Discussion: Venn Diagrams and Argument Validity

Number of replies: 85

Consider how you might adapt Venn diagrams to evaluate the validity of these arguments. 

  1. Most cooks are men. Most men are idiots. So most cooks are idiots. 
  2. Very few plants are purple. Very few purple things are edible. So very few plants are edible.

Share your thoughts on the discussion forum. Make sure to review and respond to other students' posts, as well.

In reply to First post

Re: Discussion: Venn Diagrams and Argument Validity

by Catherine Quinn -
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.
In reply to First post

Re: Discussion: Venn Diagrams and Argument Validity

by Olha Semeniuk -
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.
In reply to Olha Semeniuk

Re: Discussion: Venn Diagrams and Argument Validity

by Gift Kabengele -
This is a good analysis of both statements. As it brings out details of arguments.
In reply to Olha Semeniuk

Re: Discussion: Venn Diagrams and Argument Validity

by Dominique Vittorio -
Draw two circles: one representing cooks (A) and another representing men (B). Most of the area of the cooks’ circle (A) should overlap with the men’s circle (B).
Draw a third circle representing idiots (C), with most of its area overlapping with the men’s circle (B).

The conclusion “Most cooks are idiots” would be valid if most of the cooks (A) were also part of the idiots’ circle (C). However, the Venn diagram shows that the overlap between cooks and idiots is not guaranteed. Since “most” in logic doesn’t imply all, it’s possible for many men to be idiots without most cooks being idiots. Therefore, the argument is invalid because it incorrectly assumes a transitive relationship between the sets.


Draw two circles: one representing plants (A) and another representing purple things (B). The overlap between these two should be minimal, indicating that very few plants are purple.
Draw a third circle representing edible things (C), with minimal overlap with the purple things circle (B).

The conclusion “Very few plants are edible” would be valid if the small overlap between purple things and edible things somehow extended to the plants’ circle (A). However, the argument is invalid because it assumes that the small overlap between purple and edible things necessarily affects the overlap between plants and edible things. The Venn diagram shows that just because very few plants are purple and very few purple things are edible, it doesn’t logically follow that very few plants are edible. The argument commits a logical error by conflating separate small overlaps.
In reply to First post

Re: Discussion: Venn Diagrams and Argument Validity

by Gift Kabengele -
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.
In reply to Gift Kabengele

Re: Discussion: Venn Diagrams and Argument Validity

by Shaqoria Hay -
I agree both of this would have similar diagrams. The first one wants us to believe that all men that cook are idiots, but of course we know that is not true. The second one can also be proven from during argument because there are several plant that are purple and edible. They may be rare but it is true. I think the diagram will allow views, viewing the arguments to gain a better understanding.
In reply to Shaqoria Hay

Re: Discussion: Venn Diagrams and Argument Validity

by Dominique Vittorio -
I agree with your assessment. The first argument indeed tries to lead us to an illogical conclusion by oversimplifying the relationships between the groups. Similarly, the second argument ignores the possibility that even rare exceptions (like edible purple plants) can exist. Venn diagrams are definitely a useful tool in these cases, as they visually demonstrate why these conclusions don’t hold up, helping us see the gaps in logic more clearly.
In reply to First post

Re: Discussion: Venn Diagrams and Argument Validity

by asifa shaikh -
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.

In reply to First post

Re: Discussion: Venn Diagrams and Argument Validity

by John Heathcliff -
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.
In reply to First post

Re: Discussion: Venn Diagrams and Argument Validity

by Rehan Ullah -
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.
In reply to First post

Re: Discussion: Venn Diagrams and Argument Validity

by Saurabh Umbarkar -
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.
In reply to First post

Re: Discussion: Venn Diagrams and Argument Validity

by Michael Starnes -
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 reply to First post

Re: Discussion: Venn Diagrams and Argument Validity

by JOSAFAT VANDULF ELANO -
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.
In reply to First post

Re: Discussion: Venn Diagrams and Argument Validity

by WLLM12 G -
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.
In reply to First post

Re: Discussion: Venn Diagrams and Argument Validity

by Valentin Ionescu -
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
In reply to Valentin Ionescu

Re: Discussion: Venn Diagrams and Argument Validity

by Shaqoria Hay -
I do both argument are not vailed because we can prove other wise. We can say that all men that cook are not idiots. We also know that there are several edible purple plants. I do feel like placing these in a diagram gives a better understanding, so we can get a better understanding of why the argument are nit valid. We want to make sure we are label the diagram is understandable to ne able to point out what is valid and not valid.
In reply to First post

Re: Discussion: Venn Diagrams and Argument Validity

by Shaqoria Hay -
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.
In reply to First post

Re: Discussion: Venn Diagrams and Argument Validity

by Leslie Tapper -
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.
In reply to First post

Re: Discussion: Venn Diagrams and Argument Validity

by Tiffany Jones -
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.
In reply to Tiffany Jones

Re: Discussion: Venn Diagrams and Argument Validity

by Siddika Koly -
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.
In reply to Tiffany Jones

Re: Discussion: Venn Diagrams and Argument Validity

by Saanvi Kundu -
You've identified the problem well ~ these arguments oversimplify complex relationships by making broad generalizations that ignore nuance and diversity. A more balanced perspective is needed to account for the inherent complexity involved.
In reply to First post

Re: Discussion: Venn Diagrams and Argument Validity

by Hudson Harper -
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.
In reply to First post

Re: Discussion: Venn Diagrams and Argument Validity

by Saanvi Kundu -
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.
In reply to First post

Re: Discussion: Venn Diagrams and Argument Validity

by Corne Botha -
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.
In reply to First post

Re: Discussion: Venn Diagrams and Argument Validity

by Cecily Acevedo -

Using Venn diagrams can be a great way to visualize the relationships between different sets and evaluate the validity of these arguments.

 Argument: Most cooks are men. Most men are idiots.  Conclusion: So, most cooks are idiots.

Venn Diagram Analysis: Circle A for "Cooks". Circle B for "Men". Circle C for "Idiots". Since "most cooks are men," the circle A (Cooks) overlaps significantly with circle B (Men). "Most men are idiots" means that circle B (Men) overlaps with circle C (Idiots), but not necessarily in a way that covers all of circle B.

Though there is an overlap between Cooks and Men and between Men and Idiots, the major overlap does not guarantee that most cooks also fall into the Idiots category. Therefore, the conclusion that "most cooks are idiots" does not logically follow from the premises.The argument is invalid because the conclusion does not necessarily follow from the premises.


