#9 - A scientific theory is a good theory if it satisfies

[cedtinsi]

Hi,
I looked at the solution for this problem, and it says that there is a if and only if relationship between Good theory and Satisfies requirements. I don't see this if and only if relationship from reading the stimulus. All I read is: "A scientific theory is a good theory IF it satisfies two requirements". In addition, nothing that follows indicates to me that there is that if and only if relationship. Where do they see the if and only if ?

Help much appreciated.

Thanks.

[Steve Stein]

Hi,

That's a great question, and a fairly unique one The author provides that a scientific theory is a good theory if it satisfies two particular requirements.

So, as long as it satisfies those requirements, it's a good theory.
(A scientific theory is a good theory if it meets those two requirements).

But let's not forget, there are two requirements for a scientific theory to be a good theory.
(A scientific theory is a good theory only if it meets those two requirements)

Putting together these two ideas:

A scientific theory is a good theory if, and only if, it meets those two requirements.

I hope that's helpful! Please let me know whether this is clear--thanks!

~Steve

[Nikki Siclunov]

To elaborate on Steve's excellent analysis above, you can have a necessary condition without the usual necessary condition indicators (then, only if, unless, etc.). If something is said to be "essential," or a "requirement," it is by definition a necessary condition. In this particular instance, it is both sufficient and necessary, due to the sufficient condition indicator "if," which you mentioned.

Great question!

[cedtinsi]

Thanks a lot guys. YOU GUYS ARE QUICK TO HELP!
Now, does that mean that when the if is in between the necessary and the sufficient condition it becomes an if and only if? and the necessary also becomes the sufficient because of it?

[Nikki Siclunov]

No. The only reason we have a bi-conditional relationship here is because the sufficient conditions (referred to by the sufficient condition indicator "if") are also described as requirements for a good scientific theory, making them necessary as well as sufficient.

We would not have a bi-conditional relationship if the stimulus had stated:

A scientific theory is a good theory if it accurately describe a large class of observations [...] and makes definite predictions about the results of future observations.

In that case, the proper diagram would be:

Accurately describe + Make definite predictions Good theory

... because neither condition is explicitly referred to as a "requirement."

Make sense? Let me know!

[Blueballoon5%]

29. A scientific theory is a good...

If all the statements in the passage are true, each of the following must also be true EXCEPT:

(E) Aristotle’s cosmological theory...


My Question: E is the wrong answer. However, I am a bit confused with the wording of this answer choice. The stimulus never says that these four were the "only" four elements. How can we infer this?

*Note: I understand why B is the right answer. But I also find E to be a possibility. The answer explanation online states that, for answer E, "Since the stimulus mentions that Aristotle’s theory satisfies the first requirement, we know that this choice is inferred, and is incorrect."

[David Boyle]

29. A scientific theory is a good theory if it satisfies two requirements, It must accurately describe a large class of observations in terms of a model that is simple enough to contain only a few elements, and it must make definite predictions about the results of future observations, For example, Aristotle’s cosmological theory, which claimed that everything was made out of four elements---earth, air, fire, and water---satisfied the first requirement, but it did not make any definite, Thus, Aristotle’s cosmological theory was not a good theory.

If all the statements in the passage are true, each of the following must also be true EXCEPT:

(E) Aristotle’s cosmological theory described a large class of observations in terms of only four elements.


My Question: E is the wrong answer. However, I am a bit confused with the wording of this answer choice. The stimulus never says that these four were the "only" four elements. How can we infer this?

*Note: I understand why B is the right answer. But I also find E to be a possibility. The answer explanation online states that, for answer E, "Since the stimulus mentions that Aristotle’s theory satisfies the first requirement, we know that this choice is inferred, and is incorrect."

Hello Blueballoon5%,

The wording is a little confusing, but one could say that the "only" is implied, in that everything is made of the four elements. E.g., if there is a fifth element, grape jelly (!), then that is not something made of the other four elements, so not everything can be made of the four elements, then.

Hope this helps,
David

[Blueballoon5%]

That makes sense! Thank you!

[mankariousc]

Hello!

While I chose the correct answer, I was stuck for a little bit on the term "many" in answer D. Could you explain how the words "many" and "few" interact in this answer choice and how to make sure I properly interpret them on other questions?

Thanks!

[Jonathan Evans]

Hi, Mankariousc,

Great question. I hope you will permit me to digress for a bit before my response because I wish to discuss the term "many." Feel free to skip over this meandering discussion to get right to the response

BEGIN DIGRESSION "Many" is indeed a nebulous term the denotation of which is hard to pin down. In other words, "many" could correspond to perhaps "ten" depending on the overall potential set size. For instance,

• In a group of twelve people, ten of them listen to rock music. Many people in this group listen to rock music.

However, take these ten people and move them into another set, this time with a thousand people.

• In a group of one thousand people, only ten of them listen to rock music. Not many people in this group listen to rock music.

"Many" kinda hovers in a zone that ranges from "all" (though it would be slightly odd to use "many" when "all" would be accurate) to even a small fraction of the overall set, depending on how many people are in the set. For instance:

• In the United States, many people drive trucks.

Now perhaps the actual fraction of people in the United States who drive trucks is rather small, let's say out of 300 million people, 30 million drive trucks, making the total number of truck drivers only one-tenth of the overall number. However, it would still be fair to say: In the United States, many people drive trucks. END DIGRESSION

Let's take a look at this answer choice:

"A scientific model that contains many elements is not a good theory."

Now contrast this statement with the information in the stimulus. What do we know about how many elements a good theory must have? From the stimulus, we know that a good theory must have only a few elements. While "many" is a nebulous term (as discussed above), "many" is definitely NOT compatible with "only a few." In other words, the statement in (D) must be true.

To recap, if a scientific model contained many elements, this scientific definitely does not have only a few elements. Since it does not have only a few elements, it cannot be a good theory.

I hope this helps!