1. TRANSITIVITY™
IDENTIFYING
STRUCTURAL
FALLACIES
...Affirming the Consequent
Copyright © 2007 Joseph A. Laronge
06-17-07

2. Good morning Judge Red.
TRANSITIVITY™ Copyright © 2007 Joseph A. Laronge

3. Good morning Mr. Green.
What is your contention
today?
TRANSITIVITY™ Copyright © 2007 Joseph A. Laronge

4. “Bill Gates won the lottery.”
TRANSITIVITY™ Copyright © 2007 Joseph A. Laronge

5. “Bill Gates won the lottery.”
B ill G ates won the lottery.
TRANSITIVITY™ Copyright © 2007 Joseph A. Laronge

6. What is the support
for your contention?
B ill G ates won the lottery.
The contention
shows no support.
TRANSITIVITY™ Copyright © 2007 Joseph A. Laronge

7. Because Bill Gates is a
millionaire. And one who wins
the lottery is a millionaire.
B ill G ates won the lottery.
TRANSITIVITY™ Copyright © 2007 Joseph A. Laronge

8. Because Bill Gates is a
millionaire. And one who wins
the lottery is a millionaire.
B ill G ates won the lottery.
TRANSITIVITY™ Copyright © 2007 Joseph A. Laronge

9. Because Bill Gates is a
millionaire. And one who wins
the lottery is a millionaire.
B ill G ates won the lottery.
B ill G ates is a millionaire.
TRANSITIVITY™ Copyright © 2007 Joseph A. Laronge

10. Because Bill Gates is a
millionaire. And one who wins
the lottery is a millionaire.
B ill G ates won the lottery.
B ill G ates is a millionaire. One who wins the lottery
is a millionaire.
TRANSITIVITY™ Copyright © 2007 Joseph A. Laronge

11. I need to check your argument
for structural validity to see if
your facts are relevant.
B ill G ates won the lottery.
B ill G ates is a millionaire. One who wins the lottery
is a millionaire.
TRANSITIVITY™ Copyright © 2007 Joseph A. Laronge

12. Lets see if the premises
fit within a transitive
inference path.
main contention
B ill G ates ...
… won the lottery.
1
?
TRANSITIVITY™ Copyright © 2007 Joseph A. Laronge

13. Lets see if the premises
fit within a transitive
inference path.
main contention
B ill G ates ...
… won the lottery.
1
?
Bill Gates...
TRANSITIVITY™ Copyright © 2007 Joseph A. Laronge

14. Lets see if the premises
fit within a transitive
inference path.
main contention
B ill G ates ...
… won the lottery.
1
?
Bill Gates...
...is a millionaire.
TRANSITIVITY™ Copyright © 2007 Joseph A. Laronge

15. Lets see if the premises
fit within a transitive
inference path.
main contention
B ill G ates ...
… won the lottery.
1
One who wins the
lottery...
?
Bill Gates...
...is a millionaire.
TRANSITIVITY™ Copyright © 2007 Joseph A. Laronge

16. Lets see if the premises
fit within a transitive
inference path.
main contention
B ill G ates ...
… won the lottery.
1
One who wins the
lottery...
?
Bill Gates...
...is a millionaire. ...is a millionaire.
TRANSITIVITY™ Copyright © 2007 Joseph A. Laronge

17. The premises do not
match to create the
transitive inference path.
main contention
B ill G ates ...
… won the lottery.
1
One who wins the
lottery...
?
Bill Gates...
...is a millionaire. ...is a millionaire.
TRANSITIVITY™ Copyright © 2007 Joseph A. Laronge

18. And the main contention
does not fit at the start
and finish of the path.
main contention
B ill G ates ...
… won the lottery.
1
One who wins the
lottery...
?
Bill Gates...
...is a millionaire. ...is a millionaire.
TRANSITIVITY™ Copyright © 2007 Joseph A. Laronge

19. So your argument is not
structurally valid.
main contention
B ill G ates ...
… won the lottery.
One who wins the
lottery...
Bill Gates...
X
...is a millionaire. ...is a millionaire.
TRANSITIVITY™ Copyright © 2007 Joseph A. Laronge

