TonesInDeepFreeze

I did not intend to imply that you personally denied it. But rather that it should not be denied. You said what the extended reals are. I noted a qual...

I did. In fifth grade, the teacher showed a wall map of the acquisitions of U.S. territory. The map omitted the Gadsen Purchase and included it in the...

Doesn't have to be that. Could be just to choose any two mathematical objects that are not real numbers for +inf and -inf. For example, +inf = w ('w' ...

I'd cobble together some of my remarks here with some other stuff. Whatever I did, I would make clear that 'infinity' and 'infinite' are not be be con...

It is not required that the extension points have infinite cardinality.

I agree with the basics in your post. One technical point though: Yes, in many (probably most or even just about all) writings, the points of infinity...

That's a terrible excuse. One shouldn't initiate further study by first publishing a dictionary entry that conflates important concepts.

What does 'it' refer to there?

Yes, there are points of infinity on the extended real line. So if by 'infinities' we mean such points and others in different number systems and such...

.I'm looking at this again with a fresh start. First, we should put aside quibbles about (a) Anderson running as Independent and (b) the mistaken clai...

Anderson ran as Independent, but he was a Republican. It doesn't matter anyway, since we don't need to mention 'Republican', as we could just say 'Rea...

There might be something lurking in the notion of 'good reason' that has to do with degrees of good reason, which also relates to degrees of confidenc...

I'm not inclined to quibble with the givens of the problem or appeal to lack of certainty. That seems not to face the structure of the problem head on...

That seems right, of course. But from a different view, there is not a good reason to believe the conclusion, since there is an overwhelming better re...

To emphasize that point. The validity of modus ponens bears upon grounds for belief, but the validity of modus ponens can be (and often is) understood...

He said there is good reason to believe the premises, but not a reason to believe the conclusion. And that is true*. The part about "constituting" or ...

Yes, and I took account of that in followup posts. Actually, he mentions both 'good reason to believe' and 'reason to believe'. I would guess he didn'...

I wouldn't. I would say they are different predicates of the form: x is infinite & Rx.

I think there is something to what you say. But I don't know whether we need the notion of domains for it. She has good reason to believe she will rec...

When I first read the claim given by the author that Reagan was decisively ahead of Carter in polling, I felt something was wrong, but I let it slide....

'is infinte' can be qualified any way you can come up with a definition of your qualifier. is countably infinite is uncountaby infinite is infinte in ...

Suppose instead of "R v A" our second premise is "R v C". Then there's no puzzle. But why did we adopt "R v A"? Because Reagan looked bound to win. So...

The domain is {apple, orange, banana}. {apple, orange} is a subset of the domain. {apple orange"} is not a "space of assumptions". It is not a set of ...

I don't have a solution, but below is one way to lay out the problem by "brute force". In case it matters, we note that the text mentions both 'good r...

My criticism of the rants (those are not reviews) is independent of the books. What she said about logic is stupid, no matter what is in the books. I ...

That's pretty good. I like it.

They're not. They reveal fundamental misunderstanding, confusions, and ignorance of the writer.

I read both her posts. They're ignorant diatribes.

Based on the quote you provided, she seems not to understand what she read, thus remaining ignorant.

You just quoted her about the ill-effects of emotion in arguments. Your feelings about the books don't make her arguments about them sound.

I see your point. But I haven't been in disagreement. I don't dispute the author's argument about the modus ponens argument. My point is to be careful...

Sure, people err, and abuse even simple logic. And logic is often not simple. Thanks, I'll look at them out if I see them somewhere. Quotes below are ...

The conclusion is not valid. The conclusion is contingent. The modus ponens argument (R v A) -> (~R -> A) R v A therefore ~R -> A is valid. But the ar...

The argument as stated is not modus ponens. It injects a modal operator in front of the conclusion. But there is still a puzzle: Maybe I'll get time t...

Of course, but that doesn't address the puzzle.

That still breaks the form of modus ponens. 'we have deductive reasons to assert is' is intensional. If it were merely a flourishing touch, then we co...

How so? Which books are those?

What is your mathematical definition of 'infinites'? Unlike the odd numbers, there is no set of all infinite sets nor of all infintie cardinals. So wh...

One infinite set may be larger than another infinite set.

It's right. The quantities are the particular cardinalities. No cardinality itself is 'infinity'. Rather, each infinite cardinality has the property o...

'is infinite' is a predicate. a set is infinite iff it is not finite. 'infinity' as a name occurs as sometimes, such as points in the extended real sy...

This post is not addressed to any specific person. I am GrandMinnow. I hadn't gotten around to answering the above. Here is a model of "ExAy yex": <{0...

Its a good bet that, if you're not taking a class, then the best way to learn is from a good textbook. 'Logic: Techniques of Formal Reasoning' by Kali...

You gave examples of arguments that symbolic logic rules as invalid. That's not a problem for symbolic logic; it's only a problem for you if you think...

The problems are: (1) Your first example is not correct syntax, and even when corrected, it is irrelevant Maybe you meant: Ax(Dx -> Bx) Ax(Cx -> Bx) t...

Of course, that argument establishes its conclusion only if the premises themselves are established. I don't see a problem.

I take it that you intend (4) as a conclusion from the premises above it. I don't know what you mean by "space of interpretations that excludes". It w...

C <-> ~(R v A) is a given ~ R -> (C v A) is a given C <-> ~A is a given Lets' say: ~R -> C is a given Then: (R v A) -> (~R -> A) (R v A) therefore (~R...

No, it's: (R v A) -> (~R -> A) (R v A) therefore ~R -> A

But the author might argue this: If modus ponens is valid, then if we believe the premises, then we believe the conclusion (not always in fact - peopl...