Argument: Very few plants are purple. Very few purple things are edible. Conclusion: So very few plants are edible.

Venn Diagram Analysis: Circle A for "Plants". Circle B for "Purple Things". Circle C for "Edible Things". "Very few plants are purple" suggests that the intersection between circles A and B is small. “Very few purple things are edible" implies a small overlap between circles B (Purple Things) and C (Edible Things). Just because very few purple things are edible and very few plants are purple does not mean anything about the overall number of edible plants. There may be many non-purple plants that are edible, which are outside both circle B and circle C. The argument is invalid as the conclusion does not logically follow from the premises.

In both cases, Venn diagrams illustrate that while there are overlaps as stated, they do not support the conclusions drawn. By visualizing the relationships, we can more easily see the flaws in the arguments' logic. 

In reply to First post

Re: Discussion: Venn Diagrams and Argument Validity

by vanessa Ur -
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.
In reply to First post

Re: Discussion: Venn Diagrams and Argument Validity

by JECEL MONTI-EL -
To evaluate the validity of the argument using Venn diagrams, we can represent the information in terms of sets and their relationships. Here’s a step-by-step guide on how to do this:

Define the Sets:

Let
𝑃
P represent the set of plants.
Let
𝐸
E represent the set of edible things.
Let
𝑅
R represent the set of purple things.
Plot the Information:

The statement "Very few plants are purple" implies that the intersection of
𝑃
P and
𝑅
R is very small. In a Venn diagram, this would mean that the overlap between the circle for
𝑃
P and the circle for
𝑅
R is minimal.
The statement "Very few purple things are edible" implies that the intersection of
𝑅
R and
𝐸
E is also very small. In the Venn diagram, this would mean that the overlap between the circle for
𝑅
R and the circle for
𝐸
E is minimal.
Draw the Venn Diagram:

Draw three circles: one for
𝑃
P (plants), one for
𝑅
R (purple things), and one for
𝐸
E (edible things).
Shade the intersections:
The intersection of
𝑃
P and
𝑅
R should be minimal.
The intersection of
𝑅
R and
𝐸
E should be minimal.
Analyze the Argument:

The argument concludes that "Very few plants are edible," which implies that the intersection of
𝑃
P and
𝐸
E should be minimal.
To test the validity, examine if the given information logically leads to the conclusion. Here's how it looks on the Venn diagram:

Since very few plants are purple, the
𝑃
∩
𝑅
P∩R intersection is small.
Since very few purple things are edible, the
𝑅
∩
𝐸
R∩E intersection is small.
To determine if very few plants are edible, observe that:

Even if the overlap
𝑃
∩
𝑅
P∩R is small and
𝑅
∩
𝐸
R∩E is small, it does not necessarily follow that
𝑃
∩
𝐸
P∩E must be small. This is because the plants that are purple and the purple things that are edible do not directly account for the entire set of plants and their edibility.
In a Venn diagram, it is possible that:

The small intersection
𝑃
∩
𝑅
P∩R means few plants are purple.
The small intersection
𝑅
∩
𝐸
R∩E means few purple things are edible.
However, if the purple things are a small subset of all plants and edible things are a small subset of purple things, there is no direct conclusion that the subset of plants that are edible is small without additional information about the sizes of the total sets or additional intersections.
Conclusion: The Venn diagram shows that the premises do not necessarily lead to the conclusion. The argument is not necessarily valid based on the given premises because there is no direct logical necessity that a small intersection between purple things and edible things implies a small intersection between all plants and edible things.
In reply to First post

Re: Discussion: Venn Diagrams and Argument Validity

by Jonathan Cuntapay -
1. To evaluate the argument "Most cooks are men; Most men are idiots; So most cooks are idiots" using Venn diagrams, we can represent the relationships by drawing three circles for cooks (C), men (M), and idiots (I). Since "most" implies a significant overlap rather than a complete one, we would shade a large portion of the C circle that overlaps with the M circle and similarly for the M circle with the I circle. After shading these areas, we analyze whether the overlap between cooks and idiots indicates that "most cooks are idiots." However, the non-absolute nature of "most" suggests that while there is a substantial overlap, it does not definitively lead to the conclusion that most cooks are idiots, thereby raising questions about the argument's validity.
2. For the argument "Very few plants are purple; Very few purple things are edible; So very few plants are edible," we would draw circles for plants (P), purple things (R), and edible things (E). Given that "very few" indicates a minimal overlap, we would shade only a tiny portion of the P circle to represent the relationship between plants and purple things and likewise for the R circle concerning edible things. Analyzing the resulting Venn diagram, we would examine whether the small overlap between plants and edible things supports the conclusion that "very few plants are edible." However, due to the limited shading, it becomes difficult to assert this conclusion based solely on the premises, leading to skepticism regarding the argument's validity.
In reply to First post

Re: Discussion: Venn Diagrams and Argument Validity

by Rachel Validum -

1.

Premises:

  1. Most cooks are men.
  2. Most men are idiots.

Conclusion: So, most cooks are idiots.

Venn Diagram:

  1. Draw one circle for "Cooks" and another for "Men." Since most cooks are men, the majority of the "Cooks" circle will overlap with the "Men" circle.
  2. Draw a third circle for "Idiots." Since most men are idiots, a significant portion of the "Men" circle will overlap with the "Idiots" circle.
  3. While there's overlap between cooks and men, and between men and idiots, the argument assumes that the overlap of cooks with idiots follows from these premises. This isn't necessarily valid; some cooks might not be idiots.

Conclusion: The argument is not valid based solely on the premises provided.


2.

Premises:

  1. Very few plants are purple.
  2. Very few purple things are edible.

Conclusion: So, very few plants are edible.

Venn Diagram

  1. Draw a circle for "Plants" and another for "Purple Things." Since very few plants are purple, the overlap will be minimal.
  2. Draw a third circle for "Edible Things." Very few purple things are edible will also result in a small overlap with the "Purple Things" circle.
  3. The argument suggests that because both categories (purple plants and purple edible things) have limited overlap, we can conclude something about the plants in general. However, the premises do not provide sufficient information to conclude that plants overall are not edible.

Conclusion: The argument is also not valid based on the premises provided.

Summary:

In both cases, Venn diagrams can help illustrate the relationships, but the conclusions drawn do not necessarily follow logically from the premises. The arguments make assumptions that aren't guaranteed by the premises, indicating their invalidity.


In reply to First post

Re: Discussion: Venn Diagrams and Argument Validity

by Rae Ramsey -

Premises:

1) most cooks are men

2) most men are idiots

C: most cooks are idiot. 

