PHIL102: Introduction to Critical Thinking and Logic

1. To represent the first argument through a Venn diagram, we can create two overlapping circles, one representing cooks and the other representing men. Since "most cooks are men," we draw a larger portion of the "cooks" circle overlapping with the "men" circle. Similarly, since "most men are idiots," we shade a portion of the "men" circle to represent idiots. The shaded area where the "cooks" circle overlaps with the "men" circle represents the group of cooks who are also men. Since a portion of the "men" circle is shaded to represent idiots, it might seem like most cooks are idiots based on this representation. However, the argument is flawed as it assumes all men who are cooks are idiots, which is not necessarily true. It oversimplifies the relationship between cooks, men, and intelligence.

2. For the second argument, we can again draw two overlapping circles, one representing plants and the other representing things that are purple. Since "very few plants are purple," draw a smaller portion of the "plants" circle overlapping with the "purple" circle. Since "very few purple things are edible," shade a portion of the "purple" circle to represent non-edible things. The shaded area where the "plants" circle overlaps with the "purple" circle represents the group of plants that are also purple. Since a portion of the "purple" circle is shaded to represent non-edible things, it might seem like very few plants are edible based on this representation. However, just like the first argument, this conclusion oversimplifies the relationship between plants, purple things, and edibility.

These examples illustrate logical fallacies, specifically the fallacy of composition and the fallacy of division. Venn diagrams can help visualize these fallacies by showing the relationship between sets of elements.

For the first example:

Set A: Cooks
Set B: Men
Set C: Idiots
The Venn diagram might show that while there is overlap between cooks and men, it doesn't mean that all men are cooks or vice versa. Additionally, there is no logical connection between being a man and being an idiot, so the conclusion that most cooks are idiots is not valid.

For the second example:

Set A: Plants
Set B: Purple things
Set C: Edible things
The Venn diagram would demonstrate that being purple doesn't necessarily mean something is a plant or edible. Similarly, being a plant doesn't guarantee that it's purple or edible. Therefore, the conclusion that very few plants are edible based solely on their color is not valid.

In both cases, the fallacies arise from making unwarranted assumptions about the relationships between different sets without considering the nuances and complexities of those relationships.

The first statement would require three venn diagrams. One representing men who are cooks, the second will represent most men who are idiots, and the last one representing cooks who are idiots.therefore, most men who are idiots and cooks who are idiots will interface, showing similar characters represented in both categories. Looking at the second statement, it reciprocate the first one.

I would first identify the sets:

In the 1st example: 1. Cooks 2: Men 3. Idiots. The use of "most" makes these particular affirmative premises. It is invalid because premise one and premise two could be TRUE but the conclusion could be FALSE.
In the 2nd example: 1. Plants 2. Things that are purple 3. Things that are edible. Though the particular is changed from "most" to "very few". Again, it is invalid because premise one and premise two could be TRUE but the conclusion could be FALSE.

Venn diagrams can be adapted to evaluate the validity of these arguments by visually representing the relationships between different categories or sets. In the case of the first argument, we can represent the sets of "cooks" and "idiots" using circles in a Venn diagram. If most cooks are indeed men, we would draw a large circle representing "men" and a smaller circle within it representing "cooks." Similarly, if most men are idiots, we would draw another circle representing "idiots" overlapping with the circle representing "men." By visually comparing the sizes of the "cooks" and "idiots" circles, we can assess whether the conclusion that "most cooks are idiots" holds true based on the given premises.

For the second argument, we would create sets representing "plants," "purple things," and "edible things" in the Venn diagram. If very few plants are purple, we would draw a small circle for "plants" and an even smaller circle within it for "purple things." Likewise, if very few purple things are edible, we would draw another circle for "edible things" that overlaps with the circle for "purple things." By examining the overlaps and sizes of the circles, we can determine whether the conclusion that "very few plants are edible" logically follows from the premises.

In the discussion forum, I would share these thoughts and encourage classmates to discuss how Venn diagrams can help visualize the relationships between different categories and assess the validity of arguments. I would also be interested in hearing other students' perspectives on how they would adapt Venn diagrams to evaluate similar arguments. Engaging in such discussions can deepen our understanding of logic and reasoning and enhance our critical thinking skills.