20. You are employing a
logical fallacy known as
affirming the consequent.
main contention
B ill G ates ...
… won the lottery.
One who wins the
lottery...
Bill Gates...
X
...is a millionaire. ...is a millionaire.
TRANSITIVITY™ Copyright © 2007 Joseph A. Laronge

21. Since your argument is
structural invalid, your
facts are not relevant.
main contention
B ill G ates ...
… won the lottery.
One who wins the
lottery...
Bill Gates...
X
...is a millionaire. ...is a millionaire.
TRANSITIVITY™ Copyright © 2007 Joseph A. Laronge

22. And since they are not
relevant, they are not
admissible.
main contention
B ill G ates ...
… won the lottery.
One who wins the
lottery...
Bill Gates...
X
...is a millionaire. ...is a millionaire.
TRANSITIVITY™ Copyright © 2007 Joseph A. Laronge

23. Judge Red. I have one more fact that
makes the fact that “Bill Gates is a
millionaire.” relevant.
main contention
B ill G ates ...
… won the lottery.
One who wins the
lottery...
Bill Gates...
X
...is a millionaire. ...is a millionaire.
TRANSITIVITY™ Copyright © 2007 Joseph A. Laronge

24. What fact is that?
main contention
B ill G ates ...
… won the lottery.
One who wins the
lottery...
Bill Gates...
X
...is a millionaire. ...is a millionaire.
TRANSITIVITY™ Copyright © 2007 Joseph A. Laronge

25. One who is a millionaire has an
increased likelihood of having won the
lottery.
main contention
B ill G ates ...
… won the lottery.
Bill Gates...
...is a millionaire.
TRANSITIVITY™ Copyright © 2007 Joseph A. Laronge

26. One who is a millionaire has an
increased likelihood of having won the
lottery.
main contention
B ill G ates ...
… won the lottery.
One who is a
millionaire...
Bill Gates...
...is a millionaire.
TRANSITIVITY™
Copyright © 2007 Joseph A. Laronge

27. One who is a millionaire has an
increased likelihood of having won the
lottery.
main contention
B ill G ates ...
… won the lottery.
One who is a
millionaire...
Bill Gates...
...is a millionaire. ...has an
increased
likelihood of
having won the
lottery.
TRANSITIVITY™
Copyright © 2007 Joseph A. Laronge

28. One who is a millionaire has an
increased likelihood of having won the
lottery.
main contention
B ill G ates ...
… won the lottery.
One who is a
millionaire...
Bill Gates...
...is a millionaire. ...has an
increased
likelihood of
having won the
lottery.
TRANSITIVITY™
Copyright © 2007 Joseph A. Laronge

29. One who is a millionaire has an
increased likelihood of having won the
lottery.
main contention
B ill G ates ...
… won the lottery.
1
One who is a
millionaire...
Bill Gates...
...is a millionaire. ...has an
increased
likelihood of
having won the
lottery.
TRANSITIVITY™

30. The premises now
correctly match.
main contention
B ill G ates ...
… won the lottery.
1
One who is a
millionaire...
?
Bill Gates...
...is a millionaire. ...has an
increased
likelihood of
having won the
lottery.
TRANSITIVITY™
Copyright © 2007 Joseph A. Laronge

31. But you still do not have
the main contention
bounding the path.
main contention
B ill G ates ...
… won the lottery.
1
One who is a
millionaire...
?
Bill Gates...
...is a millionaire. ...has an
increased
likelihood of
having won the
lottery.
TRANSITIVITY™
Copyright © 2007 Joseph A. Laronge

32. There is an implicit premise that
completes the transitive inference
path.
main contention
B ill G ates ...
… won the lottery.
1
One who is a
millionaire...
?
Bill Gates...
...is a millionaire. ...has an
increased
likelihood of
having won the
lottery.
TRANSITIVITY™
Copyright © 2007 Joseph A. Laronge

