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Firstly, the fact that the ancestor relation cannot be defined in FOL is not itself a philosophical difficulty. It relates mainly to the issue of consistency and completeness and their omega counterparts over infinite domains. It hardly means that FOL is extremely limited. Your question could reasonably be split up into separate components. Why are ...


4

TL; DR Not according to Quine, and not according to common alternatives. However, while existence of relations is ruled out by Quine, one can reconcile PFL (predicate functor logic) with both existence and non-existence of relations on alternative views. Quine's criterion and PFL Quine's criterion, "to be is to be a value of a quantifiable variable"...


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In order for predicate functorese logic (PFL) to have the same expressiveness and utility of first order language (FOL) without ontic commitment of any objects as quantified bound variables suitable for ontological nihilists, the existence of primitive relations between objects have to be maintained in compositional predicates (functors) and in fact it's one ...


3

Potentially, you could be asking one of two different questions. One is how did our ability to do logic get started? i.e. a question about origins. The other is how do we consider logic to be grounded or justified? i.e. a question about the epistemology of logic. In the case of the former question, we really just don't know. We know from studies of animals ...


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You can see: Michael Dummett, Origins of Analytical Philosophy (1993). And see some fundamental statements from Russell: B.Russell, Our Knowledge of the External World (1914), page 26: "The topics we discussed [...] all reduce themselves, in so far as they are genuinely philosophical, to problems of logic. This is not due to any accident, but to the ...


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Let me add to the existing (very good) answers. First of all, there's an implicit assumption in your question that philosophical interest comes from strength. This is unjustified, especially given the general tradeoff between strength and tameness. Weaker logics correspond to simpler types of argument, and that might be a very interesting sort of thing in a ...


2

There's a point of view that topics of inquiry move out of the realm of philosophy and into the realm of science when they become codified, standardized, well-understood and reliable. In contrast, live philosophical topics are speculative, open-ended, dimly understood, and controversial, almost by definition. In other words, philosophers invent sciences, ...


2

Short Answer FOL is a simple model of human reasoning, and much like simple models in general, it is a pedagogical aid in introducing students to the formal aspects of logic without being unwieldy and overcomplicated. One, after all, could make the argument, why teach many formal logics since they are clearly a limited aspect of human reason itself which is ...


2

Logic is commonly, though not universally, understood as separating form from content. On this understanding, the form is the logical part, and is traditionally taken to be a priori, while the content is the empirical part. If we can completely and successfully separate the parts of a sentence that are formal from the parts that are not, then we have grounds ...


2

Any low temperature event is evidence of global cooling. This follows from what we mean by evidence. Of course, one such event is poor evidence. However, suppose the climate was in fact cooling, then we would probably at some point be able to witness many cold weather events. The frequency of these events would lead us to suspect and then to confirm the ...


2

We can only argue from subjective premises, as is apparent in the principle of logical argument. But this is not a problem for logic itself. Rather, logic is the solution. It is the solution to our human nature whereby we only know the values processed by our cognitive system, values presumably concerning the real world, rather than the real world itself. As ...


2

This is one of the horns of Munchausens trilemma. I would follow Hofstadter idea of 'tangled hierarchies' & strange loops, to say language and logic are systems within a looping hierarchy, with niether a fundamental grounding nor end point or final conclusions (final vocabulary). Instead, the whole system of system is verified by self-coherence, in ...


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This subject comes up quite a bit in different forms. Sometimes as the question, Is logical empirical? Or, What justification can be given for using logic? Or, Is logic subjective? There is a distinction between a particular system or calculus of logic, of which there are many, and speaking of 'logic' in a general sense. So, one should distinguish between ...


2

I believe that it is not so much a case of dialetheism rejecting a form of LNC, but rather a case of where LNC is applicable. For the dialetheist, the Liar sentence has a literal meaning, but it has no content. It does not express a proposition. They say, don’t be fooled by the phrase “This statement”. For example, “The number that is one less than itself”...


2

Suppose that B is "All five original Take That members are American", and X is "Robbie is American". There's an intuitive sense in which X does not add falsity to B, in that the content that X has that is false is part of the content of B. But if X was, say "Robbie and Mick Jagger are both American", then X would be adding ...