(Create 2 overlapping circles and plug in respective arguments)


1)Few plants are purple 

2) few purple things are edible 

C: few plants are edible 

(Create 2 overlapping circles and plug in respective arguments) 

In reply to First post

Re: Discussion: Venn Diagrams and Argument Validity

by Ibtihaj Khan -
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.
In reply to First post

Re: Discussion: Venn Diagrams and Argument Validity

by DANIEL BACH PHAN -
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 reply to DANIEL BACH PHAN

Re: Discussion: Venn Diagrams and Argument Validity

by Samantha Tomlinson -
This explanation was very detailed and highlighted the relationships of the conditions.
In reply to First post

Re: Discussion: Venn Diagrams and Argument Validity

by Jhea galgo -
Argument 1:

All A (men) are not necessarily B (idiots)
All C (cooks) are not necessarily A (men)

Venn Diagram:

A (men) ∩ B (idiots) ≠ C (cooks)
(Intersection of men and idiots does not equal cooks)

Conclusion: The argument is invalid. Being a cook does not necessarily imply being an idiot.

Argument 2:

A (plants) ∩ B (purple) ≠ C (edible)
(Intersection of plants and purple does not equal edible)

Venn Diagram:

A (plants) ∩ B (purple) ∩ C (edible) is a small overlap
(Intersection of plants, purple, and edible is minimal)

Conclusion: The argument is invalid. Being a plant does not necessarily imply being inedible.

In both cases, the arguments commit the fallacy of:

1. Illicit minor (assuming a subset represents the whole)
2. False syllogism (incorrectly concluding a property applies to all members)
In reply to Jhea galgo

Re: Discussion: Venn Diagrams and Argument Validity

by Jessica Blackburn -
Your analysis of both arguments using Venn diagrams provides a helpful visualization of the relationships between the categories involved. Let's briefly review the conclusions you've drawn:

Argument 1:

You've rightly pointed out that the argument is invalid, as being a cook does not necessarily imply being an idiot. The Venn diagram highlights that the intersection of men and idiots does not encompass all cooks.

Argument 2:

Once again, you've correctly identified this argument as invalid. The Venn diagram illustrates that the intersection of plants, purple, and edible things is minimal, demonstrating that being a plant does not necessarily imply being inedible.

In both arguments, you've identified fallacies that help explain why they are invalid:

1. Illicit minor: This fallacy occurs when the minor term (the subject term of the conclusion) is undistributed in the minor premise but is distributed in the conclusion. In other words, it assumes that a subset represents the whole group.
2. False syllogism:This fallacy happens when a property is incorrectly concluded to apply to all members of a group without proper justification or logical reasoning.

By analyzing the arguments through Venn diagrams and identifying these fallacies, you've demonstrated a clear understanding of why the given arguments are invalid.
In reply to First post

Re: Discussion: Venn Diagrams and Argument Validity

by Jessica Blackburn -
Venn diagrams can be useful in evaluating the validity of arguments involving categorical statements. However, they have limitations in representing statements with quantifiers like "most," "very few," or other similar terms. Still, let's try to adapt the Venn diagrams to visualize these arguments.

Argument 1:
1. Premise 1: Most cooks are men.
2. Premise 2: Most men are idiots.
3. Conclusion: Most cooks are idiots.

Venn Diagram Adaptation:

- Draw a circle for cooks (C) and a circle for men (M), with a significant overlap between them to represent "most cooks are men."
- Draw a circle for idiots (I) with a significant overlap with the men (M) circle to represent "most men are idiots."

Due to the significant overlaps, the conclusion "most cooks are idiots" might seem reasonable. However, it's important to note that this is not a deductively valid argument, as it relies on probabilities rather than certainties.

Argument 2:
1. Premise 1: Very few plants are purple.
2. Premise 2: Very few purple things are edible.
3. Conclusion: Very few plants are edible.

Venn Diagram Adaptation:

- Draw a circle for plants (P) and a circle for purple things (PT), with very small overlaps between them to represent "very few plants are purple."
- Draw a circle for edible things (E) with very small overlaps with the purple things (PT) circle to represent "very few purple things are edible."

Since the overlaps in both premises are minimal, it's difficult to draw a definite conclusion about the relationship between plants and edible things. This argument is not deductively valid, as it relies on assumptions about probabilities rather than logical implications.
In reply to First post

Re: Discussion: Venn Diagrams and Argument Validity

by Mehak Pal -
To evaluate the validity of the arguments using Venn diagrams, we can visualize the relationships between the different groups mentioned.

For the first argument:
1. Draw a circle for "cooks" and a larger circle for "men." Since "most cooks are men," the cooks' circle should overlap significantly with the men's circle.
2. Next, draw another circle for "idiots" that overlaps with the men's circle, indicating that most men are idiots.
3. The conclusion states that "most cooks are idiots." However, just because most cooks are men and most men are idiots doesn’t necessarily mean that the majority of cooks are idiots. There could be a significant number of cooks who are not men, which would invalidate the conclusion. The Venn diagram shows that the overlap doesn’t guarantee that most cooks fall into the idiots category.

For the second argument:
1. Draw a circle for "plants" and a separate circle for "purple things." Since "very few plants are purple," the overlap between these two circles will be minimal.
2. Then, draw a circle for "edible things" that overlaps with the purple things circle, representing that very few purple things are edible.
3. The conclusion states that "very few plants are edible." However, the minimal overlap between plants and purple things does not provide sufficient evidence that plants in general are not edible. The Venn diagram indicates that the few purple plants may not represent the entire plant population, making the conclusion weak.
In reply to First post

Re: Discussion: Venn Diagrams and Argument Validity

by Sarath Chandra Veerla -
Venn diagrams help to illustrate the flaws in these arguments by showing that the relationships between sets are not guaranteed to lead to the conclusions proposed. In both cases, the premises do not necessarily imply the conclusion. Evaluating arguments with Venn diagrams allows for a clearer understanding of the structure of reasoning and can help identify logical gaps.

I'm curious to hear if others would approach these problems differently or if there are other strategies for evaluating arguments effectively!
In reply to First post

Re: Discussion: Venn Diagrams and Argument Validity

by Rebecca Klein -
To evaluate these arguments using Venn diagrams, I would first identify the individual categorical statements.
1. Cooks - C, Men - M, and Idiots - I
2. Plants - F, Things that are purple - P, and Things that are edible - E

I'd assign each of these categories to sections on a Venn diagram for their argument. I'd then fill in the information from the premises (shown for 1 below) and compare it to a similar Venn diagram for the conclusion. It then becomes clear that the information represented by the conclusion is not found in the diagram for the premises, meaning the argument is invalid. 

