#philosophy
#logic
#knowledge
#epistemology
#mathematic
[[Bertrand Russell]] summaries **Wittgenstein** detraction of human [[Language|language]] and [[Logic]]:
>First, there is the problem what actually occurs in our minds when we use [[Language|language]] with the intention of meaning something by it; this problem belongs to psychology. Secondly, there is the problem as to what is the relation subsisting between thoughts, words, or sentences, and that which they refer to or mean; this problem belongs to [[Epistemology|epistemology]]. Thirdly, there is the problem of using sentences so as to convey truth rather than falsehood; this belongs to the special sciences dealing with the subject-matter of the sentences in question. Fourthly, there is the question: what relation must one fact (such as a sentence) have to another in order to be capable of being a symbol for that other?
#to-digest
# Formalization
>For example, let $fx$ be a propositional function (i.e. a function whose values are propositions), such as **x is human**-then the various values of $fx$ form a set of propositions. We may extend the idea **not-p and not-q** so as to apply to simultaneous denial of all the propositions which are values of $fx$. In this way we arrive at the proposition which is ordinarily represented in mathematical logic by the words **fx is false for all values of x**. The negation of this would be the proposition **there is at least one x for which fx is true** which is represented by $(x). fx$. If we had started with $not-fx$ instead of $fx$ we should have arrived at the proposition **fx is true for all values of x** which is represented by $(x).fx$. ~ [[Bertrand Russell]]
```py
def f(x):
return f"{x} is human."
propositions = [
"Socrates",
"Plato",
"Aristotle",
"Jesus",
"Jeff Bezos"
]
import os
import openai
openai.api_key = os.getenv("OPENAI_API_KEY")
responses = [openai.Completion.create(
engine="davinci",
prompt=f"Proposition: {e}\nTruth:",
max_tokens=500,
stop=["\n"],
)["choices"][0]["text"] for e in propositions]
print("there is at least one x for which fx is true" if any(responses) \
else "fx is false for all values of x")
```