fallacy of the undistributed middle
All accountants are tennis players.
All youngsters are tennis players.
Therefore all accountants are youngsters.
To me it is obvious that the third statement DOES NOT follow from the first two premises. It is an INVALID syllogism. It is INVALID logic. It can clearly be seen in set notation:
That is basically what the three statements meant. As you can see now, the third statement is clearly ridiculous. The fallacy arises because of thinking that the statements mean:
Accountants = tennis players
Youngsters = tennis players
Accountants = Youngsters
That is false because we don’t mean accountants IS tennis players, we mean accountants ARE tennis players. tennis players is a category, and the accountants are categorized in it.
<--is that not possible?(i.e. complying with the premises of the syllogism)
That piece of erroneous deductive logic occurred to me in TOK* class in school today. The whole class including the teacher thought it was valid.
what do you think eh?
(more information:http://en.wikipedia.org/wiki/Fallacy_of_the_undistributed_middle)
*TOK (Theory of Knowledge) is a subject that is compulsory for students taking the IB (International Baccalaureate) Diploma course.
All youngsters are tennis players.
Therefore all accountants are youngsters.
To me it is obvious that the third statement DOES NOT follow from the first two premises. It is an INVALID syllogism. It is INVALID logic. It can clearly be seen in set notation:
That is basically what the three statements meant. As you can see now, the third statement is clearly ridiculous. The fallacy arises because of thinking that the statements mean:Accountants = tennis players
Youngsters = tennis players
Accountants = Youngsters
That is false because we don’t mean accountants IS tennis players, we mean accountants ARE tennis players. tennis players is a category, and the accountants are categorized in it.
<--is that not possible?(i.e. complying with the premises of the syllogism)That piece of erroneous deductive logic occurred to me in TOK* class in school today. The whole class including the teacher thought it was valid.
what do you think eh?
(more information:http://en.wikipedia.org/wiki/Fallacy_of_the_undistributed_middle)
*TOK (Theory of Knowledge) is a subject that is compulsory for students taking the IB (International Baccalaureate) Diploma course.
posted by zcer at 11:28 PM
16 Comments:
is it really invalid or your say its invalid...i think its valid too
yeah....its seems invalid and u couldnt have explain it better....
emmm ..... sometimes(almost everytime) most of the teacher are stupid are those who are rejected by the university coz they are too week to become a professor .... LOLX ... teacher please don't kill me .... think logiclly and make own hypothesis and own conclusion better .... >.<
i agree with what u have said cos i think what u write is rite
and secondly i think u don't need to think what other think on that topic cos u should believe on ur self
It's invalid as the comment of accountant as tennis players is NOT valid, for obvious reason (i.e. not all accountants are tennis players...)
GL:
at the first glance,
it seems 100% correct.
but only when you draw the Venn Diagram,
i get what did you mean.
my answer is,
there may be:
all accountants(A) are youngsters(Y)/
99% to 1% of A are Y/
none of A is Y.
so if it is virtualize through Venn diagram,
1. it is a small A/Y circle(or any shape, but circle is the easiest and the most common) in a big T(tennis player)square.[imagine the japanese national flag]
2. there are two circles in a big circle T. the two circle are on top of each other(crossing each other).[means that 1% to 99% A are Y]
3. there are 2 circles drew saperately and untouched in a big circle, as you(GL) showed.
the conclusion:
in this kind of logic,
the formula makes the answer,
"all A are Y".
too bad because they used 2 improper statements.
it is valid. no change.
Carfer Cfe
the subject should be changed:
all tennis players are accountants.
all tennis players are youngsters.
therefore all accountants that are tennis players are youngsters.
so when we switch the statement,
it has no problem.
Carfer CFE
"my answer is,
there may be:
all accountants(A) are youngsters(Y)/
99% to 1% of A are Y/
none of A is Y."
that is incorrect, what about 99.4 or something like that?
"3. there are 2 circles drew saperately and untouched in a big circle, as you(GL) showed."
i showed that, and not the other 2 because all i want to point out is that it complies with the premises too. and so the third statement is invalid
"in this kind of logic,
the formula makes the answer,
"all A are Y".
too bad because they used 2 improper statements.
it is valid. no change."
it is invalid. what do you mean by "no change"
"the subject should be changed:
all tennis players are accountants.
all tennis players are youngsters.
therefore all accountants that are tennis players are youngsters.
so when we switch the statement,
it has no problem."
you can change the premises, or you can change the implication. why must you do one over the other?
of course i had considered of the figure between 99.99dot dot percent and 0.0000000000000000unlimited000000then 1.
but it just too complicated.
so i wrote 1 to 99 %.
'no change' means that the answer didn't change.
it is just an example.
Carfer CFE
This comment has been removed by a blog administrator.
This is what the non-scientific mind comprehends and extracts from these 3 ambiguous statements. First of all, all the statements do not make any sense at all, because we know that no matter how we try to assume that all accountants are tennis players, it is impossible! Of course there will always be a minority of accountants who abhor tennis and not all tennis players are youngsters...haven't you seen geriatics playing tennis before in an attempt to 'loosen up' their arthritis-ridden joints?Hmm...maybe it's just me, or my obfuscate mind that refuses to accept the logic behind why we even study this partucular branch of so-called logic. I find it very puzzling.
Azimuth:
maybe the Accountants(A) the qustion mentioned is in a very specific group.
it may be a small club's report.
when the observer found that all A he/she meet are tennis players (TP),
he/she states out the statement:
all A are TP.
so same as the process of the report of:
all youngsters(Y) are TP.
Venn Diagram:
{assume that dots is a line.
assume that apostrophes is a line.
assume that square brakets joined to lines.
assume that round brackets are small circles.}
....................
TP[ (Y) (A) ] {Zcer showed}
''''''''''''''''''''
....................
TP[ (A()Y) ]
''''''''''''''''''''
....................
TP[ (A=Y) ]
''''''''''''''''''''
refer:
'
all students carry backpacks.
my grandfather carries a backpack.
therefore my grandfather is a student.
'
how if:
'
all students carry backpacks.
my grandfather is a student.
therefore my grandfather carries a backpack.
'
this is a better example of "fallacy of the undistributed middle".
Carfer CFE
Azi.C. : (hey, Azic)
whenever the observer(male) made a hypothesis based on his findings,
then when it is proofed that the hypothesis complies with the result he observed,
and then he made a theory:
'all A are TP',
this is scientific method.
but well,
there are some kind of flaws in this method,
and that is why there are so many people still believe in creationism.
also,
remember that a theory may not be correct all the time.
he can say that:'
whenever you use this theory in my club,
it is correct.'
isn't it scientific method?
Carfer CFE
Azic,Zcer:
the small club may only consists of 5 members.
the small club may has swimming pool, golf course, table tennis and tennis etcetera.
the small club has some/an A
the small club has some/a Y
all people being observed are in a tennis court.
so, the statement is possible.
it can be valid or invalid.
"fallacy of the undistributed middle"
Carfer CFE
VALIDITY has nothing to do with the real world. of course all the statements are untrue, but we are not now concerned with that.
what we want to know is if the two premises are true, then whether the third statement which is the implication is valid or not.
simple as that
yeah,simple as that! think it with old-school way,if a is c,if b is c,then a is b !simple,haha
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