An Argument for the Impossibility of Omniscience

In his work God and Evidence: Problems for Theistic Philosophers, Rob Lovering presents an argument for the impossibility of omniscience.

This particular argument rests on the distinction between propositional knowledge (knowledge that p) and experiential knowledge (knowledge of what it is like to x), a seemingly uncontroversial distinction.

Assuming that the distinction is justified, the argument proceeds as follows. One can differentiate between omniscience (complete, unfettered knowledge) with regard to either type of knowledge: a ‘propositionally omniscient’ entity knows all propositional knowledge, while an ‘experientially omniscient entity’ knows all experiential knowledge. A reasonable thought is that an entity isn’t fully omniscient unless it is both propositionally and experientially omniscient. Yet, no entity can be as such because necessarily, an entity that is propositionally omniscient is not experientially omniscient. This is because an experientially omniscient entity will know what it is like not to know that (‘p’ being a variable for any proposition we like), while a propositionally omniscient entity will know that and thus not know what it is like not to know that p.

Formally construed, the argument might look something like this:

1. (x) [Rx–>(Px & Ex)]
2. (x) [Ex–>~Px]
3. Rg –> (Eg & Pg)   [1, UI]
4. Eg –> ~Pg   [2, UI]
5. ~Eg V ~Pg   [4, material implication]
6. ~(Eg & Pg)   [5, DeM]
7. ~Rg   [6,3, MT]

8. (x) ~Rx [7, UG]

Where R=robustly omniscient (or, ‘fully’ omniscient), P=propositionally omniscient, E=experientially omniscient, and where g=god (though we could plug in any letter we like; the point is to instantiate the variable, use the rules of propositional logic to deduce some things, then generalize back into quantified form, which is what we do to reach premise (8))

Here are a few ways to address the argument:

A. Deny premise (1). Denying premise (1) amounts to denying the posited definition of full omniscience. “That isn’t what it is to be fully omniscient,” we might say. This is engaging in semantics — not necessarily a bad thing — since we will presumably supplant the definition of omniscience in (1) with a different one more to our liking, i.e., we will define the expression such that at least one entity can be fully omniscient.

B. Deny premise (2). This entails insisting that an entity can be both experientially and propositionally omniscient, which in this context amounts to denying that an entity that knows that p can’t also know what it is like not to know that p This may be done in a variety of ways. One way is to indicate that an entity can acquire omniscience by acquiring the knowledge of what it is like not to know that for any proposition, then acquiring the knowledge that p, thereby achieving omniscience (since the knowledge of what it is like not to know will presume remain even once one learns that p).

This particular solution won’t be to most theist’s liking, since their god is typically posited as having been timelessly omniscient, or, as having never not been omniscient. But there are strategies available — one imagines that an entity capable of creating the universe might somehow be able to decipher the knowledge of what it is like not to know that without thereby ever not knowing that p.

C. Accept the argument’s soundness; shrug shoulders. It’s not clear what the import of the argument is in a theological context, other than to deny the possibility of a maximally omniscient (in the sense defined above) god. A fair question to ask at this point is, so what if a god is propositionally omniscient but not quite experientially omniscient? What is the significance of this for theologically minded persons?

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Hilary Putnam – “Meaning and Reference” Article Summary

Putnam, Hilary ‘Meaning and Reference,’ The Journal of Philosophy 70: 19, (1973): 699-711.


Putnam seeks to undermine two doctrines of standard semantic theory (“theory of meaning,” in a broad sense) via the use of a thought experiment. The doctrines are: one, that intension (‘meaning’, more or less) determines extension (‘reference’, more or less) and in fact is always sufficient for doing so (such that two terms with the same intension must have the same extension); and, two, that intensions are concepts and thus psychological entities (such that two persons in the same psychological state must be grasping the same extension with regards to a term they both use). After presenting his thought experiment, Putnam presents an alternative thesis to explain how groups of speakers utilize intensions if not as psychological entities that fix extension, and argues that his view necessitates that natural kind terms (e.g., ‘water’ or ‘gold’) are rigid designators.

Putnam asks us to consider a world called ‘Twin Earth’ which is exactly similar to Earth – including in the languages spoken, physical properties exhibited by all things, and so forth – except that on Twin Earth, the liquid called ‘water’ isn’t H20, but rather is a molecule with a complicated chemical formula, abbreviated ‘XYZ’. XYZ functions just as H20 does on Earth, occupying the same space and exhibiting all the same physical properties. In other
words, the average resident of either planet would not be able to distinguish H20 from XYZ.

