Based on the passage, it can be concluded that the author and Broyles-González hold essentially the same attitude toward

nicolebet on March 4, 2020

Valid Deductions

I am finding it difficult to follow the some/most statements when following along the video. I have taken a symbolic logic class and have done these with symbols, however, using the some and most statement then using an arrow on the other premise is really throwing me off. I do not really know what my question is, but I hope someone can clarify for me and understand what I am missing. Thank you !

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SamA on March 9, 2020

Hello @nicolebet,

I also needed quite a bit of time to understand this. What you are talking about is the combination of quantifying statements and conditional statements. I will try to help you with some simple examples.

Premise: Some desert creatures (DC) are foxes (F).
Our quantifier word is "some."
DC - - some - - F

Premise: All foxes (F) eat eggs (EE).
"All" is technically a quantifier, but it functions as a conditional term. It introduces the sufficient condition.
F - -> EE

How can I connect these two premises in order to draw a conclusion? F is our common term.
DC - - some - - F - -> EE
This is a valid format, and it means that some desert creatures eat eggs. That is our properly drawn conclusion.

I'll try an example demonstrating a common mistake.
Premise: All forest creatures (FC) are mammals (M).
FC - -> M

Premise: Some mammals (M) eat carrots (EC).
M - - some - - EC

Like in the previous example, we seem to have a common term M.
FC - -> M - - some - - EC
At first glance, we might try to make the conclusion that some forest creatures eat carrots. However, this is not valid. Unlike the argument above, there are holes in this agrument. What if the only mammals that eat carrots live in the mountains? That doesn't violate any of our conditions, but it disproves our conclusion.

Notice how the formats of my two examples are different. My first example gives us a conclusion, but my second example does not. Try to make up some of your own examples, and I think you will start to understand these concepts pretty quickly.

Here is another quantifier tip. I refer to this as "overlap." When we have two "most" statements about the same group, there will be overlap. When we have an "all" statement and a "some" statement about the same group, there will be overlap. We can use this to learn something that must be true.

Most cats are fat. Most cats are fluffy.
cats - - most - - fat
cats - - most - - fluffy
overlap conclusion: some cats are fluffy and fat.
fluffy - - some - - fat

All people eat. Some people drive a car.
people - -> eat
people - - some - - drive car
overlap conclusion: some people drive a car and eat.
eat - - some - - drive car
(note that this is the same principle as my fox example)