A **deductive argument** is one where the conclusion
necessarily follows from the premises. However, just because
an argument is presented as **deductive** does not mean it is
necessarily **valid**. The validity of a deductive argument
depends on whether the structure of the argument ensures that
the conclusion **must** be true if the premises are true.
### **Valid vs. Invalid Deductive Arguments**
1. **Valid Deductive Argument:**
- If the premises are true, the conclusion **must** be true.
- The structure of reasoning is such that there is no way for
the premises to be true while the conclusion is false.
**Example:**
**Premise 1:** All humans are mortal.
**Premise 2:** Socrates is a human.
**Conclusion:** Socrates is mortal.
� This argument is **valid** because it is **impossible** for
the premises to be true and the conclusion to be false.
2. **Invalid Deductive Argument:**
- The argument claims to be deductive, but its structure
allows for a possibility where the premises are true but the
conclusion is false.
**Example:**
**Premise 1:** All cats are mammals.
**Premise 2:** All dogs are mammals.
**Conclusion:** Therefore, all cats are dogs.
� This argument is **invalid** because, even though the
premises are true, the conclusion does not logically follow from
them. It is possible for the premises to be true and the
conclusion to be false, which makes the argument **invalid**.
### **Key Point: Why Can a Deductive Argument Be Invalid?**
A **deductive argument** refers to the **intent** of the
argument (i.e., the argument claims that the conclusion
necessarily follows from the premises). However, if the
argument does not actually ensure this, it is **invalid**.
In short:
- A **valid deductive argument** has a logical structure where
truth in the premises **guarantees** truth in the conclusion.
- An **invalid deductive argument** attempts to be deductive
but fails because the conclusion does not logically follow with
necessity.
## **Understanding Validity in Deductive Arguments (In
Detail)**
### **What is a Deductive Argument?**
A **deductive argument** is an argument where the **premises
claim to guarantee the truth of the conclusion**.
- If the premises **truly support** the conclusion in such a way
that it is **impossible** for the premises to be true and the
conclusion false, the argument is **valid**.
- If there is even a **possibility** that the premises are true and
the conclusion is false, the argument is **invalid**.
--## **How to Test an Argument for Validity**
To determine if an argument is **valid**:
1. **Assume that all premises are true**, even if they are false
in reality.
2. **Check if the conclusion can possibly be false while the
premises remain true.**
- If it **cannot** be false, the argument is **valid**.
- If it **can** be false, the argument is **invalid**.
--## **Examples of Valid and Invalid Arguments**
### **Example 1 (Valid Argument, True Premises & True
Conclusion)**
**Premises:**
1. **All television networks are media companies.** ✅(True)
2. **NBC is a television network.** ✅(True)
**Conclusion:**
� **NBC is a media company.** ✅(True)
**Why is it valid?**
- The **premises logically lead** to the conclusion.
- If NBC is a television network and all television networks are
media companies, then NBC **must** be a media company.
- It is **impossible** for the premises to be true and the
conclusion false.
✅**Thus, the argument is valid.**
--### **Example 2 (Valid Argument, False Premises & False
Conclusion)**
**Premises:**
1. **All automakers are computer manufacturers.** ❌(False)
2. **United Airlines is an automaker.** ❌(False)
**Conclusion:**
� **United Airlines is a computer manufacturer.** ❌(False)
**Why is it valid?**
- Even though the premises and conclusion are false, the
argument **follows the correct logical structure**.
- If all automakers were truly computer manufacturers, and if
United Airlines was an automaker, then it would **necessarily**
be a computer manufacturer.
- **The premises logically support the conclusion.**
✅**Thus, the argument is valid.**
--### **Example 3 (Invalid Argument, True Premises & True
Conclusion)**
**Premises:**
1. **All banks are financial institutions.** ✅(True)
2. **Wells Fargo is a financial institution.** ✅(True)
**Conclusion:**
� **Wells Fargo is a bank.** ✅(True)
**Why is it invalid?**
- The **conclusion does not necessarily follow from the
premises**.