Putnam then modifies the thought experiment such that it becomes a counterexample to the notion that the doctrines can be jointly maintained: Putnam asks us to consider speakers on Earth and Twin Earth that existed before either planet’s scientific communities determined the precise molecular formula for water (on Earth) and ‘water’ (on Twin Earth). Such speakers will stand in the exact same psychological relation to the liquid they call ‘water’ (since the sole dissimilarity between Earth and Twin Earth – the fact that water is H20 and ‘water’ XYZ – is unknown to the speakers), despite the fact that in either instance a different liquid is under consideration. Thus, two persons in the same psychological state nonetheless are grasping a different extension. Yet if both doctrines were true – if intension were always sufficient to determine extension and if intensions were psychological entities – then sameness of psychological state would entail sameness of extension for the term being used. Putnam uses this result to indicate that it is false that intensions are psychological entities.

Putnam presents a further altered version of the thought experiment in order to reinforce the same conclusion about intensions not being psychological: supposing that pots and pans made of aluminum and molybdenum are indistinguishable, that pots and pans are made of aluminum on Earth and molybdenum on Twin Earth, and that on Twin Earth the words ‘aluminum’ and ‘molybdenum’ are switched (such that Twin Earthians refer to what we call aluminum with the word ‘molybdenum’), then speakers from Earth who travel to Twin Earth will be in the same psychological state as the locals with regard to pots and pans, yet will be referring to different things. Thus, sameness of psychological state does not entail sameness of extension; further, intensions are not psychological states: in this instance an Earth speaker and Twin Earth speaker are in the same psychological state yet are using a word to indicate a different meaning.

Putnam presents an alternative vision for how communities of speakers utilize intensions: the use of a word is a communal activity, with a “division of labor” (704) distributing the burden of proper use across a community. In other words, rather than the use of a word depending upon a solipsistic grasping of an intension (which then makes an extension clear) on the part of every speaker of a word, some in the community may simply provide ostensive definitions of words, while others (the scientifically oriented ones) may do the actual work of explicating the extension of terms. The proper determination/utilization of intensions and extensions arises from this communal work, not from the individual psychology of any given speaker.

Putnam then undermines the doctrine that intension necessarily determines extension by launching a discussion of natural kind terms – of which ‘water’ is an example. Putnam thinks that such terms are defined ostensively, i.e., by pointing to a thing in the world as an exemplar of the meaning of the term. To Putnam, to the extent that such terms are defined ostensively, their extension actually determines their intension, in the sense that a paraphrase of the meaning of the term will be of the general form ‘this thing right here,’ perhaps with an accompanying demonstration (e.g., a pointed finger). And the precise meaning of such a paraphrase will be determined by whatever the demonstratum (thing being demonstrated, pointed at) actually is. And this makes it possible for one to not know what is truly ‘meant’ by such a term until a scientific investigation reveals the thing ostended.

Besides undermining the notion that intension always determines extension, Putnam thinks that natural kind terms having as their intension their extension makes it such that these terms are ‘rigid designators’, or terms that refer to the same thing in all possible worlds. This is because a natural kind term is established (“baptized” one might say) via ostension, which relates to the actual world. Thus, such a baptismal rite will go something like, ‘Natural kind term n means this thing in the actual world’, meaning that the way the world is for Putnam as much a contributor in determining reference as is any psychological state on the part of speakers, contrary to standard semantic theory.


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Analytic Philosophy: Getting acquainted with the subject

Analytic philosophy is a rather difficult subject for most people, especially since (in the United States anyway) their first introduction to it isn’t until college. I realize I’ve not done much on this site to ameliorate that: my summaries presuppose a certain basic understanding of the subject at hand, and I haven’t even attempted to write any ‘here is what philosophy is all about’ articles. In this post I’ll detail a series of steps that will ensure understanding and, in time, enjoyment (the enjoyment doesn’t necessarily come straight away if the confusion is too great to begin with, but you’d better believe it comes in time!).

