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What are free variables and what does it mean for a statement to contain one?

I am puzzled a bit. I read the wiki page and an introductory book on logics, but I can't quite grasp it yet. The place where i came across them is Van Inwagens 'Material Beings'. Consider the following three sentences: (1) x=x (2) …
Lukas
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Why in the academic fields of art and design, the philosophy taught or mentioned is often Continental philosophy?

Is there any rationale to prefer, in academic fields of art, Continental philosophy over Analytic philosophy? I guess there might be a historical reason why philosophy evolved into two approaches but why I do not hear in my art studies anything…
Luna
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Is faith required to believe any axiomatic assumption the scientific method is built upon?

It's my understanding that the scientific method builds upon certain axiomatic assumptions, such as uniformitarianism and the principle of induction. Is faith required to believe these axiomatic assumptions?
user48437
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What is the name behind the concept of believing in God based on this logical deduction?

From my memories, there is a well defined definition / concept / name for the following: A scientist chose to believe in the Christian God because of the following logic: If God does exist, then you may have a chance to go to heaven If God does not…
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Is free will compatible with determinism? (Ramsey theorem)

Do we have free will? Or everything is already determined? Are they mutually exclusive? I think they can coexist and have something similar to a proof here and would like to know your thought There is a theorem in math which is called Ramsey Theory.…
navid
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What would you call a counterfactual theory of Justified True Belief?

Ever since I heard the characterization of knowledge as justified true belief, the proper meaning of the word "justified" has always seemed clear to me: it should mean that you acquired the belief in such a way that you would not have acquired it if…
Keshav Srinivasan
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Is the idea of a causal chain physical (or even scientific)?

I am aware that the idea is venerable, going back through Lucretius to the Stoics and Epicurus, and even to Aristotle with his prime mover argument. But isn't this a pre-scientific notion? The Atomists thought that collisions cause motion. But…
Willie Betmore
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Which if any contemporary philosophers have written about the potential negative effects of "reverse" discrimination?

In many cases when I talk about how I think, I find it useful to abstract the messy real sources of inspiration into a pure dialogue with my friend Matt. In this case, Matt and I were talking about entrance requirements into college and the practice…
davidlowryduda
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Does there exist a "valid" application of Gödel's incompleteness to "logical natural language statements"?

Does there exist a "valid" application of Gödel's incompleteness to "logical natural language statements"? It can be found to sometimes be naively applied that way, even when the incompleteness theorems are a specific application. But I find it…
mavavilj
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What does "I" really mean?

When we refer to a human being by "I"/"you"/"he"/"she"/"Mary", what do we really mean? The more I think about it, the more confused I get. Do we mean living body or emotional/psychological world or mind? Or do we mean integrity of all of the…
fiktor
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What is the utility of consciousness if free will is an illusion?

Introspectively speaking, it seems to me obvious that free will is illusion. Thoughts just emerge from background causes, and actions are just thoughts about actions that we have more thoughts about committing to bringing into being (more or less…
natojato
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what are the limits of rigid designation?

There is a gnome in my garden, which I've christened 'Barack Obama'. (This is the plaster-of-paris sort, not a fictional one.) Is there a possible world in which the two swap? What does Kripke say? Surely rigid designators do not just apply to men…
Mozibur Ullah
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Can we dispense with ontology in physics?

Is it possible to have a satisfactory physics which is content to describe everything in terms of operational (functional) properties? Could it therefore be the case that ontology is a useless concept leading us down a philosophical rabbit hole to…
Andrew Palfreyman
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Are there philosophers who examined the reasons for believing in the existence of other people?

While I am familiar with Descartes and the oft-quoted idea, I think therefore I am, I am not familiar with any philosophy that actively sought to rationalize that anybody else exists. Are there philosophers who analyzed this question? Or is it taken…
davidlowryduda
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Does mathematics always need axioms?

To do mathematics, one obviously needs definitions; but, do we always need axioms? I was thinking that a statement like For all prime numbers, there exists a strictly greater prime number. cannot be demonstrated computationally, because we'd need…
goblin GONE
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