33. There is an a millionaire has an
One who is implicit premise that
has an increased likelihood
of having the transitive inference
increased likelihood of having the
completeswon the lottery, wonwon the
lottery.
path.
main contention
B ill G ates ...
… won the lottery.
One who is a
millionaire...
Bill Gates...
...is a ...has an
millionaire. increased
likelihood of
having won
the lottery.
TRANSITIVITY™
Copyright © 2007 Joseph A. Laronge

34. One who is implicit premise that
There is an a millionaire has an
has an increased likelihood
of having the transitive inference
increased likelihood of having the
completeswon the lottery, wonwon the
lottery.
path.
main contention
B ill G ates ...
… won the lottery.
One who is a One who has an
millionaire... increased likelihood
Bill Gates...
of having won the
...is a ...has an
lottery...
millionaire. increased
likelihood of
having won
the lottery.
TRANSITIVITY™
Copyright © 2007 Joseph A. Laronge

35. There is an a millionaire has an
One who is implicit premise that
has an increased likelihood
of having the transitive inference
increased likelihood of having the
completeswon the lottery, wonwon the
lottery.
path.
main contention
B ill G ates ...
… won the lottery.
One who is a One who has an
millionaire... increased likelihood
Bill Gates...
of having won the
...is a ...has an
lottery...
millionaire. increased
likelihood of ...won the lottery.
having won
the lottery.
TRANSITIVITY™
Copyright © 2007 Joseph A. Laronge

36. There is an a millionaire has an
One who is implicit premise that
has an increased likelihood
of having the transitive inference
increased likelihood of having the
completeswon the lottery, wonwon the
lottery.
path.
main contention
B ill G ates ...
… won the lottery.
One who is a One who has an
millionaire... increased likelihood
Bill Gates...
of having won the
...is a ...has an
lottery...
millionaire. increased
likelihood of ...won the lottery.
having won
the lottery.
TRANSITIVITY™
Copyright © 2007 Joseph A. Laronge

37. One who is implicit premise that
There is an a millionaire has an
has an increased likelihood
of having the transitive inference
increased likelihood of having the
completeswon the lottery, wonwon the
lottery.
path.
main contention
B ill G ates ...
… won the lottery.
1
One who is a One who has an
millionaire... increased likelihood
Bill Gates...
of having won the
...is a ...has an
lottery...
millionaire. increased
likelihood of ...won the lottery.
having won
the lottery.
TRANSITIVITY™
Copyright © 2007 Joseph A. Laronge

38. OK. The predication is
now transitive.
main contention
B ill G ates ...
… won the lottery.
1
One who is a One who has an
millionaire... increased likelihood
Bill Gates...
of having won the
...is a ...has an
lottery...
millionaire. increased
likelihood of ...won the lottery.
having won
the lottery.
TRANSITIVITY™
Copyright © 2007 Joseph A. Laronge

39. And while the third premise
is weak, I accept that there
is some probative force.
main contention
B ill G ates ...
… won the lottery.
1
One who is a One who has an
millionaire... increased likelihood
Bill Gates...
of having won the
...is a ...has an
lottery...
millionaire. increased
likelihood of ...won the lottery.
having won
the lottery.
TRANSITIVITY™
Copyright © 2007 Joseph A. Laronge

40. So these facts are relevant
and admissible.
main contention
B ill G ates ...
… won the lottery.
1
One who is a One who has an
millionaire... increased likelihood
Bill Gates...
of having won the
...is a ...has an
lottery...
millionaire. increased
likelihood of ...won the lottery.
having won
the lottery.
TRANSITIVITY™
Copyright © 2007 Joseph A. Laronge

41. Thank you Judge red.
main contention
B ill G ates ...
… won the lottery.
1
One who is a One who has an
millionaire... increased likelihood
Bill Gates...
of having won the
...is a ...has an
lottery...
millionaire. increased
likelihood of ...won the lottery.
having won
the lottery.
TRANSITIVITY™
Copyright © 2007 Joseph A. Laronge

42. TRANSITIVITY™
argument visualization/
educational and business training
and consulting:
transitivity@comcast.net
Copyright © 2007 Joseph A. Laronge