The steps are really rather basic:

1. Get a hold of top-notch introductory texts for each sub-field of philosophy and read them. I think it makes sense to read introductions for the whole lot of sub-fields rather than an overly broad, ‘what is philosophy’ text because I think seeing philosophy in action is the best way to understand it rather than having someone else tell you what it’s all about. Here are my top choices for each sub-field (contact me if you’d like assistance, uh, ‘getting a hold of’ digital copies of these texts):




Philosophy of Biology

Philosophy of Cognitive Science

Philosophy of Language

Philosophy of Logic

Philosophy of Mathematics

  • This tends to be a rarified subject concerned primarily with technical problems within mathematics and thus isn’t of concern for most of us. Issues pertaining to more general philosophical concerns — e.g., the ontological status of numbers — are already discussed in other sub-fields.

Philosophy of Mind

Philosophy of Science

2. Begin reading the canonical texts — journal articles, mostly — and practice your summarizing/critical evaluation skills. You simply must begin to write philosophically as well as read such material if you ever plan to be genuinely competent. You can use my summaries as a model or develop your own methods (some people like to paraphrase rather than summarize, for example).

3. Get a little book on different methods for writing philosophy. This is a popular text and ought to do you right, especially since it also covers arguments, which are the bread and butter of analytic philosophy (there’s a reason my summaries include a section that reconstructs the argument(s) of the article!).

4. Take a course or two. A classroom introduction to philosophy will be a big help for most people who want to understand more of the subject, though I don’t think it’s as necessary as some suppose (once my intro course turned me on to the subject most of the learning occurred independently of the course). Another course that is actually very important is an introductory course in symbolic logic, since so much of analytic philosophy has been bound up with logic these last 120 years or so.

4. Contact me at npapadakis0 @ with questions!

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Article Summary: “Logic and Conversation” by HP Grice

HP Grice, “Logic and Conversation,” Syntax and semantics 3: Speech arts (1975), Cole et al., pp.41-58.


Grice explicates what he takes to be necessary elements of successful conversation, insisting that whatever the difference between formal and natural languages, both adhere to the same elements and thus do not significantly diverge in meaning. For Grice, successful conversation necessitates adherence to an overarching “Cooperative Principle” (or, ‘CP’: communicate that which is required of the conversation such that the purpose of the conversation is achievable) [307R], plus – in certain instances at least – further maxims which fall under the following categories: Quantity (that which pertains to the amount of information communicated); Quality (that which pertains to the veracity of the information communicated); Relation (that which pertains to the relevance of the information communicated); and Manner (that which pertains to the way information is communicated). [308L-R] Central to Grice’s analysis are the notion of implicature and the assumption that communication is an essentially rational endeavor.

Grice begins by describing two opposing views on the respective roles of formal language (i.e., symbolic logic) and natural languages (e.g., English). The views diverge in light of the apparent difference in meaning between certain semantic units in formal language (the logical connectives and quantifiers) and their counterparts in natural language (e.g., ‘some’, the counterpart of the existential quantifier). [305L] Grice calls those who would emphasize the superiority of formal language formalists and those who argue that natural language has certain features which make it impossible to supplant informalists. [305-306] After sketching a generalized version of each position, Grice asserts that the apparent difference in meaning is largely illusory and can be traced to either side’s “inadequate attention to the nature and importance of the conditions governing conversation,” [306R] which he subsequently attempts to explicate.

Grice then gives a provisional list of the maxims associated with CP :

  1. Maxims associated with Quantity: ‘Communicate information that is as informative as required’; ‘Do not communicate more information than is necessary’.
  2. Maxims associated with Quality: ‘Do not communicate things you know to be false’; ‘Do not assert that which you have insufficient evidence for’.
  3. The maxim associated with Relation: ‘Be relevant’.
  4. Maxims associated with Manner: ‘Avoid obscurity’; ‘Avoid ambiguity’; ‘Be brief’; ‘Be orderly’. [308]

Grice thinks we properly assume that speakers will adhere to CP and related maxims not just because it is an empirical fact that they do, but because they represent norms that rational agents would adhere to. In other words, rather like economics prescribes certain utility-maximizing behaviors to agents on the assumption that they are rational, CP and related maxims are prescribed to speakers on the assumption that they are rational (and hence want to fulfill the purpose of communication in any given instance). [309L]

Besides building a rationality assumption (which Grice hopes – but does not
demonstrate – is what necessitates CP and related maxims) into successful communication, Grice’s analysis deploys the notion of implicature, or implying additional meanings above and beyond what is said. Grice defines the implicatum as that which is implied and subsequently delimits conventional and conversational implicatures (instances of implication): conventional implicatures are those which can arise solely as a result of the conventional meaning of the words of a sentence, whereas conversational implicatures result necessarily from inherent features of discourse, i.e., they are a function of adherence to CP and related norms (plus certain extralinguistic facts, e.g., context and background knowledge). [307R]