2

There is no perfectly expressive logic. Every logic powerful enough to include arithmetic is incomplete. Moreover, each one of those logics can be augmented by additional axioms to be more complete than it was - to yield more true theorems than it had. This means that you can always make a logic more complete, so there is no most complete one. However, ...


2

Regarding your "It seems to be a catch-all phrase that literally means just that, and includes but not limited to empirical factors.", it's correct as your reference clearly states: The idea is that it is possible to revise logical principles (or logical rules) on the basis of extra-logical considerations—which include empirical considerations. ...


2

Perhaps the main point of divergence (though still fundamentally a refinement of rather than a wholesale repudiation of Tarski's theory) in the analytic philosophy literature was provided by Saul Kripke in his Outline of a Theory of Truth. Kripke's main point was that our language winds up being prone to deep problems of paradoxes of self-reference in a ...


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Problem of consciousness and inexpressible Let's us first try to give definition of algorithmic mind. In a colloquial terms, algorithmic mind would be akin to a machine, it would perform certain strictly defined instructions according to a strictly defined rules. Starting from initial conditions (which in our case could be axioms) it would come to certain ...


1

Maybe we have to consider what Alfred Tarski is trying to achieve [ref. to the English edition of “Der Wahrheitsbegriff in den formalisierten Sprachen” (1935)]. The purpose is (page 154) to show the difficulties involved into the definition "of truth in the colloquial language". Tarski intorduce the well-know schema (page 155): x is a true ...


1

What is logic? In simple words, logic is a set of formal rules that seem to describe the behavior of the world. For example, if A=B and B=C, so, logically A=C. Such logical rule is just the formalization of a description of the world. What provides the "validity" to the content they write? Your own experience. Someone might state that A=B and B=...


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Your question is a topic in the philosophy of logic. A great deal has been written on it and there are many different points of view. You might like to read my answer to this related question. In broad-brush terms, some consider logic to be about conceptual relationships. Others, that it is concerned with what is a priori knowable. Others, with what is ...


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To keep things simple, think of logic as (ideally) the manipulation of symbols according to certain rules that are designed to maintain the self-consistency of class property relationships. 'Extra-logical' then, is anything that does not constitute a logical rule or the manipulation of symbols within the constraints of logical rules. Premises, assumptions, ...


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The passage you quote appears in the context of a discussion of what it means to speak of the subtraction of two propositions "A-B" when A implies B. A-B should have the property that when combined with B it yields A. One proposal is that A-B is the material implication B → A. Yablo rejects this because it gives the wrong result. It would make A-B ...


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B→¬X being true for a reason that can obtain even when B is true One might interpret this as follows. Say that X adds falsity to B, when there exists a set of true premises from which we can derive B→¬X, where the premises are not inconsistent with B. Edit: This set of premises ought to be further constrained, e.g. to be chosen as a subset of a fixed, ...


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What does "a priori" truly mean? To get at something so fundamental to thought, we must look at what is physically happening as you think. From a physical perspective, your brain's neurons have certain connection weights, which cause them to activate with varying intensity, and you make inferences and assertions as a result of these weights and ...


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Your question covers quite a range of issues. When we are just imagining possibilities, we can choose what to hold constant and what to consider a variable. In the example you give of imagining light travelling at 10 mph, we could imagine all the other laws and constants of physics remaining as they are. This is because as far as we currently know, the ...


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Short Answer Asking questions about flawed logic is firmly within the domain of the philosopy of logic. Arguments and conclusions drawn from them which seem logical, but are actually not are commonly known as fallacies. Long Answer What exactly is a fallacy? Well, that depends on one's theory of fallacy, and there are differences in perspective among ...


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The example you give (at least in the way you formulated it) doesn't make sense to me, because "Every class is easy" is obviously not valid in PL and neither does it allow for the deduction that "Philosophy is easy" without further axioms. What I imagine could be meant is that sentential logic is not powerful enough to formalize the ...


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Long comemnt The key point in Tarski'approach is in the clause: "apart from purely logical constants". The logical constants (aka: syncategorematic terms) are... constants: they are not "reinterpreted" when we change the interpretation of the signs: [they are not] affected by replacing the designations of the objects refereed to in these ...


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