PHILOSOPHY - Language: Conditionals #3 [HD]

TL;DR

Strict conditionals express necessary connections but face similar issues as material conditionals.

Transcript

(intro music) Hello, my name is Justin Khoo and I'm an assistant professor[br]of philosophy at MIT. This is the third part of[br]our series on conditionals. Last time, we saw a classic problem with the material conditional theory. It predicts that it's just too easy for conditionals to be true. Recall Mitt Romney's conditional, (1): "If the safety ... Read More

Key Insights

• The strict conditional theory suggests that conditionals express necessary connections between their antecedents and consequents, unlike the material conditional theory.
• According to Peirce's strict conditional theory, a conditional is true if it's impossible for the antecedent to be true and the consequent false.
• Strict conditionals use modal terms like 'must', 'have to', and 'impossible' to express necessary truths beyond actual facts.
• The strict conditional theory offers a solution to the material conditional theory's issue of making conditionals too easily true.
• Despite its strengths, the strict conditional theory encounters problems with conditionals that have impossible antecedents.
• An example is Goldbach's conjecture, where a conditional with an impossible antecedent is wrongly predicted to be true by the strict theory.
• Both strict and material conditional theories struggle with conditionals involving false or impossible antecedents.
• A new approach may be needed for conditionals, viewing them not as categorical claims with fixed truth values when antecedents are false.

Questions & Answers

Q: What is the strict conditional theory?

The strict conditional theory, attributed to Charles Sanders Peirce, posits that conditionals express necessary connections between their antecedents and consequents. It suggests that a conditional is true if it is impossible for the antecedent to be true and the consequent to be false. This theory uses modal terms like 'must', 'have to', and 'impossible' to convey these necessary truths.

Q: How does the strict conditional theory differ from the material conditional theory?

The strict conditional theory differs from the material conditional theory by requiring a necessary connection between the antecedent and consequent for a conditional to be true. While the material conditional theory makes conditionals too easily true, the strict theory demands that it be impossible for the antecedent to be true and the consequent false, thus preventing the same ease of truth.

Q: What problem does the strict conditional theory face?

The strict conditional theory faces a problem with conditionals that have impossible antecedents. It predicts that such conditionals are true because it is impossible for the antecedent to be true and the consequent false. This leads to incorrect predictions, as illustrated by examples like Goldbach's conjecture, where the connection between antecedent and consequent is non-existent.

Q: Why is Goldbach's conjecture problematic for the strict conditional theory?

Goldbach's conjecture is problematic for the strict conditional theory because it has an impossible antecedent. If the conjecture is false, the theory incorrectly predicts that a conditional involving it is true, as it is impossible for the conjecture to be true and the consequent false. This highlights the theory's flaw with impossible antecedents.

Q: What are modals in the context of strict conditionals?

In the context of strict conditionals, modals are words like 'must', 'have to', 'impossible', and 'possible' that express claims about how things could have been, even if they didn't actually happen that way. They are used to convey the necessary connections between antecedents and consequents in strict conditionals, beyond mere actualities.

Q: How does the strict conditional theory address the material conditional theory's problems?

The strict conditional theory addresses the material conditional theory's problems by introducing a requirement for a necessary connection between antecedents and consequents. This prevents conditionals from being too easily true, as the material theory allows, by ensuring that it is impossible for the antecedent to be true and the consequent false.

Q: What insight might lead to a new approach to conditionals?

The insight that both strict and material conditional theories struggle with conditionals involving false or impossible antecedents suggests a need for a new approach. This new perspective would likely involve viewing conditionals not as categorical claims with fixed truth values when antecedents are false, but rather in a more nuanced manner.

Q: What does the video suggest about the future study of conditionals?

The video suggests that the future study of conditionals may require a radical new way of thinking, as both the strict and material conditional theories face similar issues with false or impossible antecedents. This indicates a potential shift away from viewing conditionals as categorical claims with well-defined truth values in such situations.

Summary & Key Takeaways

• The strict conditional theory posits that conditionals express necessary connections between antecedents and consequents, avoiding the material conditional theory's issue of making conditionals too easily true. However, it faces similar challenges with conditionals having impossible antecedents, suggesting a need for a new approach.

• Peirce's strict conditional theory uses modal terms to express necessary truths beyond actual facts. It suggests that a conditional is true if it's impossible for the antecedent to be true and the consequent false, offering a solution to issues faced by the material conditional theory.

• While the strict conditional theory marks an advancement over the material conditional theory, it encounters problems with false or impossible antecedents, as illustrated by Goldbach's conjecture. This parallel issue in both theories indicates the potential need for a radical new way of thinking about conditionals.