A venn diagram showing the relationships between categories in the prompt.
In reply to Rebecca Klein

Re: Discussion: Venn Diagrams and Argument Validity

by Dylan Lortie -
This is a great post and shows the difference in how a venn diagram is used.
In reply to First post

Re: Discussion: Venn Diagrams and Argument Validity

by Ademide Abdullah -
1. Most cooks are men. Most men are idiots. So most cooks are idiots.

Rephrasing the sentence because we cannot have "most" in categorical syllogism statement.

Some men are cooks.
Some men are idiots.
Some cooks are idiots.

Representing men as M
Cooks as C
Idiots as I
So

Some C are M
Some M are I
Therefore; Some C are I


Drawing a Venn diagram of three circle M, C and I.
C on the left, I on the right and M in the middle.

So from the first statement of the premise, there will be a X on the line between C and M indicating some C in M.

In the second premise, there will be a X on the line between M and I indicating that there is some in I.


So in the conclusion diagram, a X will be put in the intersection of C and I to that there is C in I


The diagram will show that the statement is not valid.
In reply to Ademide Abdullah

Re: Discussion: Venn Diagrams and Argument Validity

by Sami Al Majanini -
I think there might be a slight issue with how the conclusion is derived.

When you place the X in the intersection of C (cooks) and I (idiots) based on the premises, you’re making an assumption that isn’t explicitly supported by the information given. The overlap between C and I depends on the specific relationship between cooks and men, and men and idiots. Without further evidence or a stronger logical connection, we can’t conclusively place an X in the intersection of C and I.

For example:

The first premise states “some C are M,” so there’s overlap between cooks and men.
The second premise states “some M are I,” so there’s overlap between men and idiots.
However, this doesn’t necessarily mean there’s overlap between C and I. It’s possible for the groups to overlap with M without directly connecting C and I.
In reply to First post

Re: Discussion: Venn Diagrams and Argument Validity

by Sami Al Majanini -
Using Venn Diagrams to Evaluate the Arguments
1. Most cooks are men. Most men are idiots. So most cooks are idiots.
To evaluate this argument using Venn diagrams:

Venn Diagram Setup:

Circle 1: Set of all cooks.
Circle 2: Set of all men.
Circle 3: Set of all idiots.
Analysis:

The statement "most cooks are men" implies significant overlap between Circle 1 (cooks) and Circle 2 (men).
The statement "most men are idiots" implies significant overlap between Circle 2 (men) and Circle 3 (idiots).
However, the conclusion that "most cooks are idiots" assumes that the overlap between cooks and men translates entirely to an overlap between cooks and idiots. This does not necessarily follow, as not all men are idiots, and not all cooks are men.
Validity: This argument is invalid because the relationships described in the premises do not guarantee the conclusion.
2. Very few plants are purple. Very few purple things are edible. So very few plants are edible.
To evaluate this argument using Venn diagrams:

Venn Diagram Setup:

Circle 1: Set of all plants.
Circle 2: Set of all purple things.
Circle 3: Set of all edible things.
Analysis:

The statement "very few plants are purple" means there is only a small overlap between Circle 1 (plants) and Circle 2 (purple things).
The statement "very few purple things are edible" means there is only a small overlap between Circle 2 (purple things) and Circle 3 (edible things).
The conclusion that "very few plants are edible" assumes that the minimal overlap between plants and purple things implies minimal overlap between plants and edible things. This is not necessarily true, as plants can be edible without being purple.
Validity: This argument is also invalid because the premises do not logically lead to the conclusion.
In reply to First post

Re: Discussion: Venn Diagrams and Argument Validity

by Toya Roberts -
Argument 1: Most cooks are men. Most men are idiots. So most cooks are idiots.
Set A: Cooks
Set B: Men
Set C: Idiots
Venn Diagram - The first premise suggests a large overlap between Set A (cooks) and Set B (men). The second premise suggests a large overlap between Set B (men) and Set C (idiots). However, there is no direct relationship established between Set A (cooks) and Set C (idiots).
The conclusion (“Most cooks are idiots”) assumes a transitive relationship that is not supported by the premises. While some cooks may also be idiots if they fall within the overlap of Set B and Set C, it does not follow logically that most cooks are idiots. This argument is invalid.

Argument 2: Very few plants are purple. Very few purple things are edible. So very few plants are edible.
Set A: Plants
Set B: Purple things
Set C: Edible things
Venn Diagram - The first premise suggests a small overlap between Set A (plants) and Set B (purple things). The second premise suggests a small overlap between Set B (purple things) and Set C (edible things). However, the overlap between Set A (plants) and Set C (edible things) is not directly established.
The conclusion (“Very few plants are edible”) does not logically follow from the premises. The premises only tell us about purple plants and their edibility but say nothing about the edibility of plants in general. This argument is also invalid.
In reply to First post

Re: Discussion: Venn Diagrams and Argument Validity

by Roselix Perez -
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.
In reply to First post

Re: Discussion: Venn Diagrams and Argument Validity

by Jevon Searight -
Let's break down these arguments using Venn diagrams to evaluate their validity.

### Argument 1: Most cooks are men. Most men are idiots. So most cooks are idiots.
To evaluate this argument, we can use three sets: Cooks (C), Men (M), and Idiots (I). Most cooks are men, meaning a large portion of the C set overlaps with the M set. Most men are idiots, meaning a large portion of the M set overlaps with the I set. The conclusion that most cooks are idiots suggests a large portion of the C set overlaps with the I set. However, the overlap between C and M, and M and I, doesn't necessarily mean there's a significant overlap between C and I. The argument assumes transitivity, which isn't always valid in this context. The Venn diagram would show that while there is some overlap, it doesn't guarantee that most cooks are idiots.

### Argument 2: Very few plants are purple. Very few purple things are edible. So very few plants are edible.
For this argument, we can use three sets: Plants (P), Purple things (Pu), and Edible things (E). Very few plants are purple, meaning a small portion of the P set overlaps with the Pu set. Very few purple things are edible, meaning a small portion of the Pu set overlaps with the E set. The conclusion that very few plants are edible suggests a small portion of the P set overlaps with the E set. The Venn diagram would show that the small overlap between P and Pu, and Pu and E, doesn't necessarily mean there's a small overlap between P and E. The argument assumes that the rarity of purple plants and edible purple things implies the rarity of edible plants, which isn't logically sound.

