Conditional Reasoning

[Tnewbill]

When completing my lesson 2 HW earlier this week I came across the statement " But no Expert" in question 14 on page 2-66 and the statement " No one who" in question 21 on page 2-67, and I was stumbled a little.

Is No one a conditional reasoning trigger? If so is it sufficient? Isn't no one like saying everyone just the opposites of course?


Here is the response from Dave K:
Thanks for the question! Yes, any absolute term such as "all," "every, "none, "no one, "never" and so on will be a conditional trigger. Depending no how each sentence is structured, the negative modifies different pieces, so it can be tricky at times. If you could do me the favor of posting this in the public forum, I'll answer in more detail because I'd love other students to see the explanation to this.

[Nikki Siclunov]

Hi Tnewbill,

Thanks for posting this question on the Forum. Indeed, "no" and "no one" can trigger a conditional relationship, but it depends on how the sentence is structured. For instance, if I told you that, "No, I can't answer your question right now!" - this is obviously not a conditional statement. But, here are a few examples where a conditional relationship is suggested, and the proper diagram for each:

No presidential candidate is guaranteed victory.

Can you turn this into an "if... then" statement? If yes, then we have a conditional relationship. Clearly, if you are a presidential candidate, then you aren't guaranteed victory. The proper diagram is therefore as follows:

Candidate NOT Guaranteed victory

Guaranteed victory NOT Candidate

or, using the Double Not arrow:

Candidate Guaranteed Victory

We can convey the same exact meaning if we said:

None of the presidential candidates are guaranteed victory.
No one who is a presidential candidate is guaranteed victory.
Anyone who is a presidential candidate is not guaranteed victory.
Presidential candidates are not guaranteed victory.
Presidential candidates are never guaranteed victory.

At the most basic level, "No A's are B's" conveys a negative conditional relationship between A and B, such that A B. Compare these examples, however, to the following:

No presidential candidate can win the election without raising enough money.

Here, the necessary condition indicator "without" takes precedence and should be considered first. Applying the Unless Equation, the term modified by the word "without" becomes the necessary condition; the remainder must be negated to become sufficient. Don't be confused by the word "enough," which is merely a part of the necessary condition ("enough money"). Just because "enough" denotes sufficiency in other contexts doesn't mean that money is sufficient to guarantee victory. Clearly, it is not. So:

PC Win Raise $

We can convey the same exact meaning in several different ways:

No candidate (or "no one") can win unless they raise enough money.
Anyone who wins must raise enough money.
No candidate can win until they raise enough money.
Candidates never win unless they raise enough money.
Whenever a candidate wins, he or she must raise enough money.

As you can see, "no one" - along with other absolute terms such as "everyone," "anyone," "none," etc. - are conditional triggers. However, you need to take into account the entire statement holistically before you start diagramming it. Sentence structure matters a lot, and the conditional relationship changes according to their contextual usage.

Let me know if this answers your question.

Thanks!