# What's wrong with this syllogism?

No one held for murder is given bail

Smith isn't held for murder

Hence Smith is given bail

no M is B

s is not M

s is B

What's wrong with the conclusion?

• The fallacy here is NOT denying the antecedent as you think. What you provided is a categorical syllogism. Modern logic is Mathematical logic and has a different rule set. You can't call logic logic as most math people do because all logic is not Mathematical. Aristotelian logic surely was not Mathematical. Mathematical logic was invented in the 19th century and Aristotelian logic is over 2,000 years old. The rules and terminology do not always match either. Math people have redefined some common words. The context in philosophy can be different from math for the same words. Commented Aug 27, 2020 at 17:50
• Are you asking about what general type of logical fallacy this commits, or just asking to be convinced it doesn't make sense? One could easily show why it doesn't work with a Venn diagram, or with some real-world example with the same logical form but where the conclusion is obviously wrong, like "No cat is a rabbit. Donald Duck is not a cat. Therefore Donald Duck is a rabbit." Commented Aug 28, 2020 at 4:00
• Incidentally, looking into this I don't think it's a formal logical fallacy at all, rather it's an informal fallacy, the "false dichotomy" (see discussion here for example). In my example, there was no premise saying every entity in the domain of discourse must be either a cat or a rabbit, but I implicitly assume that when I say that if Donald Duck is not a cat, he must be a rabbit. Similarly in your example there's no premise saying every person is either given bail or held for murder. Commented Aug 28, 2020 at 5:20

The syllogism has two negative premises. The fallacy is “exclusive premises“. Also, the syllogism draws an affirmative conclusion from a negative premise. See, e.g., Wikipedia > Syllogism.

• thanks for clarifying that this is committing two fallacies like denying the antecedent and exclusive premises, I think you should edit ur post to reflect that it'll be helpful Commented Jul 2, 2020 at 0:25
1. no M is B
1. s is not M
1. s is B

Observe that #1 is equivalent to "If x is M, then x is not B."

So, #1 and #2 do not imply #3.

• it's denying the antecedent Commented Jul 2, 2020 at 0:33
• @LazyJoe Show Smith not being held for murder says nothing about other possible rules for bailing. For all you know people named Smith are specifically not given bail because the mayor hates the name Smith. Commented Jul 3, 2020 at 1:19
• LazyJoeShow mean that the error was the fallacy of "denying the antecedent". That involves misreading "no M is B" as "not M is B". The correct interpretation is "all M are not B" which, as @Novicegrammer says, makes no claim about whether or not bail is granted to non-murder cases. Commented Aug 28, 2020 at 4:27

`no M is B`

Do not confuse this with `not-M is B`

It is actually: `every M is not B`

`s is not M`

Yes, however, we have no indication whether or not a`not-M` may be bailable. So...

`s is B`

...cannot be inferred.

I have never studied logic, but this seems quite silly.

The first statement is not restrictive enough in terms of who is or is not given bail. Many people not held for murder could still not be given bail.

Smith is not held for murder. But he could still be in one of the other groups (or in the larger Venn circle) that is not given bail. So, hence nothing....

Sorry, but to me this all seems pretty obvious, actually more obvious, without the symbols.