In summary, using Venn diagrams helps visualize the relationships between sets and evaluate the validity of these arguments. Both arguments make assumptions that aren't necessarily supported by the overlaps in the diagrams.
In reply to First post

Re: Discussion: Venn Diagrams and Argument Validity

by Dylan Lortie -
1. In order to show the first argument as a Venn diagram it will need to be broken out into two separate sections, the first will be cooks, and the second will be men. If most cooks are men then this will go over the cooks and overlapping over the section with men. The next statement that most men are idiots will go over the men section. Cooks and men will overlap and part men will be alone wit the term idiots. Just because most men are idiots does not correlate with most men are cooks, the relationship is very broad.

2. In order to show the second argument as a Venn diagram it will need to be broken out into two sections, the first is purple, and the second would be plants. The plants are purple would be go over the section that shows purple and a little over the plants. Very few purple things are edible would go over the purple side of the Venn diagram. Very few plants are edible would go on the plant side.
This argument makes sense because very plants are purple and very few purple things are edible so the likely hood of a purple plant being edible is low.
In reply to First post

Re: Discussion: Venn Diagrams and Argument Validity

by yamilkie forchue -
A = Men , B = Crooks , C= Idiots An invalid argument

A= Plants , B= Purple , C= Edible another invalid argument
In reply to First post

Re: Discussion: Venn Diagrams and Argument Validity

by Alexander Mendez -
1. Most cooks are men. Most men are idiots. So most cooks are idiots.
A Venn diagram would show overlapping circles for "cooks," "men," and "idiots." While there’s overlap between "cooks" and "men" and between "men" and "idiots," it doesn’t guarantee significant overlap between "cooks" and "idiots." The conclusion assumes transitivity where it doesn’t necessarily apply, making the argument invalid.

2.Very few plants are purple. Very few purple things are edible. So very few plants are edible.
A Venn diagram for "plants," "purple things," and "edible things" shows little overlap between each pair. However, the argument incorrectly assumes that being "purple" links "plants" and "edible" in a way that doesn’t follow logically. This makes the argument invalid.

In both cases, Venn diagrams reveal gaps in the logic. What are your thoughts on using visuals for evaluating arguments?
In reply to First post

Re: Discussion: Venn Diagrams and Argument Validity

by MUHAMMAD TANVEER -
Venn diagrams can help evaluate the validity of these arguments by visually representing the relationships between the sets.

For the first argument, "Most cooks are men" and "Most men are idiots," we cannot conclude "Most cooks are idiots" because there is no necessary overlap shown between "cooks" and "idiots" beyond their connection to "men." The Venn diagram would show partial intersections but no definitive conclusion.

For the second argument, "Very few plants are purple" and "Very few purple things are edible," there is no direct relationship established between "plants" and "edible." A Venn diagram would show minimal overlap among "plants," "purple," and "edible," revealing that the argument's conclusion does not logically follow.
In reply to First post

Re: Discussion: Venn Diagrams and Argument Validity

by Amanpreet Singh -
1. Most cooks are men. Most men are idiots. So most cooks are idiots:
Using Venn diagrams, overlap the sets of “cooks,” “men,” and “idiots.” While “most” implies a large overlap between “cooks” and “men” and between “men” and “idiots,” it doesn’t guarantee that “cooks” and “idiots” overlap significantly. The conclusion is invalid.
2. Very few plants are purple. Very few purple things are edible. So very few plants are edible:
Using Venn diagrams, the small overlap between “plants” and “purple” and between “purple” and “edible” does not imply a significant overlap between “plants” and “edible.” The conclusion is invalid.
In reply to First post

Re: Discussion: Venn Diagrams and Argument Validity

by Kayla Woods -
i think this is opinionated. I also think this is just an example of how differently humans each think
In reply to First post

Re: Discussion: Venn Diagrams and Argument Validity

by rafsha hossain -
Argument 1:
Premises:

Most cooks are men.
Most men are idiots.
Conclusion: Most cooks are idiots.
Venn Diagram Analysis:
We have three groups: Cooks (C), Men (M), and Idiots (I).
The first premise suggests that a large portion of C is within M.
The second premise suggests that a large portion of M is within I.
However, this does not logically imply that a large portion of C is within I.
Example: Suppose 60% of cooks are men, and 60% of men are idiots. It does not necessarily follow that 60% of cooks are idiots; the overlap between these groups might not be significant.
Conclusion: The argument is invalid. The error lies in assuming that overlapping "most" relationships carry through multiple categories.
Argument 2:
Premises:

Very few plants are purple.
Very few purple things are edible.
Conclusion: Very few plants are edible.
Venn Diagram Analysis:
The key groups here are Plants (P), Purple things (Pu), and Edible things (E).
The first premise states that only a small portion of P falls inside Pu.
The second premise states that only a small portion of Pu falls inside E.
However, this does not mean that only a small portion of P falls inside E because there may be a large portion of non-purple plants that are edible.
Conclusion: The argument is invalid. It assumes that "very few" in overlapping categories affects the whole group, which is not necessarily true.
Final Thoughts:
Both arguments make the fallacy of composition, assuming that properties of parts (or overlapping groups) apply to the whole. Venn diagrams would show that while some overlap exists, the conclusions do not logically follow from the premises.
In reply to rafsha hossain

Re: Discussion: Venn Diagrams and Argument Validity

by Salvador de Jesus Farfan Sanchez -
Just a note. In Logic, Venn Diagrams represent categories, not sets. This distinction will keep us from being distracted by terms like "most", "very few", etc. These terms all mean the same thing: "At least one".
In reply to First post

Re: Discussion: Venn Diagrams and Argument Validity

by Tom Pine -
First I would draw three overlapping circles representing cooks, men, and idiots respectively, let's call them A, B, and C. Then I would place an X on each line that surrounds the area that represents A, B, and C. I would then draw the conclusion Venn which would end up as 2 circles representing cooks and idiots. I would put an X in the middle where both circles meet, however looking at the premise Venn I see there is no such X because it is on the line diving realm A,C with ream A,B,C. Thus, it is an invalid argument.
In reply to First post

Re: Discussion: Venn Diagrams and Argument Validity

by Mikkie Gumatay -
1st Argument: "Most cooks are men. Most men are idiots. So most cooks are idiots."
Sets:

C = Set of cooks
M = Set of men
I = Set of idiots
The first premise states that most cooks are men, meaning that a majority of the C-set overlaps with M.

The second premise states that most men are idiots, meaning a majority of M overlaps with I.

However, this does not necessarily mean that most cooks are idiots. Some cooks might not be men, and even though most men are idiots, that does not guarantee that the subset of men who are cooks are also mostly idiots.

