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12 votes
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Are "if smoke then fire" arguments deductive or inductive?

Such inferences are neither deductive (which assumes application of a valid inference rule) nor inductive (which assumes a generalization from a pattern of cases). This type of inference is called ...
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10 votes

How far can/should one press philosophical doubt?

Descartes was the modern founder of what is called foundationalism about knowledge, the idea that we must find a secure self-evident ground from which all the rest of our knowledge can be justified. ...
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8 votes

Are "if smoke then fire" arguments deductive or inductive?

If the question is raised in an intro to philosophy course (like critical thinking or scientific reasoning), the answer should be that the above inference is an example of inductive logic. There are ...
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6 votes
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What is the relation between 'knowledge-that' and 'knowledge-how'?

The unit of knowledge-that is proposition, expressed linguistically in declarative sentences, the unit of knowledge-how is skill. The use of "knowledge" here refers to non-propositional uses like "...
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6 votes

Are concepts necessarily false even if useful?

I think you need to distinguish between "concepts" in general and the specific type of concept you raise here, models. Models are useful simplification of mechanisms. They are not "false," they just ...
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5 votes

Origin of Charles Sander Peirce's model of triadic signs diagram?

Peirce' Theory of Signs is complex and - unfortunately - there are no complete treatises dedicated to semiotics by Peirce himself : Across the course of his intellectual life, Peirce continually ...
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5 votes

Peirce's law, law of the excluded middle, and intuitionism.

For the first part : (P ∨ ¬ P) ⊢ [((P→Q)→P)→P] we can prove it using the following axiom system for (propositional) Intuitionistic logic and modus ponens. Proof 1) P --- assumed 2) ((P→Q)→P)→P -...
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5 votes

Is there any reason for the heavy focus on binary relations in formal logic?

This is an important question and you make a number of points worth thinking about more deeply. I offer the following not as an answer, but as a formal prelude to more worthy answers. We start with ...
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4 votes
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What are the similarities/differences between how Kant thinks 'noumenon' limits understanding compared to C.S. Peirce?

Interpretation of Peirce's realism which grew out of combining Kantian epistemology with scholastic ontology of Duns Scotus (Peirce calls himself "a scholastic realist of a somewhat extreme ...
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4 votes

Is Peirce's pragmatic maxim self-evident?

Not exactly. Peirce himself considered it a distillation of "common sense", but he offered it as an alternative to the then dominant Cartesian foundationalism. Many disputed the pragmatic ...
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3 votes
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What would be an intuitive understanding of Peirce's law?

Peirce himself notes that this is hardly "axiomatical", i.e. self-evident. But it helps to convert implications into derivations. Then (P→Q)→P becomes P→Q ⊢ P, which is obviously invalid because it is ...
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3 votes

Derive |- [(P>Q)>P]>P using only primitive rules

Here is one way to show this using modus tollens (MT), contradiction introduction (⊥I), explosion (X), conditional introduction (→I) and indirect proof (IP). For context, what you are trying to show ...
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2 votes

Peirce's law, law of the excluded middle, and intuitionism.

You have two questions here, which don't really relate to each other. It may be worth asking two seperate ones. I'll answer the first here. Pierces law states: ((p implies q) implies p) implies p ...
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2 votes

What are the main differences between Peirce, James, & Dewey?

James and Dewey were students of Peirce. Peirce opposed their pragmatism to such a degree that he thought it necessary to term his original pragmatism "pragmaticism," distinguishing it from their ...
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2 votes

Origin of Charles Sander Peirce's model of triadic signs diagram?

Peirce invented the so-called "existential graphs". A good description of this is found in §4.7 "The geometry of thought: Existential graphs" (pp. 69-72) of Peirce: A Guide for the Perplexed by ...
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2 votes

Is Peirce's pragmatic maxim self-evident?

Is what self-evident about this pragmatic maxim? For example, is it self-evident that it has a flaw? For instance, consider the difference between these two presentations: Consider what effects, ...
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2 votes

How far can/should one press philosophical doubt?

Should we keep on questioning until nothing is left to question or is there a point on which we need to stand (which we often tend to do). Descartes used 'I think' as this fixed point, there may be ...
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2 votes

What did evolutionary epistemology discover about our tendency to guess right abductively?

Alas, this is something that modern cognitive scientists concluded Peirce was overly optimistic about, there is no unified faculty of "guessing right" that he supposed. Heuristic guessing in ...
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2 votes
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Why can one abstract (prescind) space from color but not color from space? (from C. S. Peirce's article "On a New List of Categories")

Why can one abstract space from colour but not colour from space? Colour is extensive and hence presupposes space and hence we can abstract space from colour. But space does not presuppose colour. A ...
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2 votes

Why can one abstract (prescind) space from color but not color from space? (from C. S. Peirce's article "On a New List of Categories")

As defined in the passage, prescision "arises from attention to one element and neglect of the other", where "exclusive attention consists in a definite conception or supposition of one ...
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1 vote

What did C. S. Peirce mean by this remark about the phrase "necessary and sufficient condition"?

As far as I can make out, Peirce is saying that necessary and sufficient condition is doubly tautological. Firstly because condition implies that it's required and doesn't just follow on i.e. isn't ...
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1 vote

What did C. S. Peirce mean by this remark about the phrase "necessary and sufficient condition"?

Peirce seems to be saying is that the phrase "indecomposable element" seems redundant because an element by definition is something that is "indecomposible" (at least in some respect).* Similarly ...
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1 vote

How far can/should one press philosophical doubt?

Yes, we should question everything. Just not all at once. That, according to a central strand in modern philosophy, for which Descartes himself has been a guiding example. Descartes's so called fixed ...
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1 vote

Origin of Charles Sander Peirce's model of triadic signs diagram?

It's not the Charles Key Ogden & Ivor Armstrong Richards diagram, that uses the terms Symbol, Thought or Reference and Referent and there is no indication of Semiosis. I think I may have ...
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1 vote

Is there any reason for the heavy focus on binary relations in formal logic?

I'd suggest its due to history, and ease of use. The first mathematical operations we are exposed to (beyond counting) is addition & multiplcation. Here a sum such as 5+6+12+14 can be decomposed ...
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1 vote

Is there any reason for the heavy focus on binary relations in formal logic?

I work in the field of fine art shipping, and clients often ask me how much it will cost to ship a certain artwork and then give me two dimensions. I try to suggest as gently as possible that, ...
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