germany) is true and the conclusion (Messi is in Germany) is false 

    However, inference 2 is an invalid argument because the premise (It is snowing in Frankfurt therefore) could be true and the conclusion (The airport in Frankfurt is closed) false.

     

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  • 2

    This questionnaire is in 3 stages:

    • Initial stage: 8 questions with pairs of inferences; our aim here is to acquaint you with the kind of arguments we are interested in; you can run through these questions if you like
    • Training stage: consist of 3 sets of exercises 
    • Final stage: same form as initial stage but different questions; please answer calmly.


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  • 3
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  • 4
    • University student
    • University Professor
    • University Administration
    • Self-employed
    • IT Admin
    • Programmer
    • Other
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  • 5
    • Philosophy
    • Humanities
    • Science
    • Law
    • Medicine
    • IT
    • Business
    • Other
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  • 6
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  • 7
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  • 8
    Obama tweeted yesterday ⇒ Obama tweeted yesterday vs  Messi travelled to Argentina ⇒ Messi travelled to Argentina  i.e A ⇒ A vs A ⇒ A
    • The top inference is clearly valid
    • I lean towards the top inference
    • Indifferent: none looks more valid than the other to me
    • I lean towards the bottom inference
    • The bottom inference is clearly valid
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  • 9

    IQ1. Which inference looks valid to you?

    Obama tweeted yesterday ⇒ Obama tweeted yesterday

    vs

    Messi travelled to Argentina ⇒ Messi travelled to Argentina

    i.e

    A ⇒ A

    vs

    A ⇒ A

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  • 10
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  • 11
    Aristotle is smiling ⇒ Aristotle is smiling vs Albert Einstein had dinner ⇒ Joe Biden is in France i.e A ⇒ A  vs A ⇒ B
    • The top inference is clearly valid
    • I lean towards the top inference
    • Indifferent: none looks more valid than the other to me
    • I lean towards the bottom inference
    • The bottom inference is clearly valid
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  • 12

    IQ2. Which inference looks valid to you?

     

    Aristotle is smiling ⇒ Aristotle is smiling

    vs

    Albert Einstein had dinner ⇒ Joe Biden is in France

    i.e

    A ⇒ A  

    vs

    A ⇒ B

     

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  • 13
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  • 14
    The clock is brown OR The grass is green => The clock is brown vs It will rain tomorrow OR It will not rain tomorrow => It will rain tomorrow i.e A ∨ B ⇒ A  vs A ∨ ¬A ⇒ A
    • The top inference is clearly valid
    • I lean towards the top inference
    • Indifferent: none looks more valid than the other to me
    • I lean towards the bottom inference
    • The bottom inference is clearly valid
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  • 15

    IQ3. Which inference looks valid to you?

     

    The clock is brown or the grass is green => the clock is brown

    vs

    It will rain tomorrow or It will not rain tomorrow => It will rain tomorrow

    i.e

    A ∨ B ⇒ A 

    vs 

    A ∨ ¬A ⇒ A

     

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  • 16
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  • 17
    She is a friend AND She is not a friend => 5 + 5 = 11 vs 2+2=4 => It is snowing OR It is not snowing  i.e A ⋀ ¬A ⇒ ⏊ vs ⏉ ⇒ A ∨ ¬A 
    • The top inference is clearly valid
    • I lean towards the top inference
    • Indifferent: none looks more valid than the other to me
    • I lean towards the bottom inference
    • The bottom inference is clearly valid
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  • 18

    IQ4. Which inference looks valid to you?

     

    She is a friend and She is not a friend => 5 + 5 = 11

    vs

    2+2=4 => It is snowing or It is not snowing 

    i.e

    A ⋀ ¬A ⇒ ⏊

    vs

    ⏉ ⇒ A ∨ ¬A 

     

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  • 19
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  • 20
    The correct spelling for “colour” is with a ‘u’ AND The correct spelling for “colour” is without a ‘u’ => 5+5=11 vs Galicia is in Spain AND Galicia is in Spain => Galicia is in Spain i.e A ⋀ ¬A ⇒ ⏊ vs  A ⋀ A ⇒ A
    • The top inference is clearly valid
    • I lean towards the top inference
    • Indifferent: none looks more valid than the other to me
    • I lean towards the bottom inference
    • The bottom inference is clearly valid
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  • 21

    IQ5. Which inference looks valid to you?

     

    The correct spelling for “colour” is with a ‘u’ and The correct spelling for “colour” is without a ‘u’ => 5+5=11

    vs

    Galicia is in Spain and Galicia is in Spain => Galicia is in Spain

    i.e

    A ⋀ ¬A ⇒ ⏊

    vs

    A ⋀ A ⇒ A

     

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  • 22
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  • 23
    2+2=4 => I know your name OR I do not know your name vs  The boy is my brother OR The boy is my brother => The boy is my brother  i.e  ⏉⇒ A ∨ ¬A vs  A ∨ A ⇒ A
    • The top inference is clearly valid
    • I lean towards the top inference
    • Indifferent: none looks more valid than the other to me
    • I lean towards the bottom inference
    • The bottom inference is clearly valid
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  • 24

    IQ6. Which inference looks valid to you?

    2+2=4 => I know your name or I do not know your name

    vs

    The boy is my brother or The boy is my brother => The boy is my brother 

     

    i.e 

    ⏉⇒ A ∨ ¬A

    vs

    A ∨ A ⇒ A

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  • 25
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  • 26
    The chair is green OR The chair is not green => The chair is green vs Aristotle is a philosopher AND Aristotle is not a philosopher => 5+5=11 i.e A ∨ ¬A ⇒ A vs A ⋀ ¬A ⇒ ⏊
    • The top inference is clearly valid
    • I lean towards the top inference
    • Indifferent: none looks more valid than the other to me
    • I lean towards the bottom inference
    • The bottom inference is clearly valid
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  • 27

    IQ7. Which inference looks valid to you?

     

    The chair is green or The chair is not green => The chair is green

    vs

    Aristotle is a philosopher and Aristotle is not a philosopher => 5+5=11

    i.e

    A ∨ ¬A ⇒ A

    vs 

    A ⋀ ¬A ⇒ ⏊

     

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  • 28
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  • 29
    Aristotle is a philosopher OR Messi is a footballer => Aristotle is a philosopher vs  2+2=4 => She is a friend OR She is not a friend i.e A ∨ B ⇒ A vs  ⏉ ⇒ A ∨ ¬A 
    • The top inference is clearly valid
    • I lean towards the top inference
    • Indifferent: none looks more valid than the other to me
    • I lean towards the bottom inference
    • The bottom inference is clearly valid
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  • 30

    IQ8. Which inference looks valid to you?

     

    Aristotle is a philosopher or Messi is a footballer => Aristotle is a philosopher

    vs

    2+2=4 => she is a friend or she is not a friend

    i.e

    A ∨ B ⇒ A

    vs

    ⏉ ⇒ A ∨ ¬A 

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  • 31
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