Proposition: I have hazel eyes.

Truth Value: True

Truth Conditions: For this to be true, I would need to have hazel eyes.

Entailment: “I have hazel eyes” entails that I have hazel colored eyes.

Proposition: I have a divers license.

Truth value: false

Truth Conditions: For this to be true, I would need to have a drivers license.

Entailment: “I have a drivers license” entails that I have a drivers license.

Proposition: There are other planets with life forms.

Truth Value: Unknown

Truth Conditions: For this to be true, there would have to be other planets that have existing life forms.

Entailment: “There are other planets with life forms” entails that life can be sustained on other planets.

1. Proposition: I have black hair

Truth value: False

Truth conditions: For this to be true, I would need to have black hair.

Entailment: “I have black hair” entails that the color of my hair is black.

2. Proposition: There are giant sea creatures living in unexplored parts of the ocean.

Truth value: Unknown

Truth conditions: In order for this to be true, there would have to be giant sea creatures living in unexplored parts of the ocean.

Entailment: “There are giant sea creatures living in unexplored parts of the ocean” entails that there are parts of the ocean not yet investigated and massive marine animals live there.

3. Proposition: I have Arachnophobia

Truth value: True

Truth conditions: For this to be true, when I see a spider my heart rate would increase, and I would start to panic.

Entailment: “I have Arachnophobia” entails that I have an intense fear of spiders.

1)Proposition: I have globophobia 

Truth value: True 

Truth conditions: For this to be true, I need to be anxious when a balloon is around me.

Entailment: “I have Globophobia” entails “ I am fearful around balloons”

2)Proposition: all cats are reptiles

Truth value: false

Truth conditions: cats would have to be reptiles, not mammals 

Entailment: “All cats are reptiles” entails “some reptiles can purr”

3)Proposition: An undiscovered flower only blooms at midnight, in the Amazon forest

Truth value: Unknown

Truth condition: For this to be true there should be evidence of such a flower.

Entailment:” An undiscovered flower only blooms at midnight, in the Amazon forest” entails “biodiversity in the Amazon forest is not fully documented”

1. Proposition: There is a black hole at the center of our galaxy, the Milky Way.

Truth value: True.

Truth conditions: This proposition is true if there exists a supermassive black hole located at the center of the Milky Way galaxy.

Entailment: “There is a black hole at the center of our galaxy, the Milky Way” entails “The Milky Way galaxy harbors a supermassive black hole.”

2. Proposition: There are no planets outside our solar system that can support life.

Truth value: False.

Truth conditions: This proposition would be true only if it were impossible for any exoplanets beyond our solar system to support life, which is currently unknown.

Entailment: “There are no planets outside our solar system that can support life” entails “If it’s a planet outside our solar system, then it can’t support life.”

3. Proposition: There exists a rogue planet wandering the depths of interstellar space.

Truth value: Unknown.

Truth conditions: For this proposition to be true, there must be at least one planet not gravitationally bound to any star, roaming through interstellar space.

Entailment: “There exists a rogue planet wandering the depths of interstellar space” would entail “Planets can exist without orbiting a star.”

As we learned in class recently, propositions are claims expressed by a sentence, which either are true or false. Each proposition has a truth value, which is whether a statement has a true or false choice. This ties in with truth conditions, which are the conditions the world would be in for a proposition to be true. Lastly, entailment relates to two statements, where one implies the other. Three examples of all of these aspects of a proposition are shown below.

1) Proposition- There was an earthquake in New York City on April 5th 2024. Truth value- True Truth conditions- In order for this to be true, an earthquake would have had to take place in New York on that exact date. Entailment- “There was an earthquake in New York City on April 5th 2024” entails “An earthquake took place on April 5th somewhere in the world”

2) Proposition- I have two sisters Truth value- False Truth conditions- I would have to have exactly two sisters in my immediate family. Entailment- “I have two sisters” entails “I have at least one sister”

3) Proposition- More people drink coffee compared to tea. Truth value- Unknown Truth conditions- A valid scientific study would have to be conducted to show that a majority of people favor coffee. Entailment- “Most people drink coffee compared to tea” entails “People can drink coffee and tea”