Grice provides a procedure for determining conversational implicature on the basis of CP and related norms: when a speaker says that p implicates q, such implication will be successful assuming: one, the speaker is adhering to CP (at the very least), two, the speaker genuinely thinks p must be so in order for his words to be in accord with CP, and three, the speaker thinks that listeners are aware of the latter point and that they know (or think) he is aware of it as well. [310]

After providing a catalog of examples meant to demonstrate how the calculus of conversational implicature in general ought to proceed [311-314], Grice expresses what he takes to be several properties of conversational implicature which result from his analysis: one, conversational implicature can be canceled in any given instance, since to provide such implicature necessitates adhering to CP, something no speaker is obligated to do; two, to the extent that the manner of expression plays no role in determining conversational implicature, there will be no alternative way of saying the same thing that does not also have the same implicature; three, the implacatum (implied meaning) of an expression is not a part of the meaning of the expression itself, since such meanings are conventional and implicata are by definition conversational implicatures (and thus determined by CP and related norm adherence), a class of non-conventional implicature; and four , it is possible for indeterminacy to result in instances where more than one explanation of what a speaker is implying adheres to the assumption that they are utilizing CP. [314R-315]


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Article Summary: “Der Gedanke” by Gottlob Frege

“The Thought: A Logical Inquiry”. Gottlob Frege. Mind, New Series, Vol. 65, No. 259. (Jul., 1956), pp. 289-311 (‘Der Gedanke’ is the untranslated name of the same work)


Frege explores the cognitive phenomenon of taking something to be true. His central claim is that to take something as true is to enter into a relation with an abstract entity called a ‘Thought,’ which to Frege is a specific sort of meaning, expressible through sentences, which may be either true or false.* In the midst of formulating this answer, Frege clarifies what he means by ‘true’, explains what he thinks are some basic properties of Thoughts, and engages in a discussion of the precise ontological status of Thoughts.

Frege begins by clarifying what he means by ‘truth,’ since without a more clear notion of this term his thesis about what it is to take something as true does not have meaning. Frege eschews several commonsense uses of the word before stating that the sort of truth he wishes to discuss is that which is sought out by the sciences (326).

In an attempt to explicate the notion further, Frege gives a tentative catalog of things truth – which for the sake of discussion he assumes is a property – may be predicated of: pictures, ideas, sentences, and Thoughts. Frege rejects the claim that truth may genuinely be predicated of pictures and ideas, for he thinks such predication requires a correspondence theory of truth, or, a theory which states that truth consists in some correspondence between a picture or idea and item in the external world. Frege presents a convergent argument against all such theories (a cluster of independently reinforcing points): one, such theories go against the use of the word ‘true’ as they require a relation between two things, something the word typically does not assert; two, if two items corresponded perfectly, they would be identical, and this is not what a person predicating truth wishes to say; and, three, if one wishes to specify what sort of correspondence truth consists in, it may always be sensibly asked, “Is this definition true?” The coherence of the question for all such definitions indicates to Frege that none of them are capturing the essence of truth, because otherwise the question would be incoherent. These results lead Frege to conclude that truth is indefinable. (326-327)

Frege then asserts that, while we often speak of sentences as being true or false, what this talk actually consists in is ascribing truth or falsehood to the senses (contents) of such sentences. And the specific sorts of senses which may be sensibly ascribed truth or falsehood are, to Frege, the Thoughts. Frege thinks as well that the ‘is true’ predicate does not add any content to a sentence.

Frege then describes several of Thought’s basic properties in an attempt to reveal their nature more clearly. Thoughts are, to Frege, imperceptible: none of our senses ever interacts with a Thought. Frege uses the example of a specific sensed phenomenon: while the Sun rising may be sensed, that the Sun is rising is a Thought with a truth value and is never sensed, instead being grasped by some other means.

Frege argues that Thoughts may be expressed without thereby being asserted: Thoughts are expressed by propositional questions (which are not assertoric) as well as interrogative sentences (which are assertoric), indicating that the assertion of a Thought is a separate issue from its truth value (e.g., one can say something true and yet not assert it) – a difference Frege thinks can be explained by sentence-forms and the conventions surrounding their use. Thoughts and their associated truth values exist independently of use.