- Just because **all banks** are financial institutions does
**not** mean that **all financial institutions are banks**.
- Wells Fargo **could** be another type of financial institution
(like an insurance company).
- It is **possible** for the premises to be true while the
conclusion is false.
❌**Thus, the argument is invalid.**
--## **Key Takeaways**
### **1. Validity Does Not Depend on Truth**
- A valid argument can have **false premises and a false
conclusion**.
- A valid argument can have **true premises and a true
conclusion**.
- **Validity depends only on the structure of reasoning.**
### **2. The One Sure Test of Invalidity**
If an argument has:
✅**True premises**
❌**False conclusion**
� **It must be invalid!**
This is because **a deductive argument should never allow us
to move from truth to falsity**.
--## **Final Rule for Validity**
✔ **If the premises are true, the conclusion must be true →
VALID.**
❌**If the premises are true and the conclusion is false →
INVALID.**
Would you like me to provide more examples or clarify anything
further? �
This table provides a classification of deductive
arguments based on **validity**, **truth of premises and
conclusion**, and **soundness**. Let's break this down
step by step:
---
## **Key Definitions**
1. **Validity**: A deductive argument is valid if it is
**impossible** for the premises to be true and the
conclusion false. Validity is about the logical
structure, not the truth of the premises or conclusion.
2. **Soundness**: A deductive argument is sound if:
- It is valid, **and**
- All its premises are actually true.
3. **Unsound Argument**: If an argument is invalid or if
it has one or more false premises, it is unsound.
--## **How to Interpret the Table**
### **Row 1: True Premises, True Conclusion**
- **Valid and Sound Example**:
Premises:
1. All wines are beverages.
2. Chardonnay is a wine.
Conclusion: Therefore, Chardonnay is a beverage.
- The premises are true, and the conclusion follows
logically from them.
- The argument is valid and sound.
- **Invalid Example**:
Premises:
1. All wines are beverages.
2. Chardonnay is a beverage.
Conclusion: Therefore, Chardonnay is a wine.
- Even though the premises and conclusion are true,
the argument is invalid because the conclusion does not
logically follow from the premises.
--### **Row 2: True Premises, False Conclusion**
- **Valid Case Does Not Exist**:
- It is impossible for a deductive argument to have
true premises and a false conclusion while still being
valid.
- This is the core definition of invalidity.
- **Invalid Example**:
Premises:
1. All wines are beverages.
2. Ginger ale is a beverage.
Conclusion: Therefore, Ginger ale is a wine.
- Here, the premises are true, but the conclusion is
false.
- The argument is invalid because the premises do not
logically support the conclusion.
--### **Row 3: False Premises, True Conclusion**
- **Valid but Unsound Example**:
Premises:
1. All wines are soft drinks.
2. Ginger ale is a wine.
Conclusion: Therefore, Ginger ale is a soft drink.
- The premises are false, but if we assume them to be
true, the conclusion logically follows.
- The argument is valid but unsound because the
premises are false.
- **Invalid Example**:
Premises:
1. All wines are whiskeys.
2. Chardonnay is a whiskey.
Conclusion: Therefore, Chardonnay is a wine.
- The premises are false, and the conclusion does not
logically follow from the premises.
--### **Row 4: False Premises, False Conclusion**
- **Valid but Unsound Example**:
Premises:
1. All wines are whiskeys.
2. Ginger ale is a wine.
Conclusion: Therefore, Ginger ale is a whiskey.
- The premises are false, but if we assume them true,
the conclusion logically follows.
- The argument is valid but unsound because the
premises are false.
- **Invalid Example**:
Premises:
1. All wines are whiskeys.
2. Ginger ale is a whiskey.
Conclusion: Therefore, Ginger ale is a wine.
- Both premises and the conclusion are false, but the
premises do not logically support the conclusion.
- The argument is invalid and unsound.
--## **Summary**
1. **Valid arguments** preserve logical structure,
regardless of truth or falsity in premises and
conclusion.
2. **Sound arguments** require validity and true
premises.
3. **Invalid arguments** fail logical structure, making
it possible for premises to be true and conclusion
false.
--Would you like more examples or clarifications about any
specific row?