Freges Conception of Logic

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So far so good. I look forward with interest to your review of the dividing line between syntax and semantics in various authors. Those adhering to a somewhat formalist view might not accept your example of difference in schemata, however. For instance Boolos in Provability on page 3 introduces the principle of substitution inductively, which would include the two examples in a single schema. Loving Lady Hale's brooch game. Wiki tells me that in Ancient Egypt, spiders were associated with the goddess Neith in her aspect as spinner and weaver of destiny.

I mean.

Philosophy 290-4

Logic Matters. Skip to content. It holds, supposedly, that the subject matter of logic consists of logical properties of sentences and logical relations among sentences. This entry was posted in Logic.

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Bookmark the permalink. July 29, at pm. Search for:. Get email about updates. Retweet on Twitter Peter Smith Retweeted. But the True cannot be predicated. Frege ; a famously maintains that truth is indefinable. The problem is that the True seems to be definable. If so, the True which is definable cannot be truth. If this critique is correct and truth cannot be an object for Frege, we are lost in regards to his conception of truth. If truth is neither a property nor an object, what is it then? Greimann presents an alternative reading.

Or so argues Greimann. My first aim is to show that Frege cannot accept the main claims of the assertion theory.

If my argument is correct, the A-theory reading should be discarded. Section 2 explains the A-theory reading. Section 3 is my critique of the reading.

The Mathematical Paradigm in Philosophy: On Frege's Concept‐Script

Section 4 is the elaboration and defense of the object reading. Asserting is judging externally manifested. One possible answer is that we do so by predicating the property truth of a thought. This answer is not available for Frege because he gainsays that truth is a property. However, Frege has an independent reason to deny the answer. This reason is relevant to our discussion. By combining subject and predicate, one reaches only a thought Frege c: 64 [7]. But the actor would not thereby acknowledge its truth.

Though grasping a thought is necessary for acknowledging its truth, it is not sufficient.

Predicating is confused with judging Once we have grasped a thought, we can recognize it as true [i. Frege a: [10]. For Frege, acknowledging the truth of a thought cannot be merely predicating the property truth of the thought even if there were such a property. In the mature Begriffsschrift , writing down. We thus need a special sign in order to be able to assert something. To this end I make use of a vertical stroke at the left end of the horizontal, so that, e. Frege here seems to be arguing that. Its critical claim Greimann is that.

The judgment stroke is constitutive of the form of assertoric sentences and it is a truth-operator by which we can express a genuine truth-claim. This shows that, for Frege, legitimate truth-bearers are thoughts andhence a truth-claim should be about a thought. However, the claim we express by the judgment stroke in.

We can construe the role played by the notion of truth in judging and asserting as follows. The judgment stroke is a truth-operator, and to combine it with a proper sentence into an assertoric sentence is to make a judgment. Thus, the role played by the notion of truth in judging should correspond to the role played by the judgment stroke in an assertoric sentence. The role of the judgment stroke in an assertoric sentence is to express the truth-claim that the truth-value of a thought is identical with the True.

The role played by the notion of truth is then to identify the truth-value of a given thought with the True Greimann ; —; Thus, acknowledging the truth of a thought is identifying the truth-value of the thought with the True. Frege cannot accommodate this. However, the A-theory reading claims that the assertion theory of truth has additional components that cancel out this implication.

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Concepts are functions the value of which is always a truth-value. Frege ; b looks upon functions as unsaturated. To say that a function is unsaturated is to say that a function has empty places that must be saturated by arguments in order for the function to provide an object as its value.

Concepts are also unsaturated. Saturated, they provide a truth-value as its value. A concept is thus predicative Greimann — We may also say the object falls under the concept prime. This also creates the impression that the relation of subsumption is a third element supervenient upon the object and the concept. Object and concept are fundamentally made for each other, and in subsumption we have their fundamental union. Frege is talking about a particular kind of saturation: Subsumption.

Frege seems to be suggesting that subsumption as a kind of saturation is not a genuine relation: Subsumption occurs just because concepts immediately engage with objects by their own nature and hence no special cement or relation is necessary for that. That is indeed how the A-theory reading understands this passage.

Greimann, who suggests the A-theory reading, writes,. Greimann ; italics mine. Therefore, what Greimann is arguing here is that subsumption holds between 2 and the concept prime if 2 is prime. What is crucial is that this kind of relation is found in every sentence. For instance, say John loves Mary.

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We may say that John stands in the relation love to Mary. Note that because of the very special role that this relation plays in judgment it cannot be substituted by ordinary relations. While the role of ordinary relations is to form the predicative part of judgments, the role of saturation is to connect this part with the non-predicative parts.

Therefore, saturation, subsumption and kindred relations like the standing of two objects in a relation. Greimann But logical relations fall under none of those categories. Accordingly, the assertion theory of truth has the following:. For every thought, there is always a logical relation relevant to it. Based on the above passage, the A-theory reading holds that Frege would be willing to say that the truth-value of a thought being the True consists in the obtaining of the relevant logical relation.

Hence, A6. Thus, there is no problem with attributing the assertion theory of truth to Frege. In the assertion theory, truth is not a concept, that is, a property. It is not an object, either. It is not even an entity. Recall that the role of the notion of truth in judging or asserting, embodied by the judgment stroke, is to identify the truth-value of a thought with the True.

In judging and asserting, we identify the truth-value of a thought with the True and thereby decide that the relevant logical relation obtains. The A-theory reading fits the textual evidence we have seen in the last section. It can explain why Frege contends that truth is not a property by saying that truth is the obtaining of a logical relation that is not even a genuine entity.

Because truth is not even an entity, it is indefinable as Frege argues.

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