Venn Diagram Analysis: The argument is invalid because overlapping "most" relationships do not necessarily transfer across three sets in a way that ensures the conclusion.


2nd Argument: "Very few plants are purple. Very few purple things are edible. So very few plants are edible."
Sets:

P = Set of plants
Pu = Set of purple things
E = Set of edible things
The first premise states that very few plants are in the purple category (meaning a small overlap between P and Pu).

The second premise states that very few purple things are edible (meaning a small overlap between Pu and E).

However, this does not necessarily mean that very few plants are edible. There could be many edible plants that are not purple, meaning the overall relationship between P and E is not determined by Pu.

Venn Diagram Analysis: The argument is invalid because limiting overlap between P and Pu and between Pu and E does not restrict the direct relationship between P and E.


Both arguments fall into the logical trap of the fallacy of the undistributed middle. In each case, the premises establish relationships between overlapping categories, but these do not necessarily extend to the overall conclusion. Venn diagrams help make these errors more visible by showing that the necessary overlap for the conclusion to be valid does not exist.
In reply to Mikkie Gumatay

Re: Discussion: Venn Diagrams and Argument Validity

by Pamela Kuczkowski -

Hello Mikkie,

I saw four categories in the second argument: plants, purple plants, things that are purple, and things that are edible.  Since you cannot accurately compare four categories in a Venn diagram, I thought you would have to use a different system of comparison that a Venn to test the validity of this argument.


However, now that I've read your post, I’m pondering whether there should be only three categories: plants, things that are purple, and things that are edible. I'm still not sure.

In reply to First post

Re: Discussion: Venn Diagrams and Argument Validity

by Pamela Kuczkowski -

Here is the first argument: “Most cooks are men. Most men are idiots. So most cooks are idiots.”

I would arrange the categories as follows:

C= cooks

I= idiots

M= men


Then, I would draw a Venn diagram with 3 circles (one for each category).  I would create this symbol, x+, to stand for the word “most,” since there is no accepted symbol for “most.” This symbol is the symbol for “some,” which is x, with the addition of a plus sign. Then, I would diagram the argument.  For, “most cooks are men,” I would place my x+ symbol on the line which intersects the C and M overlap.  For the, “Most men are idiots,” I would put the symbol x+ on the line which intersects the I and M overlap.  Then I would put an X, which is the standard way to label “some,” in areas 1, 5, and 7.  Finally, I will examine the diagram and see that the area where C and I overlap has a x+ in it.  This area represents the conclusion.  Since it has a x+ in it, which is my made-up symbol for “most,” the conclusion (most cooks are idiots) is valid.


Here is argument 2: “Very few plants are purple. Very few purple things are edible.  So, very few plants are edible.”  


This argument does not follow the S, P, M of a categorical syllogism, as it has four categories.  These categories are plants, purple plants, things that are purple, and things that are edible. Four categories can not be represented accurately in a Venn diagram.  Even so, one can see that this argument is not valid because the conclusion does not logically follow from the premises, because not all categories have been compared to each other.


These two arguments show some of the limitations of Venn diagrams.  They cannot accurately be used to show “Many” and “few.”

In reply to First post

Re: Discussion: Venn Diagrams and Argument Validity

by Hima Varshini Nallala -
Venn diagrams help visualize logical relationships between groups to check if the conclusion follows from the premises. Let’s break down each argument:

1. "Most cooks are men. Most men are idiots. So most cooks are idiots."
Premises:
Most cooks are in the group of men.
Most men are in the group of idiots.
Conclusion: Most cooks are in the group of idiots.
Problem:
A Venn diagram would show that while there is some overlap between cooks and idiots through men, it does not mean most cooks must be idiots. Some cooks might not be in the "idiots" group. This is a fallacy of the undistributed middle.

2. "Very few plants are purple. Very few purple things are edible. So very few plants are edible."
Premises:
A small portion of plants are in the "purple" group.
A small portion of purple things are in the "edible" group.
Conclusion: A small portion of plants are in the "edible" group.
Problem:
A Venn diagram would show that while "plants" and "edible things" both overlap slightly with "purple things," there is no direct link between "plants" and "edible things." Some plants may still be edible without being purple. This is a faulty generalization.
Both arguments seem logical at first but fail when visualized with Venn diagrams. The first commits the fallacy of the undistributed middle, and the second is a faulty generalization.
In reply to First post

Re: Discussion: Venn Diagrams and Argument Validity

by Dhumal Suraj Nandkumar -
First Argument (Cooks, Men, and Idiots):
To represent the first argument using a Venn diagram, we can create two overlapping circles—one for "cooks" and one for "men." Since the premise states that "most cooks are men," we draw a large portion of the "cooks" circle overlapping with the "men" circle. Next, since "most men are idiots," we shade a portion of the "men" circle to represent idiots. The overlap between "cooks" and "men" shows the group of cooks who are men, and the shaded area within the "men" circle represents those men who are idiots.

At first glance, it might appear that most cooks are idiots, since the "cooks" circle overlaps with the "men" circle, and a large portion of the "men" circle is shaded to indicate that most men are idiots. However, the argument is flawed. It assumes that all cooks who are men are also idiots, which is not necessarily the case. The diagram does not guarantee that the portion of "cooks" who are men also falls within the "idiots" section of the "men" circle. Therefore, the argument oversimplifies the relationship between cooks, men, and intelligence and is ultimately invalid.

Second Argument (Plants, Purple Things, and Edibility):
For the second argument, we can create two overlapping circles, one for "plants" and one for "purple things." Since "very few plants are purple," we draw a small portion of the "plants" circle overlapping with the "purple things" circle. Then, since "very few purple things are edible," we shade a portion of the "purple things" circle to represent non-edible items.

The small overlap between the "plants" and "purple things" circles represents the plants that are purple, and the shaded portion of the "purple things" circle represents those things that are not edible. Based on this setup, one might assume that because so few purple plants are edible, "very few plants are edible" in general.