The final properties Frege discusses are the under- and over-determination of Thoughts by sentential content. Thoughts may both be expressed in sentences with more content than is needed to express the Thought, or not expressed at all due to a sentence lacking certain features. Regarding the former case, Frege cites expressive and poetic words as not assisting in the expression of Thoughts; logically, such words are extraneous, whatever their function in everyday language use. Frege uses the word ‘there’ to explain underdetermination: if a sentence uses the word ‘there’ along with an accompanying demonstration (e.g., a pointed finger), then we are not grasping a genuine Thought by looking at the sentence alone; certain extralinguistic facts must be known as well (in this example, we must know where the finger is pointing). (332)

Frege concludes his exploration with a discussion of the ontological status of Thoughts . As already mentioned, Frege does not think Thoughts are external, sensible objects: truth attaches to Thoughts, but not to sensed objects, and so they cannot be the same. Frege next considers the claim that Thoughts are ‘Ideas’, a term he uses to refer to the internal items of a person’s mental life, viz., sensations, desires, intentions, and so forth. Frege thinks Thoughts cannot be Ideas, for Ideas have specific properties that Thoughts do not: they are possessed by persons, and they are a constituent of a person’s consciousness. If Thoughts were mere items of a given person’s consciousness, they and their truth would be relativized to that person, for it is impossible to share bits of one’s consciousness with another. Yet Frege takes it as obvious that Thoughts – he here uses the example of the Pythagorean Theorem – are mutually grasped entities the truth of which has nothing to do with any given person’s consciousness. (336) Since identical things will have all the same properties, and Frege has just found that any given Thought and Idea will have divergent properties, it follows that Thoughts are not Ideas.

Frege disarms the skeptical claim that, for all we know, Ideas are all that exist. Frege levels two arguments against the claim: one, at least one independent object is needed to best explain our experiences. To Frege, selves – conscious entities that possess Ideas – cannot be explained in terms of Ideas. He finds it is far more reasonable to posit the self as an independent object than it is to attempt an explanation of selves as specific portions of conscious content. The second argument is pragmatic: to accept the claim that only Ideas exist is to give up on all substantive inquiry, all of which assumes the existence of external objects in order to be meaningful. This is an unacceptable outcome and thus skepticism is to be rejected.

Thus, Thoughts are the bearers of truth, but do not exist as external objects nor as Ideas. Given that there can be independent objects – a claim which follows from Frege’s refutation of skepticism – the only option left is to posit a “third realm” where Thoughts exist. (337) This realm is outside of time and space, although its constituents are ‘graspable’. This grasping in turn leads us to action; Thoughts as such have an indirect causal impact on the world. Through explaining what it is to treat something as true, Frege has discovered what he takes to be the nature of thinking more generally.

*Frege’s ‘Thoughts’ are what we’d now call propositions, though their exact nature — including whether they exist or not — is still a matter of debate.

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Article Summary: “Descriptions” by Bertrand Russell

(in A.W. Moore, ed., Meaning and Reference, OUP 1993)

An extract from Chapter XVI of Russell’s Introduction to Mathematical Philosophy (London: Allen & Unwin, 1919).


In this excerpt, Russell presents a semantic theory (a theory of meaning) for a particular type of expression: descriptions. Russell delimits definite descriptions from indefinite ones, saying that the former take the form ‘the so-and-so’ while the latter take the form ‘a so-and-so’. Russell attempts to establish two fundamental points: one, descriptions do not have meaning in isolation, and two, the propositions in which descriptions occur include a quantifier phrase plus a propositional function rather than singular terms.

Russell establishes the first point separately for both sorts of description. In the case of indefinite descriptions, Russell argues that to define an indefinite description (and thus assign it meaning) would require specifying a definite object it describes. Since such descriptions are necessarily ambiguous, they do not describe any definite object and as such cannot be assigned meaning in isolation (e.g., there is no definite object described by the indefinite description ‘a man’, making it impossible to define the term and thus impossible to assign it meaning). (49, ¶2)

Russell then argues that definite descriptions do not have meaning in isolation either, since their doing so would require that they be singular terms. Since definite descriptions are not singular terms, they do not have meaning in isolation (Russell here uses the term ‘name’ for a singular term, defining it as a symbol with parts that are not symbols and which has as its meaning its referent). (50, ¶4)

Russell thinks definite descriptions aren’t singular terms because substituting a singular term for a definite description in a proposition – even when the definite description is describing the referent of the singular term – always results in the expression of a different proposition. (52, ¶3) Russell gives the example of substituting ‘Scott’ (a singular term) for ‘the author of Waverly’ (a definite description) in the proposition ‘Scott is the author of Waverly’. The result is the proposition ‘Scott is Scott’, which is clearly a different proposition than when the definite description is included. If definite descriptions were singular terms, then swapping them out for singular terms whose referents they describe would not change the proposition expressed; since such change occurs, it follows that such descriptions are not singular terms, and hence not meaningful in isolation.