1. To represent the first argument through a Venn diagram, we can create two overlapping circles, one representing cooks and the other representing men. Since "most cooks are men," we draw a larger portion of the "cooks" circle overlapping with the "men" circle. Similarly, since "most men are idiots," we shade a portion of the "men" circle to represent idiots. The shaded area where the "cooks" circle overlaps with the "men" circle represents the group of cooks who are also men. Since a portion of the "men" circle is shaded to represent idiots, it might seem like most cooks are idiots based on this representation. However, the argument is flawed as it assumes all men who are cooks are idiots, which is not necessarily true. It oversimplifies the relationship between cooks, men, and intelligence.

2. For the second argument, we can again draw two overlapping circles, one representing plants and the other representing things that are purple. Since "very few plants are purple," draw a smaller portion of the "plants" circle overlapping with the "purple" circle. Since "very few purple things are edible," shade a portion of the "purple" circle to represent non-edible things. The shaded area where the "plants" circle overlaps with the "purple" circle represents the group of plants that are also purple. Since a portion of the "purple" circle is shaded to represent non-edible things, it might seem like very few plants are edible based on this representation. However, just like the first argument, this conclusion oversimplifies the relationship between plants, purple things, and edibility.

Venn diagrams can be adapted to visually represent the relationships between sets of objects or concepts and help evaluate the validity of arguments. Let's adapt them for the two arguments provided:

Argument 1:
Premise 1: Most cooks are men.
Premise 2: Most men are idiots. To represent this argument using a Venn diagram, we could have two overlapping circles: one representing "cooks" and the other representing "idiots." The area where the two circles overlap would represent "men." We can label the portions of the circles accordingly to indicate the proportions of cooks and men who are idiots. However, it's important to note that this argument relies on stereotypical and flawed assumptions.
Argument 2:
Premise 1: Very few plants are purple.
Premise 2: Very few purple things are edible. Similarly, we can represent this argument using a Venn diagram with two overlapping circles: one representing "plants" and the other representing "edible things." The area where the two circles overlap would represent "purple things." Again, we can label the portions of the circles to indicate the proportions of plants and edible things that are purple. However, this argument might overlook exceptions, such as some edible purple plants.
Adapting Venn diagrams in this way allows us to visually assess the logical connections between different categories or sets of objects described in the arguments. However, it's essential to critically evaluate the premises of the arguments and consider potential counterexamples or flaws in the reasoning.

In this diagram, the non-overlapping area between Plants and Purple Things represents very few plants being purple. The non-overlapping area between Purple Things and Edible represents very few purple things being edible. The conclusion that very few plants are edible can be inferred from this, as the overlap between Plants and Edible is limited.

Adapting Venn Diagrams for Argument Evaluation:

1. Most cooks are men. Most men are idiots. So most cooks are idiots.
We could represent this argument using overlapping circles for "cooks" and "idiots".
If most cooks are men and most men are idiots, then there would be a significant overlap between the circles representing cooks and idiots, suggesting that most cooks are indeed idiots.
However, it's important to note that the validity of the argument depends on the accuracy of the premises ("most cooks are men" and "most men are idiots").

2. Very few plants are purple. Very few purple things are edible. So very few plants are edible.
We could use overlapping circles for "plants" and "edible things".
If very few plants are purple and very few purple things are edible, then there would be little to no overlap between the circles representing plants and edible things, suggesting that very few plants are indeed edible.
Again, the validity of the argument relies on the truthfulness of the premises ("very few plants are purple" and "very few purple things are edible").
In both cases, Venn diagrams can help visually represent the relationship between the categories mentioned in the arguments and aid in evaluating their validity.

Both are not valid, as when we construct a two category Venn for the conclusion, we see that it contain information that wasn't already contained in the premise Venn.
1. we have Category A = Cooks, Category B = Men and Category C = Idiots
2. we have Category A = Plants, Category B = Purple things and Category C = Edible things

1. It would make sense to have to over lapping circle since you need one for "most cooks are men", "cooks" , and "most cooks are idiots". The overlapping in the middle would represent "cooks". While the outer two represent "most cooks are men" and "most cooks are idiots". I do believe that this argument makes us assume that all all men that cook are idiots. But we can disagree and say all men that cooks are not idiots.
2. I would use the two circle methods again. left side being "plants, the right being "edible" and the middle being "purple things are edible". I do believe that this argument makes us believe that there are not many of purple edible plants. Which that is not true there are some purple plants that are edible and some that are not edible.