Jul
22
awarded  Nice Answer
Feb
16
comment Is infinite regress of causation possible? Is infinite regress of causation necessary?
@PeterJ: If you agree about the usefulness of premisses, then what are the premisses, and the logical rules of inference which you use, to conclude that infinite causal chains are illogical?
Feb
15
comment Is infinite regress of causation possible? Is infinite regress of causation necessary?
@PeterJ: You and I have different concepts of what 'logic' is. Perhaps you mean 'a sound line of argument starting from some obvious premises'. To me, 'logic' on its own is the machinery of that argument, not the argument itself; and without the 'input' of the 'obvious premises', logic has nothing to operate on. You need more than just logic; you need the premises on which the logic is to act.
Feb
8
awarded  Good Question
2018
Nov
22
awarded  Good Answer
Oct
15
awarded  Nice Question
Oct
9
awarded  Famous Question
Oct
4
awarded  Famous Question
Sep
17
awarded  Nice Answer
Sep
16
comment What is the correct, pragmatic, reasoning response to conspiracy theories?
@DavidBlomstrom: you seem not to have caught on that I'm not just talking about conspiracy, or even mostly about conspiracy. The whole point of my post is in fact that the world is complicated enough that we have to tend to the means by which we learn and teach things. But then, if you think that the world is not really complicated enough that this could ever be a concern, this could be a perfectly good alternative reason to downvote my post, and indeed to do so without reading it.
Sep
5
awarded  Yearling
May
23
comment What formal logical systems “resolve” the Liar Paradox?
@SigurdVojnov: The paradox is as most paradoxes are: that we have a situation that appears to produce a result which is not intelligible. In fact, many paradoxes are presented as though they are logical contradictions, though they mostly turn out to be logical contradictions only as a result of inferences from somewhat rigid premisses. TO deduce a logical contradiction is then usually considered an indication of a paradox: that some set of 'intuitive' premisses is in fact logically inconsistent. The Liar Paradox is such a contradiction, but perhaps a meta-logical one.
Apr
8
awarded  Famous Question
Feb
24
awarded  Popular Question
Feb
22
comment Does mathematics always need axioms?
@possibleWorld: I would, indeed, count suitably formulated inference rules as 'principles equivalent to axioms'. The division between an axiom and a rule of inference is only conventional: a formal system consists of a sequence of allowed moves by the explorer, such as reference to some principle, or a manoeuvre which can produce similar by-products as such a reference. In either case what matters is what collections/sequences of propositions can be reached. --- The usual distinction is introduced, I think, for the purpose of considering general-purpose (unspecialised) inference systems.
Jan
16
comment Is infinite regress of causation possible? Is infinite regress of causation necessary?
@PeterJ: I sympathise with aspects of that idea, but it appears to apply equally well to finite chains of causation as well --- one can always simply accept a state of affairs rather than enquire. Rather, for both finite and infinite chains of causation, the notion of causation itself is asking after regularities which makes every small part of the chain comprehensible in terms of patterns which also apply in other circumstances.
2017
Nov
6
comment Can something be actually possible yet logically impossible?
@PeterJ: That proposition certainly would be debatable, and as a matter of fact I would not usually assert such a thing without the first, qualifying, part of the sentence.
Nov
3
comment Can something be actually possible yet logically impossible?
@PeterJ: The question itself was a misunderstanding, in my opinion, and I was merely attempting to answer it on its own terms. It is not clear how something can be logically impossible without this being a consequence of rules of inference and axioms; and should it prove to be actually possible, this should meta-logically imply something about the relation of the rules of inference or axioms to reality. This seems true to me even exotic varieties of logic, though they more often embrace exotic possibilities (e.g. that of both a proposition and its negation) than exotic impossibilities.
Sep
5
awarded  Yearling
Aug
1
comment Motivations for dialetheism?
Once I would want to start reasoning about apparently contradictory utterances in the way you describe, I would want to provide a framework which explicitly allows for the difference in interpretation. Let R="It is raining": for your two utterances I might write C(R) & D(¬R), where C and D stand in for two contexts through which the two utterances are to be interpreted (different locations, times, definition of 'rain', etc). But just because the utterances differ by a negation, doesn't mean that the semantics also differ by a negation: C(R) & D(¬R) is not the same as C(R) & ¬C(R).