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.

Firstly, Iets break down these arguments:
P1.1 - Most cooks are men
P1.2 - Most men are idiots
Conclusion - So most cooks are idiots

P2.1 - Very few plants are purple
P2.2 - Very few purple things are edible.
Conclusion 2 - So very few plants are edible.

Next, we'll draw circles for each of the premises and conclusions before filling according to the premises. Additionally, I'd represent the quantifiers before comparing the diagram.

Recognize where the argument reduces complex relationships into overly simple connections.Break down the argument into its parts to understand how they are connected and what assumptions are being made. Provide a more nuanced perspective that acknowledges complexity and challenges the oversimplified conclusion. In both situations, I notice a tendency to oversimplify complex connections. In the first case, the idea that most cooks are idiots because they're men oversimplifies the diversity of intelligence among male cooks. Similarly, in the second scenario, assuming few plants are edible because they're not purple oversimplifies what makes a plant edible and ignores the variety of edible plants regardless of color. These arguments miss the mark by oversimplifying and failing to acknowledge the intricate relationships between the elements involved.

1.
A.Cooks
B. Men
C. Idiots
It is true that cooks are men and men are idiots. Although it is not valid that most cooks are idiots.
2.
A. Plants
B.Things that are purple
C. Things that are edible.
It is that that very few plants are purple and very few purple things are edible. Although according to the ven it is not valid that few plants are edible.

For the first argument: This argument is flawed because the conclusion does not necessarily follow from the premises. Even if most cooks are men and most men are idiots, it does not automatically mean that most cooks are idiots. There could be many competent male cooks who are not idiots.

For the second argument: This argument is also flawed; the fact that very few plants are purple and very few purple things are edible does not imply that very few plants are edible. There are many edible plants that are not purple, so the conclusion does not logically follow from the premises.

1. Circles of Cooks and Men will overlap (majority), but circles Men and Idiots will also overlap majority, the circles show that not most cooks are idiots (smaller overlap) - argument not valid.
2. Plants and purple overlap is small. purple and edible overlap is also small. not sure how do overlap the plants and edible, as not all edible items are purple - argument not valid.

To evaluate the validity of the arguments using Venn diagrams, we need to represent the relationships between the categories involved and determine if the conclusion logically follows from the premises.

### Argument 1:

**Premises:**
1. Most cooks are men.
2. Most men are idiots.

**Conclusion:**
Most cooks are idiots.

**Venn Diagram Analysis:**

1. **Draw the Venn Diagram:**
- Create three circles: Cooks (C), Men (M), and Idiots (I).
- Since "most cooks are men," the majority of the Cooks circle should overlap with the Men circle.
- For "most men are idiots," the majority of the Men circle should overlap with the Idiots circle.

2. **Analyze the Overlap:**
- If the majority of Cooks are within the Men circle, and most Men are within the Idiots circle, it does not necessarily follow that most Cooks are Idiots.
- The overlap of the Cooks and Idiots circles depends on the size of the overlap between Men and Idiots circles. We cannot determine from the premises alone that most Cooks end up being Idiots.

**Conclusion:**
The argument is not valid. The Venn diagram will show that even with the given overlaps, the conclusion "most cooks are idiots" does not logically follow from the premises.

### Argument 2:

**Premises:**
1. Very few plants are purple.
2. Very few purple things are edible.

**Conclusion:**
Very few plants are edible.

**Venn Diagram Analysis:**

1. **Draw the Venn Diagram:**
- Create three circles: Plants (P), Purple (Pu), and Edible (E).
- Represent "very few plants are purple" by showing a small overlap between the Plants and Purple circles.
- Represent "very few purple things are edible" by showing a small overlap between the Purple and Edible circles.

2. **Analyze the Overlap:**
- If very few things are both Purple and Edible, and very few plants are Purple, the overlap between Plants and Edible will also be minimal because the intersection with Purple is small.

**Conclusion:**
The argument is valid. Given the premises, the small overlap between the relevant categories supports the conclusion that very few plants are edible.

### Summary:

- The first argument fails to be valid as the relationship between the categories does not ensure that the conclusion logically follows.
- The second argument is valid because the limited overlap between the categories supports the conclusion based on the premises.

When reviewing other posts, consider whether others correctly apply Venn diagrams to assess the relationships between categories and whether they accurately determine the validity of the arguments.