Russell thinks this first part of his theory is a virtue because it is supposed to explain how discourse about non-existent entities is possible: such discourse is possible because, given that descriptions aren’t meaningful in isolation, there aren’t non-existent entities (e.g., ‘a unicorn’) as constituents of propositions; rather, descriptions which do not describe anything are constituents of propositions. On the contrary, if terms denoting non-existent entities were singular terms rather than descriptions, then the entities denoted would have to be constituents of propositions and thus would have to exist in some sense. (48, ¶2)

Since descriptions in isolation have no meaning, in order to provide a semantic theory for these expressions Russell must analyze the propositions in which they occur. Russell does so for either sort of description. In both cases, the proposition expressed is said to include a quantifier phrase with a propositional function as a part*.

Russell early in the excerpt provides an example, indicating that ‘I met a man’ should be translated as “The propositional function ‘I met x and x is human’ is sometimes true.” (47,¶1) It is obvious that this proposition includes a propositional function. But it also includes a quantifier phrase because it can be translated into ‘∃x[I met x and x is human]’, which means the same thing since both indicate that at least one proposition resulting from the propositional function ‘I met x and x is human’ is true.

Russell thinks the same of the propositions in which definite descriptions occur, albeit with an added proviso: such propositions must uniquely denote an object, i.e., there can only be a single object denoted. We cannot speak of ‘the inhabitant of London’, since there is more than one person inhabiting London. (52, ¶3) Thus, the proposition ‘I met the author of Waverly’ will have the same form as ‘I met a man’, except that the former will also have in its translation an element indicating that there is only one such author, viz., “The propositional function ‘I met x and x wrote Waverly and only x wrote Waverly’ is sometimes true”, which in turn can be translated into ‘∃x∀y[I met x and (y wrote Waverly↔y=x)]’. The latter format is to be preferred because it succinctly captures what Russell takes to be the logical form of the propositions in which descriptions occur.

A subsidiary issue Russell discusses in the latter portion of the excerpt is the status of proper names. To Russell, the fact that one can question the existence of a so-and-so, i.e., of a description, and not a name (it would be meaningless to question the existence of a name since the term wouldn’t have meaning if it didn’t refer, i.e., if the object named didn’t exist) indicates that what we take to be proper names oftentimes are properly construed as descriptions, since we do in fact legitimately question the existence of that which is named. (54, ¶2) It is worth noting, however, the Russell does not indicate that all uses of what we take to be proper names are in fact descriptions: early in the excerpt Russell differentiates the propositions expressed by ‘I met John’ and ‘I met a man.’ (47, ¶1) If all proper names really functioned as descriptions, then these two sentences ought to have propositions of the same form, viz, propositions with a quantifier phrase and propositional function, since descriptions would occur in both. But Russell denies this, indicating that ‘I met John’ “names an actual person.” (ibid.) Therefore, Russell seems to think that at least some uses of proper names succeed in expressing a proposition with a named object as constituent.

*Unfortunately, it isn’t readily abundant what Russell means by ‘propositional function’, despite its centrality to his work here. On a provisional basis I took it to mean a basic function that maps a proposition onto objects in a domain, e.g., ‘I met x and x is human’ maps onto objects  O(1) … O(n) such that the propositions ‘I met O1 and O1 is human’ and so forth result. Then ‘I met a man’ is true iff at least one of the propositions resulting from the propositional function is true.

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Veteran’s Day Update

Hey folks,

I’ve not updated this site for the better part of a year. That doesn’t mean I haven’t been doing work worth uploading, however, nor that I’ve abandoned the site.

In fact, I’ll be uploading a bunch of new summaries in analytic philosophy and (probably) more logic solutions. Though real life stuff — like the small matter of my LSAT studies — will always be higher on my priority list, I’ll still maintain this site as best as I’m able, I promise (all 4 of you).

Also, I’ve got a personal website at where similar sorts of content can be found.


Nick Pappy

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