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Hi! Tarski's World is a program that consists of two file types: .wld and .sen. Think about it this way: When you want to save a Word file or you want to save an Excel file, the extension is different for each, which tells the computer what type of program to use when you reopen them. Does that make sense?

Hi, @v_isforvictory9366. Short answer: No! It is imperative that, in addition to understanding concepts, you practice to develop the associated skills. Think of studying logic the way you'd think about studying playing a musical instrument, a sport, working out -- anything that involves practice to improve!

Hi, @nothingmatters321. Thanks for writing. I apologize for the delayed response! OK, so here are a couple of examples to pump the idea that the actual truth value of the sentences in a valid argument are not relevant to the assessment of validity: 1) Since a=b, and b=c, it follows that a=c. 2) The moon is made of blue cheese or green cheese. Since the moon is not made of blue cheese, it follows that it's made of green cheese. In example #1, we don't know the values of the premises. We infer the conclusion on the basis of a, b, and c representing the same thing in each iteration. In other words, "a" does not stand in the first instance for "Alysha," and in the second instance for "Ahmad." Moreover, the symbol, =, is understood as "is identical with/to." Despite not knowing if the sentences, a=b and b=c are true or false, we know that IF the sentences are true, the conclusion MUST be true. In example #2, we know that the first sentence is false, i.e., it's not the case that the moon is made of blue or green cheese. We also know that the conclusion, the moon is made of green cheese, is false. Again, however, IF both premises are true, the conclusion must be true, on pain of contradiction. The argument is valid because of its form, not its content. We could replace the content as follows: Either California is in the eastern United States or California is in the western United States. It's not the case that California is in the eastern United States. So, California is in the western United States. Notice in the California argument, all the sentences are true -- premises and conclusion. That fact is not what guarantees the truth of the conclusion... Does that help a bit? Thanks! -Mia

Sure thing, Sara! Let me know if you have any questions. I’m here to help! -Mia

Thanks, Dr. K! I need to work on making more short videos to keep up with the explainer method, which seems to be quite helpful to many. -Mia

@@SymbolicLogicLPL What is the explainer method?

Literally

Sure thing, @andredejager3637! Thanks for writing!

Mine too :(

Hi, @fulufheloramudzwagi4551. Ah! So, we can convert the subject and predicate positions of a universal negative sentence because the move results in a logical equivalence: No S are P <=> No P are S. So, "No cats are dogs" <=> "No dogs are cats".

@@miawood8517 Thanks, I was supposed to remove my comment. I got it wrong, you are correct, Prof! Your videos are really helpful👋🏼.

Hi, DavidMrKidcolombia95! I apologize for the delayed response. The end of the academic year is always hectic! OK, so it might be useful to abstract from the content of the sentence, so that you focus on the structure. Yes, the sentence after “if” is claimed to guarantee what comes after “then.” It is said to be sufficient (though it may not be). Some sufficient conditions are conventional (e.g., “If you work 40 hours a week, then you work full time”). The reason I make the point about conventional conditions is to highlight what’s claimed (as opposed to what we believe is objectively the case, as in independently of whatever is stipulated). Suppose I claim that oxygen is sufficient for fire (“If there is oxygen, there is fire.”). You’d tell me I’m wrong, and you’d only have to point out one instance where there is oxygen but no fire. So, I’ve erroneously claimed that the presence of oxygen guarantees fire, but that doesn’t change the structure of the sentence. Now let’s look at what happens when we affirm the consequent, as you did above: If I live in LA, then I live in California. I live in California. So, I live in LA. This is a formal fallacy known as affirming the consequent. We might better understand the meaning of a necessary condition when we DENY the consequent (the argument form known as modus tollens): If I live in LA, then I live in California. I don’t live in California. So, I don’t live in LA. The necessary condition is what must be the case, or without which, some other event does not obtain: If I eat a potato chip, I have something my stomach. I don’t have anything in my stomach. So, I didn’t eat a potato chip. If I have 10 pennies, I have 10 cents. I don’t have 10 cents. So, I don’t have 10 pennies. Since the sufficient condition is said to be a GUARANTEE of the consequent (the necessary condition), when the necessary condition does not obtain, there can’t have been (I’m using temporal terms to push the point) the sufficient condition. So now let’s go back to simply switching the places of the antecedent and consequent: If ANTECEDENT, then CONSEQUENT, or If A then C. To assert, If C then A is incorrect, i.e., we know the mere swap doesn’t work. (Here’s a logical analog: We can’t say that, for example, “All dogs are animals,” is equivalent to “All animals are dogs.”) But we can negate each, which should make more sense now that we’ve discussed modus tollens/denying the consequent: If A then C is equivalent to If not C then not A: “If you live in LA, then you live in California,” is equivalent to “If you don’t live in California, then you don’t live in L.A.” (There is a Los Angeles in another country, but let’s suppose we’ve stipulated otherwise.) I hope this helps!

Hi, Alfred. Ack! Sorry about that. I'll address the issue ASAP! -Mia

Hmm, yes. Even with the volume set to high, my voice is pitched low or something. I'll redo the audio ASAP. One thing you might try is the captions -- they're not perfect, but they at least offset the volume issue.

Hi, Alfred. Ack! Sorry about that. I'll address the issue ASAP! -Mia

But there are nicely explained

@@preciousachebbs1115 Oh, no! Let's see if we can clarify. First, can you tell me if you're comfortable explaining the rules? Second, are you more comfortable with Venn diagrams or the rules? Third, how comfortable are you with the concept of validity? Don't worry, Precious! You can do this! -Mia

HI, Amish Skincare! I'm glad you found the video helpful. -Mia

No problem, CcA! FYI, if you are registered at www.gradegrinder.net/, you can access videos made by the authors. If not, you might check out a free online course hosted by the authors: online.stanford.edu/courses/sohs-xlpl-sp-language-proof-and-logic. I mention all this because more resources are always helpful! -Mia

@@SymbolicLogicLPL wow thank you so much. What a great resource of help you are! I just enrolled in a symbolic logic course and we are using LPL. Thanks a ton!!

Hi, Ahmadreza! I apologize for the delayed response. OK, so the subject of a singular sentence, such as "John is happy," is not itself a class, as is, e.g., "dog." So, my understanding is that singular sentences are not included in Aristotle's syllogistic system (and also not in immediate inferences). That said, if we consider the fact that Aristotle thinks affirmative quantified sentences have existential import -- there is at least one member of the subject class -- then, at least as far as universal claims go, 'John' is included. Particular claims, however, are tricker. Asserting "Some people are happy people," does not necessarily include John. One way to effectively subsume the subject of a singular proposition into a universal is to include identity, e.g., "All people identical with John are happy people." I hope that helps a bit. Great question! -Mia

@@SymbolicLogicLPL Thank you so much for your answer and insights. The comments were very useful.