However, just as with the first argument, this conclusion oversimplifies the relationship between plants, purple things, and edibility. The small overlap between "plants" and "purple things" does not imply that the "plants" circle as a whole overlaps minimally with the "edible things" circle. There could still be many plants that are edible but not purple. Therefore, the argument is invalid, as it makes an unwarranted leap in assuming that the limited overlap between "purple" and "edible" directly translates to the overall edibility of plants.
In reply to First post

Re: Discussion: Venn Diagrams and Argument Validity

by Salvador de Jesus Farfan Sanchez -
1. Most cooks are men. Most men are idiots. So most cooks are idiots.
We have three categories: cooks, idiots, and men. I draw a circle per category.
For the first premise, I put an X in the intersection of cooks and men, but on the borderline of the idiots circle to denote that no claims are made about the idiots category. For the second premise, I put an X in the intersection between men and idiots, but on the borderline of the cooks circle.
For the conclusion, I simply draw the circles for cooks and idiots with an X inside their intersection.
It won't find a match in the Venn diagram for the premises because none of those first Xs ever got resolved. One never fell either inside or outside of idiots, and the other one stayed on the cooks boundary.
The conclusion mentions both categories, so they cannot remain unresolved.
This shows that using exaggerated words won't make an argument any more valid.
Note that by rendering the argument invalid, the claim that most cooks are idiots remained undecided.

2. Very few plants are purple. Very few purple things are edible. So very few plants are edible.
This case has the same structure.
We have three categories: plants, things that are purple, and things that are edible. I draw a circle per category.
For the first premise, I put an X in the intersection of plants and things that are purple, but on the borderline of the things that are edible to denote that no claims are made about the edible things. For the second premise, I put an X in the intersection between purple things and edible things, but on the borderline of the plants circle.
For the conclusion, I simply draw the circles for plants and things that are edible with an X inside their intersection.
We again end up with two unresolved Xs that leave the two categories mentioned in the conclusion unresolved.
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Re: Discussion: Venn Diagrams and Argument Validity

by mallory stamper -
Using a Venn diagram for the argument's conclusion that most cooks are idiots, three sections would be needed. The first section would be a circle representing cooks. The second section would be a circle representing men, which would overlap the "cooks" circle. The third section would be a circle representing idiots, which would overlap both the "cooks" and "men" circle. However, these three sections are separate for a reason and do not fully overlap. This is because not all men are cooks, not all cooks are only men, not all men are idiots, not all idiots are only men, not all cooks are idiots, and not all idiots are cooks. In conclusion, the argument has no sustainable validity. This is equally as true for the second statement in the same way using the same layout of Venn diagram.
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Re: Discussion: Venn Diagrams and Argument Validity

by Marquita Brooks -
These examples illustrate logical fallacies, specifically the fallacy of composition and the fallacy of division.
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.
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. Therefore, the conclusion that very few plants are edible based solely on their color is not valid.
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Re: Discussion: Venn Diagrams and Argument Validity

by NIJIN S S -
No all men are not idiots,that who saying that are the idiots and fools
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Re: Discussion: Venn Diagrams and Argument Validity

by D. Tracy Design Studios -
1. Most cooks are men. Most men are idiots. So most cooks are idiots.

  • Sets:

    • CC = set of cooks
    • MM= set of men
    • II = set of idiots

  • Premises in Terms of Sets:

    1. “Most cooks are men” suggests that more than half of CC lies inside MM.
    2. “Most men are idiots” suggests that more than half of MM lies inside I.

  • Conclusion: “Most cooks are idiots” would require that more than half of CC also lies inside II.

Using a Venn Diagram Adaptation
Instead of simple overlapping circles, you could draw:

  1. A circle (or rectangle) for cooks (CC), shading most (but not necessarily all) into a circle for men (MM).
  2. Then, shade most of MM into a circle for idiots (II).

From the diagram, it will become apparent that the portion of cooks that are men might be fairly large, yet those men might only partially or minimally overlap with the “idiots” set. Because “most” only means “more than half,” you cannot definitively conclude that over half of cooks are also idiots—there is no guarantee the overlap is large enough to make “most cooks” also idiots.

Thus, the argument is not necessarily valid: even if “most cooks” are men, and “most men” are idiots, this does not ensure that “most cooks” must be idiots.

2. Very few plants are purple. Very few purple things are edible. So very few plants are edible.

  • Sets:

    • PP = set of plants
    • PuPu = set of purple things
    • EE = set of edible things

  • Premises in Terms of Sets:

    1. “Very few plants are purple” implies only a small slice of PP is inside PuPu.
    2. “Very few purple things are edible” implies only a small slice of PuPu is inside EE.

  • Conclusion: “Very few plants are edible” suggests that only a small slice of PP as a whole would lie inside EE.

Using a Venn Diagram Adaptation

  1. Draw PP (plants) and show that a small subset overlaps with PuPu (purple things).
  2. Draw PuPu so that only a small subset overlaps with EE (edible things).

Because the set of purple plants is presumably a small fraction of all plants, and the set of edible purple items is a small fraction of all purple things, there is no reason to conclude that most non-purple plants are also inedible. The argument would require all, or almost all, plants to be purple in order to link “plants” and “edible” that tightly—but the premise says very few plants are purple. In other words, a small overlap between “plants” and “purple” does not determine the status of the (potentially huge) portion of plants that are not purple.

Hence, the conclusion that “very few plants are edible” does not follow necessarily from these two premises. As your modified Venn diagram would illustrate, the non-purple portion of plants could well be edible, invalidating the conclusion.

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Re: Discussion: Venn Diagrams and Argument Validity

by D Sai Shashank HSC -
Using Venn diagrams helps show why these arguments are invalid. For the first one, just because most cooks are men and most men are idiots doesn’t mean most cooks are idiots, since the overlap might not cover most cooks. In the second, very few plants are purple and very few purple things are edible, but that doesn’t tell us much about plants in general being edible, since the groups barely overlap. Venn diagrams make it clear the connections are weak or missing.
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Re: Discussion: Venn Diagrams and Argument Validity

by B B -
In conclusion, when evaluating these arguments using Venn diagrams, it becomes clear that neither argument is valid. In the first argument, the fact that most cooks are men and most men are idiots doesn’t necessarily mean that most cooks are idiots, as the overlap between these categories isn’t guaranteed to be sufficient. Similarly, in the second argument, the fact that very few plants are purple and very few purple things are edible doesn’t logically imply that very few plants are edible, as the overlap between these categories doesn’t support the conclusion. Both arguments fail to logically connect the premises to the conclusions, making them invalid.
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Re: Discussion: Venn Diagrams and Argument Validity

by Felix Mercado -
Argument 1:
A: Most cooks are men
B: Most men are idiots
(C)onclusion #1: So, most cooks are idiots

A: Cooks
B: Men
C: Idiots

Venn Diagram:
1. Draw one circle for "A = Cooks" and another for "B = Men" With most cooks being men, "A" circle will overlap with the " B = Men" circle.
2. Draw a third circle for "C = Idiots" With most men are idiots, the " B = Men " circle will overlap with the " C = Idiots " circle.
3. Overlap between A = Cooks and B = Men, and between B = Men and C = Idiots, the argument assumes that the overlap of A = Cooks with C = Idiots follows from these premises.
4. This argument is not valid based on the premises provided.

Argument 2:
A: Very few plants are purple
B: Very few purple things are edible.
(C)onclusion #2: So very few plants are edible.

A: Plants
B: Purple Things
C: Edible

Venn Diagram
1. Draw a circle for "A = Plants" and another for "B = Purple Things", there will be an overlap.
2. Draw a third circle for "C = Edible" will overlap with the "B = Purple Things" circle.
3. The argument suggests that because both categories (A = Plants and C = Edible) have some overlap. The premises do not provide sufficient information to conclude that plants overall are not edible.
4. The argument is also not valid based on the premises provided.
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Re: Discussion: Venn Diagrams and Argument Validity

by bhimio rice -
both of these argguments are completely invalid. Though if they used all or none, they would be valid. this is a comonly missinterperated part of logic by noefytes, and so should be strongly teached.
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Re: Discussion: Venn Diagrams and Argument Validity

by Krish Patro -
1. We can see that the men circle mostly overlapping idiots does not mean that cooks circle also mostly overlaps it.
2. We can see that the plant circle barely overlapping purple does not mean that plant circle also barely overlaps edible.
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Re: Discussion: Venn Diagrams and Argument Validity

by maddie daynes -
Argument 1:
Premises:
1. Most cooks are men.
2. Most men are idiots.

Conclusion:
So most cooks are idiots.

Venn Diagram Representation:
1. Create one circle for "Cooks" and another for "Men." Since most cooks are men, a large portion of the "Cooks" circle will overlap with the "Men" circle.
2. Create a third circle for "Idiots." Since most men are idiots, a large portion of the "Men" circle will also overlap with the "Idiots" circle.
3. Since the conclusion claims that most cooks are idiots, we need to check if the overlapping area between "Cooks" and "Men" (which is significant based on the premise) also overlaps with "Idiots."

However, just because most men are idiots doesn’t necessarily mean most cooks are idiots, as the subset of cooks could be comprised of men who are not included in the subset of men categorized as idiots. Therefore, while there is a possibility that some cooks could be idiots, we cannot conclude that most cooks are idiots based on the given premises.

Conclusion of Argument 1: Invalid.

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

Conclusion:
So very few plants are edible.

Venn Diagram Representation:
1. Create a circle for "Plants" and another for "Purple things." Since very few plants are purple, the overlap between these two circles will be small.
2. Create a third circle for "Edible things." Again, since very few purple things are edible, the overlap between "Purple things" and "Edible things" will also be small.

To evaluate the conclusion "very few plants are edible," we need to consider the overlaps. The small overlap between "Plants" and "Purple things" does not provide enough information to conclude anything about the larger group of plants that are not purple. Just because very few purple things are edible does not allow us to infer anything about the edibility of plants in general.

Conclusion of Argument 2: Invalid.

Summary
Both arguments exhibit flaws in logical reasoning, and using Venn diagrams helps visualize why the conclusions drawn do not necessarily follow from their respective premises. Thus:
1. Argument 1 is invalid.
2. Argument 2 is invalid.
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Re: Discussion: Venn Diagrams and Argument Validity

by Samantha Tomlinson -
The first example would have three circles to make the diagram, the first being a circle labeled men and the second labeled cooks, and a third circle labeled cooks. The three circles should overlap in the center to create the "most cooks being idiots" section. The validity of the argument is subjective because of the ambiguity of what classifies someone as an "idiot". The Cooks category and the Men category can be tested for validity, but the Idiots section cannot.

The second example is not a statement of validity at all because the statements are not consistent within the argument. If "very few" plants are purple, "very few" plants would be inedible because of the statement "very few purple things are edible." By it's own explanation a minority of plants would be purple and therefore inedible, meaning the majority of the plants are not purple as well as edible. The Venn diagram for the second example would be composed of three circles as well, one for plants, one for purple things, and a circle for edible things.
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Re: Discussion: Venn Diagrams and Argument Validity

by Sulaiman Ibrahim Babaji -
A Venn diagram is a visual tool used to represent the relationships between different sets. It employs overlapping circles or other shapes to illustrate how sets share common elements or differ from each other. This method is widely utilized in various fields, including mathematics, logic, statistics, and computer science, to simplify complex relationships and aid in understanding set theory concepts.

Key Features of Venn Diagrams:

Representation of Sets: Each circle or shape in a Venn diagram represents a distinct set.

Overlapping Regions: The areas where circles overlap indicate elements that are common to the intersecting sets.

Non-overlapping Regions: Sections that do not overlap highlight elements unique to a particular set.
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Re: Discussion: Venn Diagrams and Argument Validity

by Sultan Soherwardi -
### **Evaluating Arguments Using Venn Diagrams:**

Venn diagrams help visualize logical relationships between sets. Let’s analyze the validity of these arguments using them.

#### **Argument 1:**
*"Most cooks are men. Most men are idiots. So most cooks are idiots."*

- **Sets:** C (Cooks), M (Men), I (Idiots)
- **Premises:**
1. Most C ⊆ M (Most cooks are men).
2. Most M ⊆ I (Most men are idiots).

- **Issue:** The conclusion assumes that "most of most" results in "most," which does not necessarily hold. Venn diagrams would show that while a large portion of C may overlap with M and M with I, this does not guarantee a large overlap between C and I. **Invalid argument.**

#### **Argument 2:**
*"Very few plants are purple. Very few purple things are edible. So very few plants are edible."*

- **Sets:** P (Plants), Pu (Purple Things), E (Edible Things)
- **Premises:**
1. Very few P ⊆ Pu (Very few plants are purple).
2. Very few Pu ⊆ E (Very few purple things are edible).

- **Issue:** Just because very few plants are purple and very few purple things are edible, it does not follow that very few plants are edible. Venn diagrams would show that P and E could still have a significant overlap outside of Pu. **Invalid argument.**

### **Conclusion:**
Both arguments fail because they assume incorrect transitive relationships. A proper Venn diagram representation would reveal gaps in reasoning, showing that the conclusions do not necessarily follow from the premises.
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Re: Discussion: Venn Diagrams and Argument Validity

by Mads Toma -

1: Just because most cooks are men, and most men are idiots doesn’t mean most cooks are idiots. The overlap isn’t strong enough.


2: Saying “very few” twice doesn’t prove the conclusion. The sets barely connect.